%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW309+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:07:04 EDT 2024 % Result : Theorem 186.01s 186.01s % Output : CNFRefutation 186.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWW309+1 : TPTP v8.2.0. Released v5.2.0. % 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.31 % Computer : n017.cluster.edu % 0.09/0.31 % Model : x86_64 x86_64 % 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.31 % Memory : 8042.1875MB % 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.31 % CPULimit : 300 % 0.09/0.31 % WCLimit : 300 % 0.09/0.31 % DateTime : Wed Jun 19 09:23:23 EDT 2024 % 0.09/0.31 % CPUTime : % 0.18/0.57 start to proof:theBenchmark % 185.58/185.82 %------------------------------------------- % 185.58/185.82 % File :CSE---1.7 % 185.58/185.82 % Problem :theBenchmark % 185.58/185.82 % Transform :cnf % 185.58/185.82 % Format :tptp:raw % 185.58/185.82 % Command :java -jar mcs_scs.jar %d %s % 185.58/185.82 % 185.58/185.82 % Result :Theorem 163.590000s % 185.58/185.82 % Output :CNFRefutation 163.590000s % 185.58/185.82 %------------------------------------------- % 185.59/185.83 %------------------------------------------------------------------------------ % 185.59/185.83 % File : SWW309+1 : TPTP v8.2.0. Released v5.2.0. % 185.59/185.83 % Domain : Software Verification % 185.59/185.83 % Problem : Hoare's Logic with Procedures 434934, 5000 axioms selected % 185.59/185.83 % Version : Especial. % 185.59/185.83 % English : % 185.59/185.83 % 185.59/185.83 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 185.59/185.83 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 185.59/185.83 % Source : [Bla11] % 185.59/185.83 % Names : hoare_434934.5000.p [Bla11] % 185.59/185.83 % 185.59/185.83 % Status : ContradictoryAxioms % 185.59/185.83 % Rating : 0.81 v8.2.0, 0.75 v8.1.0, 0.78 v7.4.0, 0.87 v7.3.0, 0.83 v7.1.0, 0.78 v7.0.0, 0.87 v6.4.0, 0.81 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 185.59/185.83 % Syntax : Number of formulae : 5228 (1699 unt; 0 def) % 185.59/185.83 % Number of atoms : 12657 (4465 equ) % 185.59/185.83 % Maximal formula atoms : 13 ( 2 avg) % 185.59/185.83 % Number of connectives : 8427 ( 998 ~; 145 |; 705 &) % 185.59/185.83 % ( 892 <=>;5687 =>; 0 <=; 0 <~>) % 185.59/185.83 % Maximal formula depth : 22 ( 6 avg) % 185.59/185.83 % Maximal term depth : 19 ( 2 avg) % 185.59/185.83 % Number of predicates : 148 ( 147 usr; 0 prp; 1-6 aty) % 185.59/185.83 % Number of functors : 396 ( 396 usr; 53 con; 0-7 aty) % 185.59/185.83 % Number of variables : 16648 (16496 !; 152 ?) % 185.59/185.83 % SPC : FOF_CAX_RFO_SEQ % 185.59/185.83 % 185.59/185.83 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 185.59/185.83 % 2011-03-01 11:38:45 % 185.59/185.83 %------------------------------------------------------------------------------ % 185.59/185.83 %----Relevant facts (4985) % 185.59/185.83 fof(fact_ext,axiom, % 185.59/185.83 ! [V_g_2,V_f_2] : % 185.59/185.83 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 185.59/185.83 => V_f_2 = V_g_2 ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_empty,axiom, % 185.59/185.83 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 185.59/185.83 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_peek__and__def,axiom, % 185.59/185.83 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 185.59/185.83 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 185.59/185.83 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_triple_Oinject,axiom, % 185.59/185.83 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2) = c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_H_2,V_com_H_2,V_fun2_H_2) % 185.59/185.83 <=> ( V_fun1_2 = V_fun1_H_2 % 185.59/185.83 & V_com_2 = V_com_H_2 % 185.59/185.83 & V_fun2_2 = V_fun2_H_2 ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_cut,axiom, % 185.59/185.83 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 185.59/185.83 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_Oinsert,axiom, % 185.59/185.83 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_bot__fun__def,axiom, % 185.59/185.83 ! [V_x_2,T_c,T_b] : % 185.59/185.83 ( class_Orderings_Obot(T_b) % 185.59/185.83 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_triple_Orecs,axiom, % 185.59/185.83 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 185.59/185.83 % 185.59/185.83 fof(fact_triple_Osimps_I2_J,axiom, % 185.59/185.83 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,c_Hoare__Mirabelle_Otriple_Otriple(T_c,V_fun1_2,V_com_2,V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 185.59/185.83 % 185.59/185.83 fof(fact_empty__not__insert,axiom, % 185.59/185.83 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 185.59/185.83 % 185.59/185.83 fof(fact_insert__not__empty,axiom, % 185.59/185.83 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.83 % 185.59/185.83 fof(fact_doubleton__eq__iff,axiom, % 185.59/185.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.83 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.83 <=> ( ( V_a_2 = V_ca_2 % 185.59/185.83 & V_ba_2 = V_d_2 ) % 185.59/185.83 | ( V_a_2 = V_d_2 % 185.59/185.83 & V_ba_2 = V_ca_2 ) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_singleton__inject,axiom, % 185.59/185.83 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.83 ( 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_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.83 => V_a_2 = V_ba_2 ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_bot__apply,axiom, % 185.59/185.83 ! [V_x_2,T_c,T_b] : % 185.59/185.83 ( class_Orderings_Obot(T_b) % 185.59/185.83 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_escape,axiom, % 185.59/185.83 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] : % 185.59/185.83 ( ! [B_Z,B_s] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_OSkip,axiom, % 185.59/185.83 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OSKIP,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 185.59/185.83 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_a2_2,c_Com_Ocom_OSKIP,V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_conseq2,axiom, % 185.59/185.83 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( ! [B_Z,B_s] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 185.59/185.83 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_insert__code,axiom, % 185.59/185.83 ! [V_x_2,V_A_2,V_y_2,T_b] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 185.59/185.83 <=> ( V_y_2 = V_x_2 % 185.59/185.83 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_insert__commute,axiom, % 185.59/185.83 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ). % 185.59/185.83 % 185.59/185.83 fof(fact_insert__absorb2,axiom, % 185.59/185.83 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ). % 185.59/185.83 % 185.59/185.83 fof(fact_the__elem__eq,axiom, % 185.59/185.83 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ). % 185.59/185.83 % 185.59/185.83 fof(fact_conseq1,axiom, % 185.59/185.83 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_H_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( ! [B_Z,B_s] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.59/185.83 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Comp,axiom, % 185.59/185.83 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Q_2,V_d_2,V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_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_b),tc_HOL_Obool)))) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_OIf,axiom, % 185.59/185.83 ! [V_d_2,V_Q_2,V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2),V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_ba_2)),V_d_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OCond(V_ba_2,V_ca_2,V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Loop,axiom, % 185.59/185.83 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2),V_ca_2,V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,c_Com_Ocom_OWhile(V_ba_2,V_ca_2),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_ba_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_conseq12,axiom, % 185.59/185.83 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 185.59/185.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_P_H_2,V_ca_2,V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 185.59/185.83 => ( ! [B_Z,B_s] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 185.59/185.83 => ! [B_s_H] : % 185.59/185.83 ( ! [B_Z_H] : % 185.59/185.83 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 185.59/185.83 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 185.59/185.83 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) % 185.59/185.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 185.59/185.83 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBC(T_b,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_b),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_b),tc_HOL_Obool)))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Ass,axiom, % 185.59/185.83 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBC(T_b,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_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_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_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_the__elem__def,axiom, % 185.59/185.83 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_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))))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Collect__conv__if,axiom, % 185.59/185.83 ! [T_b,V_a_2,V_Pa_2] : % 185.59/185.83 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.59/185.83 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 185.59/185.83 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.59/185.83 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Collect__conv__if2,axiom, % 185.59/185.83 ! [T_b,V_a_2,V_Pa_2] : % 185.59/185.83 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.59/185.83 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 185.59/185.83 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.59/185.83 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_singleton__conv,axiom, % 185.59/185.83 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Collect__def,axiom, % 185.59/185.83 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 185.59/185.83 % 185.59/185.83 fof(fact_empty__Collect__eq,axiom, % 185.59/185.83 ! [V_Pa_2,T_b] : % 185.59/185.83 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 185.59/185.83 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.59/185.83 % 185.59/185.83 fof(fact_Collect__empty__eq,axiom, % 185.59/185.83 ! [V_Pa_2,T_b] : % 185.59/185.84 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.84 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_empty__def,axiom, % 185.59/185.84 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__Collect,axiom, % 185.59/185.84 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ). % 185.59/185.84 % 185.59/185.84 fof(fact_singleton__conv2,axiom, % 185.59/185.84 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I13_J,axiom, % 185.59/185.84 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I12_J,axiom, % 185.59/185.84 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I9_J,axiom, % 185.59/185.84 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I8_J,axiom, % 185.59/185.84 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I25_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I24_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I15_J,axiom, % 185.59/185.84 ! [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 ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I14_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I45_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I44_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I27_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I26_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I5_J,axiom, % 185.59/185.84 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 185.59/185.84 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 185.59/185.84 <=> ( V_fun_2 = V_fun_H_2 % 185.59/185.84 & V_com_2 = V_com_H_2 ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I4_J,axiom, % 185.59/185.84 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 185.59/185.84 ( 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) % 185.59/185.84 <=> ( V_fun_2 = V_fun_H_2 % 185.59/185.84 & V_com1_2 = V_com1_H_2 % 185.59/185.84 & V_com2_2 = V_com2_H_2 ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I1_J,axiom, % 185.59/185.84 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 185.59/185.84 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 185.59/185.84 <=> ( V_vname_2 = V_vname_H_2 % 185.59/185.84 & V_fun_2 = V_fun_H_2 ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I3_J,axiom, % 185.59/185.84 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 185.59/185.84 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 185.59/185.84 <=> ( V_com1_2 = V_com1_H_2 % 185.59/185.84 & V_com2_2 = V_com2_H_2 ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I53_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I52_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I28_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I29_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I46_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I47_J,axiom, % 185.59/185.84 ! [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) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I16_J,axiom, % 185.59/185.84 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 185.59/185.84 % 185.59/185.84 fof(fact_com_Osimps_I17_J,axiom, % 185.59/185.84 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 185.59/185.84 % 185.59/185.84 fof(fact_the__sym__eq__trivial,axiom, % 185.59/185.84 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 185.59/185.84 % 185.59/185.84 fof(fact_the__eq__trivial,axiom, % 185.59/185.84 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__def,axiom, % 185.59/185.84 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 185.59/185.84 % 185.59/185.84 fof(fact_K__record__comp,axiom, % 185.59/185.84 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__assoc,axiom, % 185.59/185.84 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__apply,axiom, % 185.59/185.84 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 185.59/185.84 % 185.59/185.84 fof(fact_comp__cong,axiom, % 185.59/185.84 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 185.59/185.84 ( 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)) % 185.59/185.84 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__eq__dest__lhs,axiom, % 185.59/185.84 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.59/185.84 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = V_ca_2 % 185.59/185.84 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__eq__dest,axiom, % 185.59/185.84 ! [V_v_2,V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.59/185.84 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 185.59/185.84 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_o__eq__elim,axiom, % 185.59/185.84 ! [V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.59/185.84 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) % 185.59/185.84 => ! [B_v] : hAPP(V_a_2,hAPP(V_ba_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__compr__raw,axiom, % 185.59/185.84 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__compr,axiom, % 185.59/185.84 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_equalityCE,axiom, % 185.59/185.84 ! [V_ca_2,T_b,V_B_2,V_A_2] : % 185.59/185.84 ( V_A_2 = V_B_2 % 185.59/185.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) % 185.59/185.84 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_emptyE,axiom, % 185.59/185.84 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insertE,axiom, % 185.59/185.84 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 185.59/185.84 => ( V_a_2 != V_ba_2 % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insertCI,axiom, % 185.59/185.84 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 185.59/185.84 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.59/185.84 => V_a_2 = V_ba_2 ) % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_CollectI,axiom, % 185.59/185.84 ! [T_b,V_a_2,V_Pa_2] : % 185.59/185.84 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_mem__def,axiom, % 185.59/185.84 ! [V_A_2,V_x_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_eqset__imp__iff,axiom, % 185.59/185.84 ! [V_x_2,T_b,V_B_2,V_A_2] : % 185.59/185.84 ( V_A_2 = V_B_2 % 185.59/185.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_eqelem__imp__iff,axiom, % 185.59/185.84 ! [V_A_2,T_b,V_y_2,V_x_2] : % 185.59/185.84 ( V_x_2 = V_y_2 % 185.59/185.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_eq__mem__trans,axiom, % 185.59/185.84 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 185.59/185.84 ( V_a_2 = V_ba_2 % 185.59/185.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_all__not__in__conv,axiom, % 185.59/185.84 ! [V_A_2,T_b] : % 185.59/185.84 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_ex__in__conv,axiom, % 185.59/185.84 ! [V_A_2,T_b] : % 185.59/185.84 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.84 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_empty__iff,axiom, % 185.59/185.84 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_equals0D,axiom, % 185.59/185.84 ! [V_a_2,T_b,V_A_2] : % 185.59/185.84 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insertI1,axiom, % 185.59/185.84 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__iff,axiom, % 185.59/185.84 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 185.59/185.84 <=> ( V_a_2 = V_ba_2 % 185.59/185.84 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__ident,axiom, % 185.59/185.84 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.59/185.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.84 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) % 185.59/185.84 <=> V_A_2 = V_B_2 ) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insertI2,axiom, % 185.59/185.84 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.59/185.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__absorb,axiom, % 185.59/185.84 ! [V_A_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_Collect__mem__eq,axiom, % 185.59/185.84 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ). % 185.59/185.84 % 185.59/185.84 fof(fact_mem__Collect__eq,axiom, % 185.59/185.84 ! [V_Pa_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.84 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_CollectD,axiom, % 185.59/185.84 ! [V_Pa_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.84 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_CollectE,axiom, % 185.59/185.84 ! [V_Pa_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.84 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_singleton__iff,axiom, % 185.59/185.84 ! [V_a_2,V_ba_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.84 <=> V_ba_2 = V_a_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_singletonE,axiom, % 185.59/185.84 ! [V_a_2,V_ba_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.84 => V_ba_2 = V_a_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_bot__empty__eq,axiom, % 185.59/185.84 ! [V_x_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 185.59/185.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_pred__equals__eq,axiom, % 185.59/185.84 ! [V_S_2,V_R_2,T_b] : % 185.59/185.84 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) % 185.59/185.84 <=> V_R_2 = V_S_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_the__inv__into__def,axiom, % 185.59/185.84 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(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(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ). % 185.59/185.84 % 185.59/185.84 fof(fact_override__on__def,axiom, % 185.59/185.84 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 185.59/185.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_eq__mem,axiom, % 185.59/185.84 ! [V_y_2,V_x_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 185.59/185.84 <=> V_x_2 = V_y_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_override__on__emptyset,axiom, % 185.59/185.84 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ). % 185.59/185.84 % 185.59/185.84 fof(fact_image__constant,axiom, % 185.59/185.84 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_override__on__apply__in,axiom, % 185.59/185.84 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_override__on__apply__notin,axiom, % 185.59/185.84 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_vimage__singleton__eq,axiom, % 185.59/185.84 ! [V_ba_2,V_f_2,T_c,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 185.59/185.84 <=> hAPP(V_f_2,V_a_2) = V_ba_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_Diff__insert__absorb,axiom, % 185.59/185.84 ! [V_A_2,V_x_2,T_b] : % 185.59/185.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),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)))) = V_A_2 ) ). % 185.59/185.84 % 185.59/185.84 fof(fact_insert__Diff,axiom, % 185.59/185.84 ! [V_A_2,V_a_2,T_b] : % 185.59/185.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.84 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__eqI,axiom, % 185.59/185.85 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_ba_2] : % 185.59/185.85 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_DiffE,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.85 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_DiffI,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimageI,axiom, % 185.59/185.85 ! [T_c,V_B_2,T_b,V_ba_2,V_a_2,V_f_2] : % 185.59/185.85 ( hAPP(V_f_2,V_a_2) = V_ba_2 % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__code,axiom, % 185.59/185.85 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 185.59/185.85 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__idemp,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__Diff,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__image,axiom, % 185.59/185.85 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__ident,axiom, % 185.59/185.85 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__ident,axiom, % 185.59/185.85 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 185.59/185.85 % 185.59/185.85 fof(fact_rev__image__eqI,axiom, % 185.59/185.85 ! [T_c,V_f_2,V_ba_2,V_A_2,V_x_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_imageI,axiom, % 185.59/185.85 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__iff,axiom, % 185.59/185.85 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.85 <=> ? [B_x] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.85 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__is__empty,axiom, % 185.59/185.85 ! [V_A_2,V_f_2,T_b,T_c] : % 185.59/185.85 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.85 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__empty,axiom, % 185.59/185.85 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_empty__is__image,axiom, % 185.59/185.85 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.85 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) % 185.59/185.85 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__insert,axiom, % 185.59/185.85 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__compose,axiom, % 185.59/185.85 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_DiffD2,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.85 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_DiffD1,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__iff,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.85 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimageI2,axiom, % 185.59/185.85 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimageD,axiom, % 185.59/185.85 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__eq,axiom, % 185.59/185.85 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 185.59/185.85 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__cancel,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__empty,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 185.59/185.85 % 185.59/185.85 fof(fact_empty__Diff,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__empty,axiom, % 185.59/185.85 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__compose,axiom, % 185.59/185.85 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__Collect__eq,axiom, % 185.59/185.85 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_insert__image,axiom, % 185.59/185.85 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_insert__Diff__if,axiom, % 185.59/185.85 ! [V_A_2,V_B_2,V_x_2,T_b] : % 185.59/185.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) % 185.59/185.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_insert__Diff1,axiom, % 185.59/185.85 ! [V_A_2,V_B_2,V_x_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_insert__Diff__single,axiom, % 185.59/185.85 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__insert2,axiom, % 185.59/185.85 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ). % 185.59/185.85 % 185.59/185.85 fof(fact_Diff__insert,axiom, % 185.59/185.85 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) ). % 185.59/185.85 % 185.59/185.85 fof(fact_image__constant__conv,axiom, % 185.59/185.85 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.59/185.85 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.85 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.85 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.85 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_set__diff__eq,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__def,axiom, % 185.59/185.85 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_fun__diff__def,axiom, % 185.59/185.85 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.85 ( class_Groups_Ominus(T_b) % 185.59/185.85 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_minus__apply,axiom, % 185.59/185.85 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.85 ( class_Groups_Ominus(T_b) % 185.59/185.85 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_fun__upd__image,axiom, % 185.59/185.85 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,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)))))) ) % 185.59/185.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 185.59/185.85 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_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)))),V_y_2) % 185.59/185.85 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_inj__on__insert,axiom, % 185.59/185.85 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 185.59/185.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 185.59/185.85 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.85 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_diff__single__insert,axiom, % 185.59/185.85 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_subset__insert__iff,axiom, % 185.59/185.85 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 185.59/185.85 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) ) % 185.59/185.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_the__inv__into__comp,axiom, % 185.59/185.85 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) % 185.59/185.85 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) % 185.59/185.85 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_imageE,axiom, % 185.59/185.85 ! [V_A_2,V_f_2,T_c,V_ba_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.85 => ~ ! [B_x] : % 185.59/185.85 ( V_ba_2 = hAPP(V_f_2,B_x) % 185.59/185.85 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimage__const,axiom, % 185.59/185.85 ! [T_c,V_A_2,V_ca_2,T_b] : % 185.59/185.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_vimageE,axiom, % 185.59/185.85 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_order__refl,axiom, % 185.59/185.85 ! [V_x,T_a] : % 185.59/185.85 ( class_Orderings_Opreorder(T_a) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_equalityI,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.85 => V_A_2 = V_B_2 ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_top1I,axiom, % 185.59/185.85 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_fun__upd__triv,axiom, % 185.59/185.85 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ). % 185.59/185.85 % 185.59/185.85 fof(fact_subsetD,axiom, % 185.59/185.85 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_UNIV__I,axiom, % 185.59/185.85 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.85 % 185.59/185.85 fof(fact_empty__subsetI,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_inj__on__empty,axiom, % 185.59/185.85 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 185.59/185.85 % 185.59/185.85 fof(fact_inj__image__subset__iff,axiom, % 185.59/185.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) % 185.59/185.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_rev__predicate1D,axiom, % 185.59/185.85 ! [V_Q_2,T_b,V_x_2,V_Pa_2] : % 185.59/185.85 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.59/185.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 185.59/185.85 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_predicate1D,axiom, % 185.59/185.85 ! [V_x_2,V_Q_2,V_Pa_2,T_b] : % 185.59/185.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 185.59/185.85 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.59/185.85 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_subset__UNIV,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.85 % 185.59/185.85 fof(fact_top__greatest,axiom, % 185.59/185.85 ! [V_x,T_a] : % 185.59/185.85 ( class_Orderings_Otop(T_a) % 185.59/185.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_subset__refl,axiom, % 185.59/185.85 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 185.59/185.85 % 185.59/185.85 fof(fact_top__apply,axiom, % 185.59/185.85 ! [V_x_2,T_c,T_b] : % 185.59/185.85 ( class_Orderings_Otop(T_b) % 185.59/185.85 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 185.59/185.85 % 185.59/185.85 fof(fact_le__fun__def,axiom, % 185.59/185.85 ! [V_g_2,V_f_2,T_b,T_c] : % 185.59/185.86 ( class_Orderings_Oord(T_c) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.59/185.86 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_linorder__linear,axiom, % 185.59/185.86 ! [V_y,V_x,T_a] : % 185.59/185.86 ( class_Orderings_Olinorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.86 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_set__eq__subset,axiom, % 185.59/185.86 ! [T_b,V_B_2,V_A_2] : % 185.59/185.86 ( V_A_2 = V_B_2 % 185.59/185.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_order__eq__iff,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,T_b] : % 185.59/185.86 ( class_Orderings_Oorder(T_b) % 185.59/185.86 => ( V_x_2 = V_y_2 % 185.59/185.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_equalityD1,axiom, % 185.59/185.86 ! [T_b,V_B_2,V_A_2] : % 185.59/185.86 ( V_A_2 = V_B_2 % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_equalityD2,axiom, % 185.59/185.86 ! [T_b,V_B_2,V_A_2] : % 185.59/185.86 ( V_A_2 = V_B_2 % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_order__eq__refl,axiom, % 185.59/185.86 ! [V_y,V_x,T_a] : % 185.59/185.86 ( class_Orderings_Opreorder(T_a) % 185.59/185.86 => ( V_x = V_y % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_le__funD,axiom, % 185.59/185.86 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 185.59/185.86 ( class_Orderings_Oord(T_c) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_order__antisym__conv,axiom, % 185.59/185.86 ! [V_x_2,V_y_2,T_b] : % 185.59/185.86 ( class_Orderings_Oorder(T_b) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.86 <=> V_x_2 = V_y_2 ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_ord__eq__le__trans,axiom, % 185.59/185.86 ! [V_c,V_b,V_a,T_a] : % 185.59/185.86 ( class_Orderings_Oord(T_a) % 185.59/185.86 => ( V_a = V_b % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_xt1_I3_J,axiom, % 185.59/185.86 ! [V_c,V_b,V_a,T_a] : % 185.59/185.86 ( class_Orderings_Oorder(T_a) % 185.59/185.86 => ( V_a = V_b % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__trans,axiom, % 185.59/185.86 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_ord__le__eq__trans,axiom, % 185.59/185.86 ! [V_c,V_b,V_a,T_a] : % 185.59/185.86 ( class_Orderings_Oord(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.86 => ( V_b = V_c % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_xt1_I4_J,axiom, % 185.59/185.86 ! [V_c,V_a,V_b,T_a] : % 185.59/185.86 ( class_Orderings_Oorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.59/185.86 => ( V_b = V_c % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_order__antisym,axiom, % 185.59/185.86 ! [V_y,V_x,T_a] : % 185.59/185.86 ( class_Orderings_Oorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.86 => V_x = V_y ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_order__trans,axiom, % 185.59/185.86 ! [V_z,V_y,V_x,T_a] : % 185.59/185.86 ( class_Orderings_Opreorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_xt1_I5_J,axiom, % 185.59/185.86 ! [V_x,V_y,T_a] : % 185.59/185.86 ( class_Orderings_Oorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.86 => V_x = V_y ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_xt1_I6_J,axiom, % 185.59/185.86 ! [V_z,V_x,V_y,T_a] : % 185.59/185.86 ( class_Orderings_Oorder(T_a) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_equalityE,axiom, % 185.59/185.86 ! [T_b,V_B_2,V_A_2] : % 185.59/185.86 ( V_A_2 = V_B_2 % 185.59/185.86 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_le__funE,axiom, % 185.59/185.86 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 185.59/185.86 ( class_Orderings_Oord(T_c) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_linorder__le__cases,axiom, % 185.59/185.86 ! [V_y,V_x,T_a] : % 185.59/185.86 ( class_Orderings_Olinorder(T_a) % 185.59/185.86 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__def,axiom, % 185.59/185.86 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 <=> ! [B_x] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.86 => ! [B_xa] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.59/185.86 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 185.59/185.86 => B_x = B_xa ) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__idem__iff,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 % 185.59/185.86 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__upd,axiom, % 185.59/185.86 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__same,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__apply,axiom, % 185.59/185.86 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 185.59/185.86 ( ( V_z_2 = V_x_2 % 185.59/185.86 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 185.59/185.86 & ( V_z_2 != V_x_2 % 185.59/185.86 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__twist,axiom, % 185.59/185.86 ! [V_d_2,V_ba_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] : % 185.59/185.86 ( V_a_2 != V_ca_2 % 185.59/185.86 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_ba_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_ba_2) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__other,axiom, % 185.59/185.86 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 185.59/185.86 ( V_z_2 != V_x_2 % 185.59/185.86 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__fun,axiom, % 185.59/185.86 ! [T_d,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__eq,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.59/185.86 <=> V_x_2 = V_y_2 ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_injD,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.59/185.86 => V_x_2 = V_y_2 ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__inj__on,axiom, % 185.59/185.86 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__idem,axiom, % 185.59/185.86 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 185.59/185.86 ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.59/185.86 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__image__eq__iff,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 185.59/185.86 <=> V_A_2 = V_B_2 ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__comp,axiom, % 185.59/185.86 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 185.59/185.86 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__id2,axiom, % 185.59/185.86 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 185.59/185.86 % 185.59/185.86 fof(fact_vimage__subsetI,axiom, % 185.59/185.86 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_the__inv__f__f,axiom, % 185.59/185.86 ! [V_x_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__def,axiom, % 185.59/185.86 ! [V_ba_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 185.59/185.86 ( ( V_x_2 = V_a_2 % 185.59/185.86 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_ba_2),V_x_2) = V_ba_2 ) % 185.59/185.86 & ( V_x_2 != V_a_2 % 185.59/185.86 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_range__ex1__eq,axiom, % 185.59/185.86 ! [V_ba_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.86 <=> ? [B_x] : % 185.59/185.86 ( V_ba_2 = hAPP(V_f_2,B_x) % 185.59/185.86 & ! [B_y] : % 185.59/185.86 ( V_ba_2 = hAPP(V_f_2,B_y) % 185.59/185.86 => B_y = B_x ) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__image__mem__iff,axiom, % 185.59/185.86 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.86 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__image__set__diff,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.86 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_image__set__diff,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__onD,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.86 => V_x_2 = V_y_2 ) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__iff,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 185.59/185.86 <=> V_x_2 = V_y_2 ) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__contraD,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( V_x_2 != V_y_2 % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.86 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__vimage__image__eq,axiom, % 185.59/185.86 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__fun__updI,axiom, % 185.59/185.86 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.86 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__imageI2,axiom, % 185.59/185.86 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) % 185.59/185.86 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__diff,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_vimage__subsetD,axiom, % 185.59/185.86 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 185.59/185.86 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 185.59/185.86 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 185.59/185.86 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__singleton,axiom, % 185.59/185.86 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ). % 185.59/185.86 % 185.59/185.86 fof(fact_in__mono,axiom, % 185.59/185.86 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_set__rev__mp,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_set__mp,axiom, % 185.59/185.86 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_iso__tuple__UNIV__I,axiom, % 185.59/185.86 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.86 % 185.59/185.86 fof(fact_bot__least,axiom, % 185.59/185.86 ! [V_x,T_a] : % 185.59/185.86 ( class_Orderings_Obot(T_a) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__empty,axiom, % 185.59/185.86 ! [V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.86 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_UNIV__not__empty,axiom, % 185.59/185.86 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__insertI,axiom, % 185.59/185.86 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__insertI2,axiom, % 185.59/185.86 ! [V_ba_2,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_insert__mono,axiom, % 185.59/185.86 ! [V_a_2,V_D_2,V_C_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_subset__image__iff,axiom, % 185.59/185.86 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.86 <=> ? [B_AA] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 185.59/185.86 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_image__mono,axiom, % 185.59/185.86 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_Diff__subset,axiom, % 185.59/185.86 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 185.59/185.86 % 185.59/185.86 fof(fact_Diff__mono,axiom, % 185.59/185.86 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_double__diff,axiom, % 185.59/185.86 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.86 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_vimage__mono,axiom, % 185.59/185.86 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_vimage__UNIV,axiom, % 185.59/185.86 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.86 % 185.59/185.86 fof(fact_asm,axiom, % 185.59/185.86 ! [V_Ga_2,V_ts_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) % 185.59/185.86 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_weaken,axiom, % 185.59/185.86 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] : % 185.59/185.86 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 185.59/185.86 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__vimage__singleton,axiom, % 185.59/185.86 ! [V_a_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_pred__subset__eq,axiom, % 185.59/185.86 ! [V_S_2,V_R_2,T_b] : % 185.59/185.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) % 185.59/185.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_the__inv__into__into,axiom, % 185.59/185.86 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.86 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_UNIV__def,axiom, % 185.59/185.86 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ). % 185.59/185.86 % 185.59/185.86 fof(fact_range__composition,axiom, % 185.59/185.86 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 185.59/185.86 % 185.59/185.86 fof(fact_fun__upd__comp,axiom, % 185.59/185.86 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ). % 185.59/185.86 % 185.59/185.86 fof(fact_comp__inj__on__iff,axiom, % 185.59/185.86 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 185.59/185.86 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_comp__inj__on,axiom, % 185.59/185.86 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.86 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) % 185.59/185.86 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ). % 185.59/185.86 % 185.59/185.86 fof(fact_inj__on__imageI,axiom, % 185.59/185.86 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) % 185.59/185.87 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_subset__insert,axiom, % 185.59/185.87 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.59/185.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_insert__subset,axiom, % 185.59/185.87 ! [V_B_2,V_A_2,V_x_2,T_b] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) % 185.59/185.87 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_the__inv__into__f__eq,axiom, % 185.59/185.87 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.87 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.87 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_the__inv__into__f__f,axiom, % 185.59/185.87 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.87 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_rangeI,axiom, % 185.59/185.87 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ). % 185.59/185.87 % 185.59/185.87 fof(fact_range__eqI,axiom, % 185.59/185.87 ! [T_c,T_b,V_x_2,V_f_2,V_ba_2] : % 185.59/185.87 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_subset__singletonD,axiom, % 185.59/185.87 ! [V_x_2,V_A_2,T_b] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))))) % 185.59/185.87 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.87 | 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))) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_inj__on__the__inv__into,axiom, % 185.59/185.87 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.87 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_the__inv__into__onto,axiom, % 185.59/185.87 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.87 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_Diff__UNIV,axiom, % 185.59/185.87 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.87 % 185.59/185.87 fof(fact_comp__surj,axiom, % 185.59/185.87 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 185.59/185.87 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.87 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 185.59/185.87 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_image__diff__subset,axiom, % 185.59/185.87 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.87 % 185.59/185.87 fof(fact_image__vimage__subset,axiom, % 185.59/185.87 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ). % 185.59/185.87 % 185.59/185.87 fof(fact_surj__image__vimage__eq,axiom, % 185.59/185.87 ! [V_A_2,V_f_2,T_b,T_c] : % 185.59/185.87 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.87 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_f__the__inv__into__f,axiom, % 185.59/185.87 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.87 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_inj__on__iff__surj,axiom, % 185.59/185.87 ! [V_A_H_2,T_c,T_b,V_A_2] : % 185.59/185.87 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.87 => ( ? [B_f] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 185.59/185.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) ) % 185.59/185.87 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_flat__lub__def,axiom, % 185.59/185.87 ! [V_ba_2,V_A_2,T_b] : % 185.59/185.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.87 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = V_ba_2 ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.87 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 185.59/185.87 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 185.59/185.87 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 185.59/185.87 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.87 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 185.59/185.87 | ? [B_x,B_y] : % 185.59/185.87 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 185.59/185.87 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 185.59/185.87 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_diff__eq__diff__less__eq,axiom, % 185.59/185.87 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_psubset__insert__iff,axiom, % 185.59/185.87 ! [V_B_2,V_x_2,V_A_2,T_b] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) % 185.59/185.87 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 185.59/185.87 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_vimage__if,axiom, % 185.59/185.87 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] : % 185.59/185.87 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.87 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.59/185.87 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.59/185.87 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.87 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.59/185.87 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 185.59/185.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 185.59/185.87 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_rangeE,axiom, % 185.59/185.87 ! [V_f_2,T_c,V_ba_2,T_b] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 185.59/185.87 => ~ ! [B_x] : V_ba_2 != hAPP(V_f_2,B_x) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_vimage__subset__eq,axiom, % 185.59/185.87 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_inj__image__Compl__subset,axiom, % 185.59/185.87 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_image__subsetI,axiom, % 185.59/185.87 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] : % 185.59/185.87 ( ! [B_x] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) ) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_quotient__diff1,axiom, % 185.59/185.87 ! [V_a_2,V_A_2,V_r_2,T_b] : % 185.59/185.87 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.87 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_inj__uminus,axiom, % 185.59/185.87 ! [V_A_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_ComplI,axiom, % 185.59/185.87 ! [V_A_2,V_ca_2,T_b] : % 185.59/185.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_compl__eq__compl__iff,axiom, % 185.59/185.87 ! [V_y_2,V_x_2,T_b] : % 185.59/185.87 ( class_Lattices_Oboolean__algebra(T_b) % 185.59/185.87 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 185.59/185.87 <=> V_x_2 = V_y_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_uminus__apply,axiom, % 185.59/185.87 ! [V_x_2,V_A_2,T_c,T_b] : % 185.59/185.87 ( class_Groups_Ouminus(T_b) % 185.59/185.87 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_double__compl,axiom, % 185.59/185.87 ! [V_x,T_a] : % 185.59/185.87 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.87 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_fun__Compl__def,axiom, % 185.59/185.87 ! [V_x_2,V_A_2,T_c,T_b] : % 185.59/185.87 ( class_Groups_Ouminus(T_b) % 185.59/185.87 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_minus__minus,axiom, % 185.59/185.87 ! [V_a,T_a] : % 185.59/185.87 ( class_Groups_Ogroup__add(T_a) % 185.59/185.87 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_equation__minus__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Ogroup__add(T_b) % 185.59/185.87 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.59/185.87 <=> V_ba_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_less__minus__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_minus__equation__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Ogroup__add(T_b) % 185.59/185.87 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_ba_2 % 185.59/185.87 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) = V_a_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_minus__less__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_neg__equal__iff__equal,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Ogroup__add(T_b) % 185.59/185.87 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.59/185.87 <=> V_a_2 = V_ba_2 ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_neg__less__iff__less,axiom, % 185.59/185.87 ! [V_a_2,V_ba_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_linorder__cases,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Olinorder(T_a) % 185.59/185.87 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => ( V_x != V_y % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__asym,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_xt1_I10_J,axiom, % 185.59/185.87 ! [V_z,V_x,V_y,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__trans,axiom, % 185.59/185.87 ! [V_z,V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_xt1_I2_J,axiom, % 185.59/185.87 ! [V_c,V_a,V_b,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.59/185.87 => ( V_b = V_c % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_ord__less__eq__trans,axiom, % 185.59/185.87 ! [V_c,V_b,V_a,T_a] : % 185.59/185.87 ( class_Orderings_Oord(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.59/185.87 => ( V_b = V_c % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_psubset__trans,axiom, % 185.59/185.87 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_xt1_I1_J,axiom, % 185.59/185.87 ! [V_c,V_b,V_a,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( V_a = V_b % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_ord__eq__less__trans,axiom, % 185.59/185.87 ! [V_c,V_b,V_a,T_a] : % 185.59/185.87 ( class_Orderings_Oord(T_a) % 185.59/185.87 => ( V_a = V_b % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_xt1_I9_J,axiom, % 185.59/185.87 ! [V_a,V_b,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__asym_H,axiom, % 185.59/185.87 ! [V_b,V_a,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__imp__not__eq2,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => V_y != V_x ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__imp__not__eq,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => V_x != V_y ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__imp__not__less,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__not__sym,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_less__imp__neq,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Oorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => V_x != V_y ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_linorder__neqE,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Olinorder(T_a) % 185.59/185.87 => ( V_x != V_y % 185.59/185.87 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_linorder__antisym__conv3,axiom, % 185.59/185.87 ! [V_x_2,V_y_2,T_b] : % 185.59/185.87 ( class_Orderings_Olinorder(T_b) % 185.59/185.87 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 185.59/185.87 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.87 <=> V_x_2 = V_y_2 ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_Compl__eq__Compl__iff,axiom, % 185.59/185.87 ! [V_B_2,V_A_2,T_b] : % 185.59/185.87 ( 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_b,tc_HOL_Obool)),V_B_2) % 185.59/185.87 <=> V_A_2 = V_B_2 ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_linorder__less__linear,axiom, % 185.59/185.87 ! [V_y,V_x,T_a] : % 185.59/185.87 ( class_Orderings_Olinorder(T_a) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.87 | V_x = V_y % 185.59/185.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_not__less__iff__gr__or__eq,axiom, % 185.59/185.87 ! [V_y_2,V_x_2,T_b] : % 185.59/185.87 ( class_Orderings_Olinorder(T_b) % 185.59/185.87 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 185.59/185.87 | V_x_2 = V_y_2 ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_linorder__neq__iff,axiom, % 185.59/185.87 ! [V_y_2,V_x_2,T_b] : % 185.59/185.87 ( class_Orderings_Olinorder(T_b) % 185.59/185.87 => ( V_x_2 != V_y_2 % 185.59/185.87 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.87 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_double__complement,axiom, % 185.59/185.87 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 185.59/185.87 % 185.59/185.87 fof(fact_order__less__irrefl,axiom, % 185.59/185.87 ! [V_x,T_a] : % 185.59/185.87 ( class_Orderings_Opreorder(T_a) % 185.59/185.87 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_le__minus__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.87 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 185.59/185.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 185.59/185.87 % 185.59/185.87 fof(fact_minus__le__iff,axiom, % 185.59/185.87 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.88 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_neg__le__iff__le,axiom, % 185.59/185.88 ! [V_a_2,V_ba_2,T_b] : % 185.59/185.88 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_le__imp__neg__le,axiom, % 185.59/185.88 ! [V_b,V_a,T_a] : % 185.59/185.88 ( class_Groups_Oordered__ab__group__add(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.88 => 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))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_minus__diff__eq,axiom, % 185.59/185.88 ! [V_b,V_a,T_a] : % 185.59/185.88 ( class_Groups_Oab__group__add(T_a) % 185.59/185.88 => 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) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_diff__eq__diff__less,axiom, % 185.59/185.88 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.88 ( class_Groups_Oordered__ab__group__add(T_b) % 185.59/185.88 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotient__is__empty,axiom, % 185.59/185.88 ! [V_r_2,V_A_2,T_b] : % 185.59/185.88 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 185.59/185.88 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotient__is__empty2,axiom, % 185.59/185.88 ! [V_r_2,V_A_2,T_b] : % 185.59/185.88 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) % 185.59/185.88 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotient__empty,axiom, % 185.59/185.88 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__image__Compl__eq,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_compl__le__compl__iff,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Lattices_Oboolean__algebra(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_compl__mono,axiom, % 185.59/185.88 ! [V_y,V_x,T_a] : % 185.59/185.88 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.88 => 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))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_ComplE,axiom, % 185.59/185.88 ! [V_A_2,V_ca_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.59/185.88 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_ComplD,axiom, % 185.59/185.88 ! [V_A_2,V_ca_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.59/185.88 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__iff,axiom, % 185.59/185.88 ! [V_A_2,V_ca_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.59/185.88 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__empty2,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) % 185.59/185.88 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__empty1,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 185.59/185.88 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_less__fun__def,axiom, % 185.59/185.88 ! [V_g_2,V_f_2,T_b,T_c] : % 185.59/185.88 ( class_Orderings_Oord(T_c) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 185.59/185.88 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__anti__mono,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__subset__Compl__iff,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2))) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_xt1_I8_J,axiom, % 185.59/185.88 ! [V_z,V_x,V_y,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__le__less__trans,axiom, % 185.59/185.88 ! [V_z,V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Opreorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_xt1_I7_J,axiom, % 185.59/185.88 ! [V_z,V_x,V_y,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__less__le__trans,axiom, % 185.59/185.88 ! [V_z,V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Opreorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_xt1_I11_J,axiom, % 185.59/185.88 ! [V_a,V_b,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.59/185.88 => ( V_a != V_b % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__le__neq__trans,axiom, % 185.59/185.88 ! [V_b,V_a,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.88 => ( V_a != V_b % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__le__imp__less__or__eq,axiom, % 185.59/185.88 ! [V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.88 | V_x = V_y ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_linorder__antisym__conv2,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Olinorder(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> V_x_2 = V_y_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__less__imp__le,axiom, % 185.59/185.88 ! [V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Opreorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_leD,axiom, % 185.59/185.88 ! [V_x,V_y,T_a] : % 185.59/185.88 ( class_Orderings_Olinorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.88 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_xt1_I12_J,axiom, % 185.59/185.88 ! [V_b,V_a,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( V_a != V_b % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__neq__le__trans,axiom, % 185.59/185.88 ! [V_b,V_a,T_a] : % 185.59/185.88 ( class_Orderings_Oorder(T_a) % 185.59/185.88 => ( V_a != V_b % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_linorder__antisym__conv1,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Olinorder(T_b) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> V_x_2 = V_y_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_not__leE,axiom, % 185.59/185.88 ! [V_x,V_y,T_a] : % 185.59/185.88 ( class_Orderings_Olinorder(T_a) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_leI,axiom, % 185.59/185.88 ! [V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Olinorder(T_a) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__le__less,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Oorder(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 | V_x_2 = V_y_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_less__le__not__le,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Opreorder(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_order__less__le,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Oorder(T_b) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 & V_x_2 != V_y_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_linorder__le__less__linear,axiom, % 185.59/185.88 ! [V_y,V_x,T_a] : % 185.59/185.88 ( class_Orderings_Olinorder(T_a) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_linorder__not__le,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Olinorder(T_b) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_linorder__not__less,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,T_b] : % 185.59/185.88 ( class_Orderings_Olinorder(T_b) % 185.59/185.88 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 185.59/185.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_psubsetD,axiom, % 185.59/185.88 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__comp__iff,axiom, % 185.59/185.88 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 185.59/185.88 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 185.59/185.88 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__trans,axiom, % 185.59/185.88 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.88 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) % 185.59/185.88 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__imp__inj__on,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.88 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_not__psubset__empty,axiom, % 185.59/185.88 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.88 % 185.59/185.88 fof(fact_subset__psubset__trans,axiom, % 185.59/185.88 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_psubset__subset__trans,axiom, % 185.59/185.88 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_psubset__imp__subset,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_subset__iff__psubset__eq,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 | V_A_2 = V_B_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_psubset__eq,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 & V_A_2 != V_B_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_vimage__Compl,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__the__inv__into,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.88 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Collect__neg__eq,axiom, % 185.59/185.88 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_compl__top__eq,axiom, % 185.59/185.88 ! [T_a] : % 185.59/185.88 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.88 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_compl__bot__eq,axiom, % 185.59/185.88 ! [T_a] : % 185.59/185.88 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.88 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_subset__Compl__self__eq,axiom, % 185.59/185.88 ! [V_A_2,T_b] : % 185.59/185.88 ( 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)),V_A_2))) % 185.59/185.88 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__empty__eq,axiom, % 185.59/185.88 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__UNIV__eq,axiom, % 185.59/185.88 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__subset,axiom, % 185.59/185.88 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.88 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 % 185.59/185.88 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__imp__surj,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__is__surj,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__comp,axiom, % 185.59/185.88 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 185.59/185.88 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,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_d,tc_HOL_Obool))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__eq__Diff__UNIV,axiom, % 185.59/185.88 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_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_A_2) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__is__inj,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__on__imp__bij__betw,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__def,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.88 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__on__strict__subset,axiom, % 185.59/185.88 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Compl__eq,axiom, % 185.59/185.88 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ). % 185.59/185.88 % 185.59/185.88 fof(fact_surj__Compl__image__subset,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__comp__iff2,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2)) % 185.59/185.88 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) % 185.59/185.88 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__def,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 & hAPP(c_Set_Oimage(T_b,T_c,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)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bijI,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => ( hAPP(c_Set_Oimage(T_b,T_c,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)) % 185.59/185.88 => c_Fun_Obij__betw(T_b,T_c,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))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_diff__eq__diff__eq,axiom, % 185.59/185.88 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.88 ( class_Groups_Oab__group__add(T_b) % 185.59/185.88 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) % 185.59/185.88 => ( V_a_2 = V_ba_2 % 185.59/185.88 <=> V_ca_2 = V_d_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Cantor__Bernstein,axiom, % 185.59/185.88 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 185.59/185.88 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) % 185.59/185.88 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__image__Collect__eq,axiom, % 185.59/185.88 ! [V_Pa_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__vimage__eq__inv__image,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__comp,axiom, % 185.59/185.88 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) % 185.59/185.88 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotientI,axiom, % 185.59/185.88 ! [V_r_2,V_A_2,V_x_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_mk__less__def,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,V_R_2,T_b] : % 185.59/185.88 ( c_Partial__Function_Omk__less(T_b,V_R_2,V_x_2,V_y_2) % 185.59/185.88 <=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 185.59/185.88 & ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_psubset__imp__ex__mem,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.88 => ? [B_b] : hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_o__inv__distrib,axiom, % 185.59/185.88 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_fun__left__comm__idem__remove,axiom, % 185.59/185.88 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))) ). % 185.59/185.88 % 185.59/185.88 fof(fact_o__inv__o__cancel,axiom, % 185.59/185.88 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 185.59/185.88 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.59/185.88 => 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) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 185.59/185.88 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.59/185.88 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_fun__left__comm__idem__insert,axiom, % 185.59/185.88 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 185.59/185.88 ! [V_x_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.59/185.88 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__inv__into,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.88 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_f__inv__into__f,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.88 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__into,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__injective,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] : % 185.59/185.88 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.88 => V_x_2 = V_y_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__f__f,axiom, % 185.59/185.88 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__f__eq,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.88 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_image__inv__into__cancel,axiom, % 185.59/185.88 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_surj__iff__all,axiom, % 185.59/185.88 ! [V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_surj__f__inv__f,axiom, % 185.59/185.88 ! [V_y_2,V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_image__surj__f__inv__f,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__f__eq,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__f__f,axiom, % 185.59/185.88 ! [V_x_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__inv__into__eq,axiom, % 185.59/185.88 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.88 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__inv__eq,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__imp__bij__inv,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.59/185.88 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_singleton__quotient,axiom, % 185.59/185.88 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__into__image__cancel,axiom, % 185.59/185.88 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__on__inv__into,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.88 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__imp__surj__inv,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_image__inv__f__f,axiom, % 185.59/185.88 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__image__comp,axiom, % 185.59/185.88 ! [V_X_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_surj__imp__inj__inv,axiom, % 185.59/185.88 ! [V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotientE,axiom, % 185.59/185.88 ! [V_r_2,V_A_2,V_X_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.88 => ~ ! [B_x] : % 185.59/185.88 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.88 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Image__mono,axiom, % 185.59/185.88 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Image__empty,axiom, % 185.59/185.88 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__transfer,axiom, % 185.59/185.88 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => ( ! [B_y] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 185.59/185.88 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) ) % 185.59/185.88 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_quotient__def,axiom, % 185.59/185.88 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ). % 185.59/185.88 % 185.59/185.88 fof(fact_equiv__class__self,axiom, % 185.59/185.88 ! [V_a_2,V_r_2,V_A_2,T_b] : % 185.59/185.88 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,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)))))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_Diff1__fold__graph,axiom, % 185.59/185.88 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.88 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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))))),V_y_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.88 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inv__o__cancel,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__iff,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : % 185.59/185.88 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.88 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_surj__iff,axiom, % 185.59/185.88 ! [V_f_2,T_b,T_c] : % 185.59/185.88 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.88 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_bij__betw__id,axiom, % 185.59/185.88 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ). % 185.59/185.88 % 185.59/185.88 fof(fact_SUP1__I,axiom, % 185.59/185.88 ! [T_c,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.88 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 185.59/185.88 => hBOOL(hAPP(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_ba_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_less__by__empty,axiom, % 185.59/185.88 ! [V_B_2,T_b,V_A_2] : % 185.59/185.88 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_SUP1__iff,axiom, % 185.59/185.88 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.88 ( hBOOL(hAPP(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_ba_2)) % 185.59/185.88 <=> ? [B_x] : % 185.59/185.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.88 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_id__apply,axiom, % 185.59/185.88 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 185.59/185.88 % 185.59/185.88 fof(fact_id__def,axiom, % 185.59/185.88 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 185.59/185.88 % 185.59/185.88 fof(fact_Image__UN,axiom, % 185.59/185.88 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ). % 185.59/185.88 % 185.59/185.88 fof(fact_UN__o,axiom, % 185.59/185.88 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ). % 185.59/185.88 % 185.59/185.88 fof(fact_image__id,axiom, % 185.59/185.88 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 185.59/185.88 % 185.59/185.88 fof(fact_id__o,axiom, % 185.59/185.88 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ). % 185.59/185.88 % 185.59/185.88 fof(fact_o__id,axiom, % 185.59/185.88 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ). % 185.59/185.88 % 185.59/185.88 fof(fact_o__eq__id__dest,axiom, % 185.59/185.88 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 185.59/185.88 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2) % 185.59/185.88 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 185.59/185.88 % 185.59/185.88 fof(fact_inj__on__id,axiom, % 185.59/185.88 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 185.59/185.89 % 185.59/185.89 fof(fact_bij__betw__id__iff,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_b] : % 185.59/185.89 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) % 185.59/185.89 <=> V_A_2 = V_B_2 ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_vimage__id,axiom, % 185.59/185.89 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 185.59/185.89 % 185.59/185.89 fof(fact_empty__fold__graphE,axiom, % 185.59/185.89 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.89 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) % 185.59/185.89 => V_x_2 = V_z_2 ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_fold__graph_OemptyI,axiom, % 185.59/185.89 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_fold__graph_Oequations_I1_J,axiom, % 185.59/185.89 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP__UN__eq,axiom, % 185.59/185.89 ! [V_x_2,V_r_2,T_c,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 185.59/185.89 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_Image__eq__UN,axiom, % 185.59/185.89 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 185.59/185.89 % 185.59/185.89 fof(fact_surj__id,axiom, % 185.59/185.89 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_bij__id,axiom, % 185.59/185.89 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ). % 185.59/185.89 % 185.59/185.89 fof(fact_inv__id,axiom, % 185.59/185.89 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ). % 185.59/185.89 % 185.59/185.89 fof(fact_fold__graph_OinsertI,axiom, % 185.59/185.89 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 185.59/185.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.89 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.59/185.89 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__I,axiom, % 185.59/185.89 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_vimage__eq__UN,axiom, % 185.59/185.89 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ). % 185.59/185.89 % 185.59/185.89 fof(fact_image__eq__UN,axiom, % 185.59/185.89 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__equiv__class2,axiom, % 185.59/185.89 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.59/185.89 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__equiv__class,axiom, % 185.59/185.89 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => hAPP(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_r_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) = hAPP(V_f_2,V_a_2) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__extend__simps_I1_J,axiom, % 185.59/185.89 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 185.59/185.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) % 185.59/185.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__singleton,axiom, % 185.59/185.89 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) = V_A_2 ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__simps_I1_J,axiom, % 185.59/185.89 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 185.59/185.89 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.89 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__upper,axiom, % 185.59/185.89 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__insert__distrib,axiom, % 185.59/185.89 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_congruent2__implies__congruent,axiom, % 185.59/185.89 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_ball__UN,axiom, % 185.59/185.89 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.89 ( ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.89 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.59/185.89 <=> ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 => ! [B_xa] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 185.59/185.89 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP__commute,axiom, % 185.59/185.89 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__UN__flatten,axiom, % 185.59/185.89 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__simps_I9_J,axiom, % 185.59/185.89 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__extend__simps_I9_J,axiom, % 185.59/185.89 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 185.59/185.89 % 185.59/185.89 fof(fact_congruent2__implies__congruent__UN,axiom, % 185.59/185.89 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.59/185.89 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 185.59/185.89 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP__le__iff,axiom, % 185.59/185.89 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) % 185.59/185.89 <=> ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_less__SUP__iff,axiom, % 185.59/185.89 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 185.59/185.89 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.89 & class_Orderings_Olinorder(T_b) ) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) % 185.59/185.89 <=> ? [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__iff,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.59/185.89 <=> ? [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP__const,axiom, % 185.59/185.89 ! [V_M_2,T_b,V_A_2,T_c] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.59/185.89 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UNION__empty__conv_I1_J,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_c,T_b] : % 185.59/185.89 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,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) % 185.59/185.89 <=> ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__empty2,axiom, % 185.59/185.89 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__constant,axiom, % 185.59/185.89 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.59/185.89 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.89 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.89 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UNION__empty__conv_I2_J,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_b,T_c] : % 185.59/185.89 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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)) % 185.59/185.89 <=> ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.89 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__subset__iff,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 185.59/185.89 <=> ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__simps_I10_J,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_image__UN,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__extend__simps_I10_J,axiom, % 185.59/185.89 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUPR__apply,axiom, % 185.59/185.89 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.89 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__extend__simps_I6_J,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__simps_I6_J,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 185.59/185.89 % 185.59/185.89 fof(fact_vimage__UN,axiom, % 185.59/185.89 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP__subset,axiom, % 185.59/185.89 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_le__SUPI,axiom, % 185.59/185.89 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 185.59/185.89 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__equiv__class__type2,axiom, % 185.59/185.89 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 185.59/185.89 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2))) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2))) % 185.59/185.89 => ( ! [B_x1] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 185.59/185.89 => ! [B_x2] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_UN__equiv__class__type,axiom, % 185.59/185.89 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.89 => ( ! [B_x] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_fold1Set_Ointros,axiom, % 185.59/185.89 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 185.59/185.89 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_subset__equiv__class,axiom, % 185.59/185.89 ! [V_a_2,V_ba_2,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,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)))))) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_eq__equiv__class__iff2,axiom, % 185.59/185.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.89 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) % 185.59/185.89 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_equiv__class__subset,axiom, % 185.59/185.89 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_equiv__class__eq__iff,axiom, % 185.59/185.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.59/185.89 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.89 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.89 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_eq__equiv__class__iff,axiom, % 185.59/185.89 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.59/185.89 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.89 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.89 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_eq__equiv__class,axiom, % 185.59/185.89 ! [V_A_2,V_ba_2,V_a_2,V_r_2,T_b] : % 185.59/185.89 ( hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.89 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_fold__graph__permute__diff,axiom, % 185.59/185.89 ! [V_a_2,V_x_2,V_A_2,V_ba_2,T_b] : % 185.59/185.89 ( class_Groups_Oab__semigroup__mult(T_b) % 185.59/185.89 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_x_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.59/185.89 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_SUP2__I,axiom, % 185.59/185.89 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 185.59/185.89 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.89 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 185.59/185.89 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) ) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_mult__left__idem,axiom, % 185.59/185.89 ! [V_b,V_a,T_a] : % 185.59/185.89 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.59/185.89 => 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) ) ). % 185.59/185.89 % 185.59/185.89 fof(fact_mult__idem,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.59/185.90 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_times_Oidem,axiom, % 185.59/185.90 ! [V_a,T_a] : % 185.59/185.90 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 185.59/185.90 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 185.59/185.90 ! [V_c,V_b,V_a,T_a] : % 185.59/185.90 ( class_Groups_Oab__semigroup__mult(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_pred__equals__eq2,axiom, % 185.59/185.90 ! [V_S_2,V_R_2,T_c,T_b] : % 185.59/185.90 ( 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_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) % 185.59/185.90 <=> V_R_2 = V_S_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_SUP__UN__eq2,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fun__left__comm__idem,axiom, % 185.59/185.90 ! [T_b] : % 185.59/185.90 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.59/185.90 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_congruent2D,axiom, % 185.59/185.90 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2)) % 185.59/185.90 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_congruentD,axiom, % 185.59/185.90 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2)) % 185.59/185.90 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_pred__subset__eq2,axiom, % 185.59/185.90 ! [V_S_2,V_R_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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))) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_bot__empty__eq2,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) % 185.59/185.90 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fold1Set__nonempty,axiom, % 185.59/185.90 ! [V_x_2,V_A_2,V_f_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 185.59/185.90 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_empty__fold1SetE,axiom, % 185.59/185.90 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_rev__ImageI,axiom, % 185.59/185.90 ! [V_r_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__iff,axiom, % 185.59/185.90 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 185.59/185.90 <=> ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fold__graph__insert__swap,axiom, % 185.59/185.90 ! [V_z_2,V_y_2,V_A_2,V_ba_2,T_b] : % 185.59/185.90 ( class_Groups_Oab__semigroup__mult(T_b) % 185.59/185.90 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_y_2)) % 185.59/185.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fold1Set__sing,axiom, % 185.59/185.90 ! [V_ba_2,V_a_2,V_f_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_ba_2)) % 185.59/185.90 <=> V_a_2 = V_ba_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__singleton__iff,axiom, % 185.59/185.90 ! [V_a_2,V_r_2,T_c,V_ba_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_ba_2)),V_r_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equiv__class__eq,axiom, % 185.59/185.90 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.90 => hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_quotient__eqI,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.59/185.90 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_quotient__eq__iff,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 185.59/185.90 => ( V_X_2 = V_Y_2 % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__singleton,axiom, % 185.59/185.90 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_in__rel__def,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 185.59/185.90 <=> 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)),V_R_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Nitpick_Orefl_H__def,axiom, % 185.59/185.90 ! [V_r_2,T_b] : % 185.59/185.90 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 185.59/185.90 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__equiv__class__inject,axiom, % 185.59/185.90 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 185.59/185.90 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => ! [B_y] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.59/185.90 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) ) % 185.59/185.90 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_irrefl__def,axiom, % 185.59/185.90 ! [V_r_2,T_b] : % 185.59/185.90 ( c_Relation_Oirrefl(T_b,V_r_2) % 185.59/185.90 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equiv__class__nondisjoint,axiom, % 185.59/185.90 ! [V_ba_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_minus__mult__right,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Rings_Oring(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_minus__mult__left,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Rings_Oring(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_minus__mult__commute,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Rings_Oring(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_minus__mult__minus,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Rings_Oring(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf1I,axiom, % 185.59/185.90 ! [T_b,V_B_2,V_x_2,V_A_2] : % 185.59/185.90 ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.59/185.90 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf1E,axiom, % 185.59/185.90 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 185.59/185.90 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.59/185.90 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_IntI,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_IntE,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_bot2E,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_SUP2__iff,axiom, % 185.59/185.90 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) % 185.59/185.90 <=> ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_rev__predicate2D,axiom, % 185.59/185.90 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_predicate2D,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf1D1,axiom, % 185.59/185.90 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 185.59/185.90 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf1D2,axiom, % 185.59/185.90 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 185.59/185.90 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__absorb,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__commute,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__left__absorb,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__left__commute,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__assoc,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf_Oidem,axiom, % 185.59/185.90 ! [V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__idem,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__fun__def,axiom, % 185.59/185.90 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( class_Lattices_Olattice(T_b) % 185.59/185.90 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf_Ocommute,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I1_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__commute,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf_Oleft__idem,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I4_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__left__idem,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf_Oleft__commute,axiom, % 185.59/185.90 ! [V_c,V_a,V_b,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I3_J,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__left__commute,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf_Oassoc,axiom, % 185.59/185.90 ! [V_c,V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I2_J,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__assoc,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__apply,axiom, % 185.59/185.90 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( class_Lattices_Olattice(T_b) % 185.59/185.90 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__infE,axiom, % 185.59/185.90 ! [V_b,V_a,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( 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))) % 185.59/185.90 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__mono,axiom, % 185.59/185.90 ! [V_d,V_b,V_c,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.59/185.90 => 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))) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__greatest,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 185.59/185.90 => 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))) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__infI,axiom, % 185.59/185.90 ! [V_b,V_a,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.59/185.90 => 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))) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__absorb2,axiom, % 185.59/185.90 ! [V_x,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__absorb1,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__infI2,axiom, % 185.59/185.90 ! [V_a,V_x,V_b,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.59/185.90 => 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)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__infI1,axiom, % 185.59/185.90 ! [V_b,V_x,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.59/185.90 => 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)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__inf__iff,axiom, % 185.59/185.90 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_b) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__iff__inf,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_b) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.90 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__le2,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__ord_I2_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__le1,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__ord_I1_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_less__infI1,axiom, % 185.59/185.90 ! [V_b,V_x,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 185.59/185.90 => 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)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_less__infI2,axiom, % 185.59/185.90 ! [V_a,V_x,V_b,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 185.59/185.90 => 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)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__bot__left,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__bot__right,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__eq__top__iff,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__top(T_b) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 185.59/185.90 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 185.59/185.90 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__top__right,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__top(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__top__left,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__top(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__iff,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_IntD1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_IntD2,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__empty__left,axiom, % 185.59/185.90 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__empty__right,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_disjoint__iff__not__equal,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( 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)) % 185.59/185.90 <=> ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => ! [B_xa] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 185.59/185.90 => B_x != B_xa ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_insert__inter__insert,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__lower1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__lower2,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__absorb2,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__absorb1,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__greatest,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__mono,axiom, % 185.59/185.90 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__UNIV__left,axiom, % 185.59/185.90 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__UNIV__right,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Int__distrib,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_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_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__Diff,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Int__distrib2,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Int2,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inj__on__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.90 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.59/185.90 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_vimage__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fun__left__comm__idem__inf,axiom, % 185.59/185.90 ! [T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__inf(T_b) % 185.59/185.90 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__Int__eq,axiom, % 185.59/185.90 ! [V_x_2,V_S_2,V_R_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Collect__conj__eq,axiom, % 185.59/185.90 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__UN__distrib2,axiom, % 185.59/185.90 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__extend__simps_I4_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__UN__distrib,axiom, % 185.59/185.90 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__extend__simps_I5_J,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__simps_I4_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__simps_I5_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__compl__bot,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_compl__inf__bot,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_diff__eq,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__left__if1,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__right__if1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__left__if0,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.59/185.90 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__right__if0,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.59/185.90 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__left,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,V_a_2,T_b] : % 185.59/185.90 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 185.59/185.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__insert__right,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_a_2,T_b] : % 185.59/185.90 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 185.59/185.90 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__Int__subset,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__triv,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( 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)) % 185.59/185.90 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__disjoint,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__disjoint2,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__disjoint,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__Int__subset,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Compl,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__def,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__Collect,axiom, % 185.59/185.90 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.90 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inj__on__image__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.90 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.90 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_disjoint__eq__subset__Compl,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( 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)) % 185.59/185.90 <=> 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)),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__vimage__eq,axiom, % 185.59/185.90 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_linorder__neqE__linordered__idom,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Rings_Olinordered__idom(T_a) % 185.59/185.90 => ( V_x != V_y % 185.59/185.90 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_quotient__disj,axiom, % 185.59/185.90 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.59/185.90 => ( V_X_2 = V_Y_2 % 185.59/185.90 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_square__eq__iff,axiom, % 185.59/185.90 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.90 ( class_Rings_Oidom(T_b) % 185.59/185.90 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ba_2) % 185.59/185.90 <=> ( V_a_2 = V_ba_2 % 185.59/185.90 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equivp__equiv,axiom, % 185.59/185.90 ! [V_A_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 185.59/185.90 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_ImageE,axiom, % 185.59/185.90 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 185.59/185.90 => ~ ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fold1Set_Oequations,axiom, % 185.59/185.90 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) % 185.59/185.90 <=> ? [B_a,B_A] : % 185.59/185.90 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 185.59/185.90 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 185.59/185.90 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_insert__fold1SetE,axiom, % 185.59/185.90 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) % 185.59/185.90 => ~ ! [B_a,B_A] : % 185.59/185.90 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 185.59/185.90 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Id__on__def,axiom, % 185.59/185.90 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,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_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inj__on__Un,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.90 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.59/185.90 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__Collect__mono,axiom, % 185.59/185.90 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => ( ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.59/185.90 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_same__fstI,axiom, % 185.59/185.90 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 185.59/185.90 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_total__on__def,axiom, % 185.59/185.90 ! [V_r_2,V_A_2,T_b] : % 185.59/185.90 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 185.59/185.90 <=> ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => ! [B_xa] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.59/185.90 => ( B_x != B_xa % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) % 185.59/185.90 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup1CI,axiom, % 185.59/185.90 ! [T_b,V_A_2,V_x_2,V_B_2] : % 185.59/185.90 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 185.59/185.90 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 185.59/185.90 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup1E,axiom, % 185.59/185.90 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 185.59/185.90 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 185.59/185.90 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UnCI,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 185.59/185.90 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UnE,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Image,axiom, % 185.59/185.90 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__apply,axiom, % 185.59/185.90 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( class_Lattices_Olattice(T_b) % 185.59/185.90 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__assoc,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I6_J,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup_Oassoc,axiom, % 185.59/185.90 ! [V_c,V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__left__commute,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I7_J,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup_Oleft__commute,axiom, % 185.59/185.90 ! [V_c,V_a,V_b,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__left__idem,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I8_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup_Oleft__idem,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__commute,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__aci_I5_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup_Ocommute,axiom, % 185.59/185.90 ! [V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__fun__def,axiom, % 185.59/185.90 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( class_Lattices_Olattice(T_b) % 185.59/185.90 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__idem,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup_Oidem,axiom, % 185.59/185.90 ! [V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_ball__Un,axiom, % 185.59/185.90 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.59/185.90 <=> ( ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.59/185.90 & ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_bex__Un,axiom, % 185.59/185.90 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.59/185.90 <=> ( ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.59/185.90 | ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.59/185.90 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__assoc,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__left__commute,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__left__absorb,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__commute,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__absorb,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup1I2,axiom, % 185.59/185.90 ! [V_A_2,T_b,V_x_2,V_B_2] : % 185.59/185.90 ( hBOOL(hAPP(V_B_2,V_x_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup1I1,axiom, % 185.59/185.90 ! [V_B_2,T_b,V_x_2,V_A_2] : % 185.59/185.90 ( hBOOL(hAPP(V_A_2,V_x_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equivp__transp,axiom, % 185.59/185.90 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equivp__symp,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_R_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equivp__reflp,axiom, % 185.59/185.90 ! [V_x_2,V_R_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_equivp__def,axiom, % 185.59/185.90 ! [V_R_2,T_b] : % 185.59/185.90 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 185.59/185.90 <=> ! [B_x,B_y] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 185.59/185.90 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_identity__equivp,axiom, % 185.59/185.90 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__ord_I3_J,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__ge1,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__ord_I4_J,axiom, % 185.59/185.90 ! [V_x,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__ge2,axiom, % 185.59/185.90 ! [V_x,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => 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))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__iff__sup,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_b) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.59/185.90 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__sup__iff,axiom, % 185.59/185.90 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_b) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__supI1,axiom, % 185.59/185.90 ! [V_b,V_a,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.59/185.90 => 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))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__supI2,axiom, % 185.59/185.90 ! [V_a,V_b,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.59/185.90 => 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))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__absorb2,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__absorb1,axiom, % 185.59/185.90 ! [V_x,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__supI,axiom, % 185.59/185.90 ! [V_b,V_x,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.59/185.90 => 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)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__least,axiom, % 185.59/185.90 ! [V_z,V_x,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 185.59/185.90 => 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)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__mono,axiom, % 185.59/185.90 ! [V_d,V_b,V_c,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.59/185.90 => 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))) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__supE,axiom, % 185.59/185.90 ! [V_x,V_b,V_a,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( 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)) % 185.59/185.90 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_less__supI2,axiom, % 185.59/185.90 ! [V_a,V_b,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 185.59/185.90 => 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))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_less__supI1,axiom, % 185.59/185.90 ! [V_b,V_a,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_a) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.59/185.90 => 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))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__eq__bot__iff,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,T_b] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__bot(T_b) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 185.59/185.90 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 185.59/185.90 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__bot__right,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__bot__left,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__bot(T_a) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__inf__distrib2,axiom, % 185.59/185.90 ! [V_x,V_z,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Odistrib__lattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__distrib2,axiom, % 185.59/185.90 ! [V_x,V_z,V_y,T_a] : % 185.59/185.90 ( class_Lattices_Odistrib__lattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__inf__distrib1,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Odistrib__lattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__distrib1,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Odistrib__lattice(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__inf__absorb,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__sup__absorb,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__top__left,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__top(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__top__right,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Obounded__lattice__top(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UnI2,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UnI1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__iff,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 185.59/185.90 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__empty,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hAPP(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)) % 185.59/185.90 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__empty__right,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__empty__left,axiom, % 185.59/185.90 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__insert__left,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__insert__right,axiom, % 185.59/185.90 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__mono,axiom, % 185.59/185.90 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__least,axiom, % 185.59/185.90 ! [V_B_2,V_C_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__absorb2,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__absorb1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_subset__Un__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__upper2,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__upper1,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__UNIV__right,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__UNIV__left,axiom, % 185.59/185.90 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__Un,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Int__crazy,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Int__distrib2,axiom, % 185.59/185.90 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__Un__distrib2,axiom, % 185.59/185.90 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Int__distrib,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Int__Un__distrib,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Diff,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Diff__cancel2,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Diff__cancel,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__Un,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_vimage__Un,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_fun__left__comm__idem__sup,axiom, % 185.59/185.90 ! [T_b] : % 185.59/185.90 ( class_Lattices_Osemilattice__sup(T_b) % 185.59/185.90 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__Un__eq,axiom, % 185.59/185.90 ! [V_x_2,V_S_2,V_R_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Collect__disj__eq,axiom, % 185.59/185.90 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__Un__distrib,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__Un,axiom, % 185.59/185.90 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_distrib__sup__le,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_distrib__inf__le,axiom, % 185.59/185.90 ! [V_z,V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Olattice(T_a) % 185.59/185.90 => 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)))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_compl__sup,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_compl__inf,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__compl__top,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_compl__sup__top,axiom, % 185.59/185.90 ! [V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => 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) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_insert__is__Un,axiom, % 185.59/185.90 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Int__assoc__eq,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__partition,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__subset__conv,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 185.59/185.90 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Int,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Diff__Un,axiom, % 185.59/185.90 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Diff__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_inj__on__Un__image__eq__iff,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) % 185.59/185.90 <=> V_A_2 = V_B_2 ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf__Int__eq2,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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)) % 185.59/185.90 <=> 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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__partition2,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__partition,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__Int,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__Un,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Compl__Diff__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__def,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__absorb,axiom, % 185.59/185.90 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_insert__def,axiom, % 185.59/185.90 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__extend__simps_I2_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.59/185.90 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 185.59/185.90 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__extend__simps_I3_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.59/185.90 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 185.59/185.90 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__simps_I2_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.59/185.90 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.90 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__simps_I3_J,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.59/185.90 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.90 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.90 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_UN__insert,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Collect__imp__eq,axiom, % 185.59/185.90 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_total__on__empty,axiom, % 185.59/185.90 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_vimage__insert,axiom, % 185.59/185.90 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_bij__betw__Disj__Un,axiom, % 185.59/185.90 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] : % 185.59/185.90 ( 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)) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 185.59/185.90 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 185.59/185.90 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) % 185.59/185.90 => c_Fun_Obij__betw(T_b,T_c,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_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_bij__betw__combine,axiom, % 185.59/185.90 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.90 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.90 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 185.59/185.90 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Id__on__empty,axiom, % 185.59/185.90 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Image__Id__on,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_if__image__distrib,axiom, % 185.59/185.90 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,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_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_compl__unique,axiom, % 185.59/185.90 ! [V_y,V_x,T_a] : % 185.59/185.90 ( class_Lattices_Oboolean__algebra(T_a) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 185.59/185.90 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 185.59/185.90 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Id__on__iff,axiom, % 185.59/185.90 ! [V_A_2,V_y_2,V_x_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) % 185.59/185.90 <=> ( V_x_2 = V_y_2 % 185.59/185.90 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Id__on__eqI,axiom, % 185.59/185.90 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 185.59/185.90 ( V_a_2 = V_ba_2 % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Field__insert,axiom, % 185.59/185.90 ! [V_r_2,V_ba_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_in__lex__prod,axiom, % 185.59/185.90 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) % 185.59/185.90 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) % 185.59/185.90 | ( V_a_2 = V_a_H_2 % 185.59/185.90 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Id__onE,axiom, % 185.59/185.90 ! [V_A_2,V_ca_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) % 185.59/185.90 => ~ ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_SUP2__E,axiom, % 185.59/185.90 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) % 185.59/185.90 => ~ ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_RangeI,axiom, % 185.59/185.90 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_DomainI,axiom, % 185.59/185.90 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__empty,axiom, % 185.59/185.90 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inf__binary,axiom, % 185.59/185.90 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.90 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.90 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_ba_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_congruentI,axiom, % 185.59/185.90 ! [T_c,V_f_2,V_r_2,T_b] : % 185.59/185.90 ( ! [B_y,B_z] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 185.59/185.90 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) ) % 185.59/185.90 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf2I,axiom, % 185.59/185.90 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf2E,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 185.59/185.90 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.59/185.90 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_InterE,axiom, % 185.59/185.90 ! [V_X_2,V_C_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_InterD,axiom, % 185.59/185.90 ! [V_X_2,V_C_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_PowI,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf2D1,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_inf2D2,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Field__def,axiom, % 185.59/185.90 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Cantors__paradox,axiom, % 185.59/185.90 ! [V_A_2,T_b] : % 185.59/185.90 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inter__UNIV,axiom, % 185.59/185.90 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inter__anti__mono,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inter__Un__distrib,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__insert,axiom, % 185.59/185.90 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Domain__Un__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),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(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__mono,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__UNIV,axiom, % 185.59/185.90 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__Pow__surj,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 185.59/185.90 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 185.59/185.90 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Un__Pow__subset,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__Int__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__top,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Range__Un__eq,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_le__Inf__iff,axiom, % 185.59/185.90 ! [V_A_2,V_ba_2,T_b] : % 185.59/185.90 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) % 185.59/185.90 <=> ! [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inf__less__iff,axiom, % 185.59/185.90 ! [V_a_2,V_S_2,T_b] : % 185.59/185.90 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.90 & class_Orderings_Olinorder(T_b) ) % 185.59/185.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 185.59/185.90 <=> ? [B_x] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.59/185.90 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Domain__Id__on,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__not__empty,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Range__Id__on,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__def,axiom, % 185.59/185.90 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Field__Un,axiom, % 185.59/185.90 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ). % 185.59/185.90 % 185.59/185.90 fof(fact_sup__Un__eq2,axiom, % 185.59/185.90 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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)) % 185.59/185.90 <=> 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inter__Un__subset,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Inter__lower,axiom, % 185.59/185.90 ! [V_A_2,V_B_2,T_b] : % 185.59/185.90 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Domain__Int__subset,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),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_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_Pow__bottom,axiom, % 185.59/185.90 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ). % 185.59/185.90 % 185.59/185.90 fof(fact_image__Pow__mono,axiom, % 185.59/185.90 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__Diff__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_PowD,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Pow__iff,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__empty,axiom, % 185.59/185.91 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__empty__iff,axiom, % 185.59/185.91 ! [V_r_2,T_c,T_b] : % 185.59/185.91 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__Int__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__mono,axiom, % 185.59/185.91 ! [V_s_2,V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__Diff__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inter__empty,axiom, % 185.59/185.91 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inter__insert,axiom, % 185.59/185.91 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__empty,axiom, % 185.59/185.91 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__empty__iff,axiom, % 185.59/185.91 ! [V_r_2,T_b,T_c] : % 185.59/185.91 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inf__lower,axiom, % 185.59/185.91 ! [V_A_2,V_x_2,T_b] : % 185.59/185.91 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inf__singleton,axiom, % 185.59/185.91 ! [V_a_2,T_b] : % 185.59/185.91 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.91 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inf__empty,axiom, % 185.59/185.91 ! [T_b] : % 185.59/185.91 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.91 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inf__UNIV,axiom, % 185.59/185.91 ! [T_b] : % 185.59/185.91 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.91 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inf__insert,axiom, % 185.59/185.91 ! [V_A_2,V_a_2,T_b] : % 185.59/185.91 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.91 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Field__empty,axiom, % 185.59/185.91 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mono__Field,axiom, % 185.59/185.91 ! [V_s_2,V_r_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__iff,axiom, % 185.59/185.91 ! [V_r_2,T_c,V_a_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 185.59/185.91 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__iff,axiom, % 185.59/185.91 ! [V_r_2,T_c,V_a_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 185.59/185.91 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__insert,axiom, % 185.59/185.91 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_UN__Pow__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__insert,axiom, % 185.59/185.91 ! [V_r_2,V_ba_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_ba_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Int__eq__Inter,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Powp__Pow__eq,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_RangeP__Range__eq,axiom, % 185.59/185.91 ! [V_x_2,V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,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_r_2)),V_x_2)) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_DomainP__Domain__eq,axiom, % 185.59/185.91 ! [V_x_2,V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,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_r_2)),V_x_2)) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_RangeE,axiom, % 185.59/185.91 ! [V_r_2,T_c,V_ba_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 185.59/185.91 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_DomainE,axiom, % 185.59/185.91 ! [V_r_2,T_c,V_a_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 185.59/185.91 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_in__measure,axiom, % 185.59/185.91 ! [V_f_2,V_y_2,V_x_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) % 185.59/185.91 <=> 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))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mlex__leq,axiom, % 185.59/185.91 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 185.59/185.91 ( 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))) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mlex__less,axiom, % 185.59/185.91 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 185.59/185.91 ( 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))) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_sup2CI,axiom, % 185.59/185.91 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 185.59/185.91 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 185.59/185.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_sup2E,axiom, % 185.59/185.91 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_RangeP_Ointros,axiom, % 185.59/185.91 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.59/185.91 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_ba_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_DomainP_Ointros,axiom, % 185.59/185.91 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.59/185.91 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_sup2I2,axiom, % 185.59/185.91 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_sup2I1,axiom, % 185.59/185.91 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_termination__basic__simps_I5_J,axiom, % 185.59/185.91 ! [V_y,V_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_RangeP_Oequations,axiom, % 185.59/185.91 ! [V_a2_2,V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 185.59/185.91 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Powp__mono,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__less__mono,axiom, % 185.59/185.91 ! [V_c,V_b,V_a] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 185.59/185.91 => 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))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__diff__iff,axiom, % 185.59/185.91 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.59/185.91 => ( 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))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__or__eq__imp__le,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 | V_m = V_n ) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__neq__implies__less,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => ( V_m != V_n % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__imp__le__nat,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__eq__less__or__eq,axiom, % 185.59/185.91 ! [V_n_2,V_m_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 | V_m_2 = V_n_2 ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__less__le,axiom, % 185.59/185.91 ! [V_n_2,V_m_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 & V_m_2 != V_n_2 ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_inj__on__Inter,axiom, % 185.59/185.91 ! [V_f_2,T_c,T_b,V_S_2] : % 185.59/185.91 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 185.59/185.91 => ( ! [B_A] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 185.59/185.91 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 185.59/185.91 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__commute,axiom, % 185.59/185.91 ! [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) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__mult__distrib2,axiom, % 185.59/185.91 ! [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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__mult__distrib,axiom, % 185.59/185.91 ! [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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__less__cases,axiom, % 185.59/185.91 ! [V_Pa_2,V_n_2,V_m_2] : % 185.59/185.91 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.59/185.91 => ( ( V_m_2 = V_n_2 % 185.59/185.91 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.59/185.91 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 185.59/185.91 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__not__refl3,axiom, % 185.59/185.91 ! [V_t,V_s] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 185.59/185.91 => V_s != V_t ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__not__refl2,axiom, % 185.59/185.91 ! [V_m,V_n] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 185.59/185.91 => V_m != V_n ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__irrefl__nat,axiom, % 185.59/185.91 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_linorder__neqE__nat,axiom, % 185.59/185.91 ! [V_y,V_x] : % 185.59/185.91 ( V_x != V_y % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__neq__iff,axiom, % 185.59/185.91 ! [V_n_2,V_m_2] : % 185.59/185.91 ( V_m_2 != V_n_2 % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__not__refl,axiom, % 185.59/185.91 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__less__mono2,axiom, % 185.59/185.91 ! [V_l,V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 185.59/185.91 => 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))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__imp__diff__less,axiom, % 185.59/185.91 ! [V_n,V_k,V_j] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 185.59/185.91 => 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)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__le__self,axiom, % 185.59/185.91 ! [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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__le__mono2,axiom, % 185.59/185.91 ! [V_l,V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => 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))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__le__mono,axiom, % 185.59/185.91 ! [V_l,V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => 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))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_diff__diff__cancel,axiom, % 185.59/185.91 ! [V_n,V_i] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 185.59/185.91 => 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 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_eq__diff__iff,axiom, % 185.59/185.91 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.59/185.91 => ( 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) % 185.59/185.91 <=> V_m_2 = V_n_2 ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Nat_Odiff__diff__eq,axiom, % 185.59/185.91 ! [V_n,V_m,V_k] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 185.59/185.91 => 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) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__diff__iff,axiom, % 185.59/185.91 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 185.59/185.91 => ( 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))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__antisym,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.59/185.91 => V_m = V_n ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__trans,axiom, % 185.59/185.91 ! [V_k,V_j,V_i] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_eq__imp__le,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( V_m = V_n % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__le__linear,axiom, % 185.59/185.91 ! [V_n,V_m] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.91 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__refl,axiom, % 185.59/185.91 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__square,axiom, % 185.59/185.91 ! [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))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_le__cube,axiom, % 185.59/185.91 ! [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)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mult__le__mono1,axiom, % 185.59/185.91 ! [V_k,V_j,V_i] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.91 => 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))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mult__le__mono2,axiom, % 185.59/185.91 ! [V_k,V_j,V_i] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.91 => 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))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mult__le__mono,axiom, % 185.59/185.91 ! [V_l,V_k,V_j,V_i] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 185.59/185.91 => 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))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Inter__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( ! [B_X] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__Un,axiom, % 185.59/185.91 ! [V_s_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ( c_Wellfounded_Owf(T_b,V_s_2) % 185.59/185.91 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_InterI,axiom, % 185.59/185.91 ! [V_A_2,V_C_2,T_b] : % 185.59/185.91 ( ! [B_X] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Pow__Compl,axiom, % 185.59/185.91 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_irrefl__diff__Id,axiom, % 185.59/185.91 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__lessI2,axiom, % 185.59/185.91 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 185.59/185.91 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_congruent2I_H,axiom, % 185.59/185.91 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] : % 185.59/185.91 ( ! [B_y1,B_z1] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2)) % 185.59/185.91 => ! [B_y2,B_z2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2)) % 185.59/185.91 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) ) % 185.59/185.91 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_UN__least,axiom, % 185.59/185.91 ! [V_C_2,V_B_2,T_c,V_A_2,T_b] : % 185.59/185.91 ( ! [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__empty,axiom, % 185.59/185.91 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__lex__prod,axiom, % 185.59/185.91 ! [V_rb_2,T_c,V_ra_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_ra_2) % 185.59/185.91 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 185.59/185.91 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__measure,axiom, % 185.59/185.91 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_IdI,axiom, % 185.59/185.91 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__mult__commute,axiom, % 185.59/185.91 ! [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) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__mult__assoc,axiom, % 185.59/185.91 ! [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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__pair__less,axiom, % 185.59/185.91 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Id__def,axiom, % 185.59/185.91 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__subset,axiom, % 185.59/185.91 ! [V_p_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2)) % 185.59/185.91 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__Int1,axiom, % 185.59/185.91 ! [V_r_H_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__Int2,axiom, % 185.59/185.91 ! [V_r_H_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Image__Id,axiom, % 185.59/185.91 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 185.59/185.91 % 185.59/185.91 fof(fact_DomainP_Oequations,axiom, % 185.59/185.91 ! [V_a1_2,V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 185.59/185.91 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__mlex,axiom, % 185.59/185.91 ! [V_f_2,V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.91 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__not__refl,axiom, % 185.59/185.91 ! [V_a_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__not__sym,axiom, % 185.59/185.91 ! [V_x_2,V_a_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 185.59/185.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__asym,axiom, % 185.59/185.91 ! [V_x_2,V_a_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) % 185.59/185.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__irrefl,axiom, % 185.59/185.91 ! [V_a_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__lessI1,axiom, % 185.59/185.91 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.59/185.91 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__in__Id__conv,axiom, % 185.59/185.91 ! [V_ba_2,V_a_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Relation_OId(T_b))) % 185.59/185.91 <=> V_a_2 = V_ba_2 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Domain__Id,axiom, % 185.59/185.91 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Range__Id,axiom, % 185.59/185.91 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfE__pf,axiom, % 185.59/185.91 ! [V_A_2,V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2))) % 185.59/185.91 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_total__on__diff__Id,axiom, % 185.59/185.91 ! [V_r_2,V_A_2,T_b] : % 185.59/185.91 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) % 185.59/185.91 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_reflcl__set__eq,axiom, % 185.59/185.91 ! [V_y_2,V_x_2,V_r_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__leqI2,axiom, % 185.59/185.91 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 185.59/185.91 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_smin__insertI,axiom, % 185.59/185.91 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_smax__insertI,axiom, % 185.59/185.91 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__leqI1,axiom, % 185.59/185.91 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.59/185.91 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfI__pf,axiom, % 185.59/185.91 ! [V_R_2,T_b] : % 185.59/185.91 ( ! [B_A] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) % 185.59/185.91 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 185.59/185.91 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfP__wf__eq,axiom, % 185.59/185.91 ! [V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) % 185.59/185.91 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_IdE,axiom, % 185.59/185.91 ! [V_p_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 185.59/185.91 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfP__empty,axiom, % 185.59/185.91 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_smin__emptyI,axiom, % 185.59/185.91 ! [V_X_2] : % 185.59/185.91 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 185.59/185.91 => 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)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfP__subset,axiom, % 185.59/185.91 ! [V_p_2,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2)) % 185.59/185.91 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__leq__def,axiom, % 185.59/185.91 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))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__in__rel,axiom, % 185.59/185.91 ! [V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.91 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wmax__insertI,axiom, % 185.59/185.91 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wmin__insertI,axiom, % 185.59/185.91 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wmin__emptyI,axiom, % 185.59/185.91 ! [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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_min__strict__def,axiom, % 185.59/185.91 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.59/185.91 % 185.59/185.91 fof(fact_less__than__iff,axiom, % 185.59/185.91 ! [V_y_2,V_x_2] : % 185.59/185.91 ( 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)) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__same__fst,axiom, % 185.59/185.91 ! [T_b,V_R_2,T_c,V_Pa_2] : % 185.59/185.91 ( ! [B_x] : % 185.59/185.91 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.59/185.91 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 185.59/185.91 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__ext__additive,axiom, % 185.59/185.91 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wfP__SUP,axiom, % 185.59/185.91 ! [T_b,V_r_2,T_c] : % 185.59/185.91 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 185.59/185.91 => ( ! [B_i,B_j] : % 185.59/185.91 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 185.59/185.91 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.59/185.91 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__less__than,axiom, % 185.59/185.91 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__ext__wf,axiom, % 185.59/185.91 ! [V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__weak__def,axiom, % 185.59/185.91 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)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_pair__less__def,axiom, % 185.59/185.91 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 185.59/185.91 % 185.59/185.91 fof(fact_min__weak__def,axiom, % 185.59/185.91 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)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_min__ext__wf,axiom, % 185.59/185.91 ! [V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__strict__def,axiom, % 185.59/185.91 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__extp__max__ext__eq,axiom, % 185.59/185.91 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_mlex__prod__def,axiom, % 185.59/185.91 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_max__rpair__set,axiom, % 185.59/185.91 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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_min__rpair__set,axiom, % 185.59/185.91 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)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wmax__emptyI,axiom, % 185.59/185.91 ! [V_X_2] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 185.59/185.91 => 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)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_smax__emptyI,axiom, % 185.59/185.91 ! [V_Y_2] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 185.59/185.91 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 185.59/185.91 => 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)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_measure__def,axiom, % 185.59/185.91 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__eq__minimal,axiom, % 185.59/185.91 ! [V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 <=> ! [B_Q] : % 185.59/185.91 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 185.59/185.91 => ? [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 185.59/185.91 & ! [B_y] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) % 185.59/185.91 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite_OemptyI,axiom, % 185.59/185.91 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite_OinsertI,axiom, % 185.59/185.91 ! [V_a_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__imageI,axiom, % 185.59/185.91 ! [V_h_2,T_c,V_F_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Int,axiom, % 185.59/185.91 ! [V_Ga_2,V_F_2,T_b] : % 185.59/185.91 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Diff,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Inter,axiom, % 185.59/185.91 ! [V_M_2,T_b] : % 185.59/185.91 ( ? [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 185.59/185.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__conjI,axiom, % 185.59/185.91 ! [V_Q_2,V_Pa_2,T_b] : % 185.59/185.91 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.91 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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),V_Pa_2)),V_Q_2)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__inv__image,axiom, % 185.59/185.91 ! [V_f_2,T_c,V_r_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.59/185.91 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__subsets,axiom, % 185.59/185.91 ! [V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Plus__UNIV__iff,axiom, % 185.59/185.91 ! [T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) % 185.59/185.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__option__UNIV,axiom, % 185.59/185.91 ! [T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Prod__UNIV,axiom, % 185.59/185.91 ! [T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Field,axiom, % 185.59/185.91 ! [V_r_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite,axiom, % 185.59/185.91 ! [V_A_2,T_b] : % 185.59/185.91 ( class_Finite__Set_Ofinite(T_b) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__code,axiom, % 185.59/185.91 ! [V_A_2,T_b] : % 185.59/185.91 ( class_Finite__Set_Ofinite(T_b) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Pow__iff,axiom, % 185.59/185.91 ! [V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Domain,axiom, % 185.59/185.91 ! [V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Range,axiom, % 185.59/185.91 ! [V_r_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite_Oequations_I1_J,axiom, % 185.59/185.91 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__insert,axiom, % 185.59/185.91 ! [V_A_2,V_a_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__fun__UNIVD2,axiom, % 185.59/185.91 ! [T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__subset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rev__finite__subset,axiom, % 185.59/185.91 ! [V_A_2,V_B_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__UNIV,axiom, % 185.59/185.91 ! [T_b] : % 185.59/185.91 ( class_Finite__Set_Ofinite(T_b) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Un,axiom, % 185.59/185.91 ! [V_Ga_2,V_F_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) % 185.59/185.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__UnI,axiom, % 185.59/185.91 ! [V_Ga_2,V_F_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Diff2,axiom, % 185.59/185.91 ! [V_A_2,V_B_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__UN,axiom, % 185.59/185.91 ! [V_B_2,T_c,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.91 <=> ! [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_bij__betw__finite,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_fold__graph__imp__finite,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_nat__seg__image__imp__finite,axiom, % 185.59/185.91 ! [V_n_2,V_f_2,T_b,V_A_2] : % 185.59/185.91 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__disjI,axiom, % 185.59/185.91 ! [V_Q_2,V_Pa_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_Pa_2)),V_Q_2)))) % 185.59/185.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__surj,axiom, % 185.59/185.91 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Diff__insert,axiom, % 185.59/185.91 ! [V_B_2,V_a_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_a_2),V_B_2)))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__imageD,axiom, % 185.59/185.91 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 185.59/185.91 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__compl,axiom, % 185.59/185.91 ! [V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__image__set,axiom, % 185.59/185.91 ! [V_f_2,T_c,V_Pa_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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)),V_f_2)))),V_Pa_2))))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__bounded__ex,axiom, % 185.59/185.91 ! [V_Q_2,T_c,V_Pa_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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),V_Pa_2))),V_Q_2))))) % 185.59/185.91 <=> ! [B_y] : % 185.59/185.91 ( hBOOL(hAPP(V_Pa_2,B_y)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__not,axiom, % 185.59/185.91 ! [V_Pa_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__range__imageI,axiom, % 185.59/185.91 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__surj__inj,axiom, % 185.59/185.91 ! [V_f_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2))) % 185.59/185.91 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_endo__inj__surj,axiom, % 185.59/185.91 ! [V_f_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2)) % 185.59/185.91 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 185.59/185.91 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__UNIV__inj__surj,axiom, % 185.59/185.91 ! [V_f_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.91 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.91 => hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__UNIV__surj__inj,axiom, % 185.59/185.91 ! [V_f_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.91 => ( hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool)) % 185.59/185.91 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__vimageD,axiom, % 185.59/185.91 ! [V_F_2,V_h_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 185.59/185.91 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_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)) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__vimageI,axiom, % 185.59/185.91 ! [V_h_2,T_c,V_F_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 185.59/185.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__vimage__iff,axiom, % 185.59/185.91 ! [V_F_2,V_h_2,T_c,T_b] : % 185.59/185.91 ( c_Fun_Obij__betw(T_b,T_c,V_h_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))) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 185.59/185.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_in__inv__image,axiom, % 185.59/185.91 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_in__finite__psubset,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Oremove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Oremove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 185.59/185.91 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => 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_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)))))) ) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Oremove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.59/185.91 => 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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image_Oreindex,axiom, % 185.59/185.91 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 185.59/185.91 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ounion,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Oinsert__remove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Ounion__inter,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__less__nat,axiom, % 185.59/185.91 ! [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)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__Collect__le__nat,axiom, % 185.59/185.91 ! [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)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 185.59/185.91 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__comp,axiom, % 185.59/185.91 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__left__comp,axiom, % 185.59/185.91 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Oempty,axiom, % 185.59/185.91 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image_Odistrib,axiom, % 185.59/185.91 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),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)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 185.59/185.91 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__comp_H_H,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__left__comp_H,axiom, % 185.59/185.91 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ocommute__comp_H,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Oempty,axiom, % 185.59/185.91 ! [V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Osingleton,axiom, % 185.59/185.91 ! [V_x_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Oinsert,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Ounion__inter,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.91 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__finite__psubset,axiom, % 185.59/185.91 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Oinsert,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding_Ounion__inter,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Oinsert,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Oinsert__remove,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.59/185.91 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_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)))))) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.91 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Ounion__disjoint,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => ( 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)) % 185.59/185.91 => 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)) ) ) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__M__bounded__by__nat,axiom, % 185.59/185.91 ! [V_i_2,V_Pa_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_Pa_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))))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Ounion__idem,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => 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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Oinsert__idem,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one_Oclosed,axiom, % 185.59/185.91 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Oin__comp__idem,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rp__inv__image__rp,axiom, % 185.59/185.91 ! [V_f_2,T_c,V_Pa_2,T_b] : % 185.59/185.91 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.59/185.91 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_infinite__UNIV__nat,axiom, % 185.59/185.91 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Oidem__left__comp,axiom, % 185.59/185.91 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__idem_Oidem__comp,axiom, % 185.59/185.91 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 185.59/185.91 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__nat__set__iff__bounded,axiom, % 185.59/185.91 ! [V_N_2] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 185.59/185.91 <=> ? [B_m] : % 185.59/185.91 ! [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 185.59/185.91 ! [V_N_2] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 185.59/185.91 <=> ? [B_m] : % 185.59/185.91 ! [B_x] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 185.59/185.91 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 185.59/185.91 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OatLeastLessThan__iff,axiom, % 185.59/185.91 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 185.59/185.91 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 185.59/185.91 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 185.59/185.91 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OatLeastAtMost__iff,axiom, % 185.59/185.91 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) % 185.59/185.91 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 185.59/185.91 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OgreaterThan__iff,axiom, % 185.59/185.91 ! [V_k_2,V_less_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OlessThan__iff,axiom, % 185.59/185.91 ! [V_k_2,V_less_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OatLeast__iff,axiom, % 185.59/185.91 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_ord_OatMost__iff,axiom, % 185.59/185.91 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 185.59/185.91 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__empty__induct,axiom, % 185.59/185.91 ! [V_Pa_2,V_A_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 185.59/185.91 => ( ! [B_a,B_A] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 185.59/185.91 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 185.59/185.91 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) % 185.59/185.91 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one__idem_Ounion__idem,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.91 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => 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)) ) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_finite__subset__induct,axiom, % 185.59/185.91 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 185.59/185.91 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.91 => ( ! [B_a,B_F] : % 185.59/185.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.59/185.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 185.59/185.91 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 185.59/185.91 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 185.59/185.91 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one__idem_Osubset__idem,axiom, % 185.59/185.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.91 => 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) ) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_reduction__pairI,axiom, % 185.59/185.91 ! [V_S_2,V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 185.59/185.91 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(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)),V_R_2),V_S_2)) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 185.59/185.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.59/185.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__compI,axiom, % 185.59/185.91 ! [V_s_2,V_ca_2,T_d,V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ba_2),V_ca_2)),V_s_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_O__assoc,axiom, % 185.59/185.91 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_folding__one__idem_Oidem,axiom, % 185.59/185.91 ! [V_x_2,V_F_2,V_f_2,T_b] : % 185.59/185.91 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.59/185.91 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__comp__self,axiom, % 185.59/185.91 ! [V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.91 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__mono,axiom, % 185.59/185.91 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 185.59/185.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 185.59/185.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 185.59/185.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__empty1,axiom, % 185.59/185.91 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__empty2,axiom, % 185.59/185.91 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__distrib2,axiom, % 185.59/185.91 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__distrib,axiom, % 185.59/185.91 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_Id__O__R,axiom, % 185.59/185.91 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ). % 185.59/185.91 % 185.59/185.91 fof(fact_R__O__Id,axiom, % 185.59/185.91 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__UNION__distrib,axiom, % 185.59/185.91 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_rel__comp__UNION__distrib2,axiom, % 185.59/185.91 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__no__loop,axiom, % 185.59/185.91 ! [V_R_2,T_b] : % 185.59/185.91 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.91 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_wf__union__merge,axiom, % 185.59/185.91 ! [V_S_2,V_R_2,T_b] : % 185.59/185.91 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 185.59/185.91 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ). % 185.59/185.91 % 185.59/185.91 fof(fact_union__comp__emptyL,axiom, % 185.59/185.91 ! [V_B_2,V_C_2,V_A_2,T_b] : % 185.59/185.91 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.91 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_union__comp__emptyR,axiom, % 185.59/185.92 ! [V_C_2,V_B_2,V_A_2,T_b] : % 185.59/185.92 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.92 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_wf__union__compatible,axiom, % 185.59/185.92 ! [V_S_2,V_R_2,T_b] : % 185.59/185.92 ( c_Wellfounded_Owf(T_b,V_R_2) % 185.59/185.92 => ( c_Wellfounded_Owf(T_b,V_S_2) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 185.59/185.92 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_folding__one__idem_Oin__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.92 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_max__ext__compat,axiom, % 185.59/185.92 ! [V_S_2,V_R_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_min__ext__compat,axiom, % 185.59/185.92 ! [V_S_2,V_R_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_pred__comp__rel__comp__eq,axiom, % 185.59/185.92 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,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_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2)) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_finite__conv__nat__seg__image,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_rp__inv__image__def,axiom, % 185.59/185.92 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(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(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(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_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_max__extp_Oequations,axiom, % 185.59/185.92 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 185.59/185.92 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 185.59/185.92 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 185.59/185.92 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 185.59/185.92 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 & ! [B_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 185.59/185.92 => ? [B_xa] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 185.59/185.92 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_max__ext_Ointros,axiom, % 185.59/185.92 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 185.59/185.92 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( ! [B_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 185.59/185.92 => ? [B_xa] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 185.59/185.92 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__Un,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Groups_Oab__semigroup__mult(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff1__less,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_pred__comp_Ointros,axiom, % 185.59/185.92 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_ba_2,V_a_2,V_r_2] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(V_s_2,V_ba_2),V_ca_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_pred__comp_Oequations,axiom, % 185.59/185.92 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 185.59/185.92 <=> ? [B_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 185.59/185.92 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_bij__betw__same__card,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.59/185.92 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.59/185.92 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__image,axiom, % 185.59/185.92 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_BIJ,axiom, % 185.59/185.92 ! [V_B_2,T_c,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.92 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) % 185.59/185.92 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__singleton__def,axiom, % 185.59/185.92 ! [V_a_2,V_f_2,T_b,V_g_2] : % 185.59/185.92 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 185.59/185.92 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__singleton,axiom, % 185.59/185.92 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2 ). % 185.59/185.92 % 185.59/185.92 fof(fact_folding__one_Oeq__fold,axiom, % 185.59/185.92 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.92 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__insert__le,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__seteq,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 185.59/185.92 => V_A_2 = V_B_2 ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__mono,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__image__le,axiom, % 185.59/185.92 ! [V_f_2,T_c,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_eq__card__imp__inj__on,axiom, % 185.59/185.92 ! [V_f_2,T_c,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) % 185.59/185.92 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inj__on__iff__eq__card,axiom, % 185.59/185.92 ! [V_f_2,T_c,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.92 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_pigeonhole,axiom, % 185.59/185.92 ! [V_A_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) % 185.59/185.92 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__quotient__disjoint,axiom, % 185.59/185.92 ! [V_r_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_psubset__card__mono,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__def,axiom, % 185.59/185.92 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__bij__eq,axiom, % 185.59/185.92 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 185.59/185.92 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff__subset,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff__subset__Int,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_diff__card__le__card__Diff,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => 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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__psubset,axiom, % 185.59/185.92 ! [V_A_2,V_B_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__insert__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__Un2,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff1__le,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__inj__on__le,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inj__on__iff__card__le,axiom, % 185.59/185.92 ! [V_B_2,T_c,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.59/185.92 => ( ? [B_f] : % 185.59/185.92 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 185.59/185.92 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) ) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__insert,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Groups_Oab__semigroup__mult(T_b) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff2__less,axiom, % 185.59/185.92 ! [V_y_2,V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_pair__imageI,axiom, % 185.59/185.92 ! [V_f_2,T_d,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_ba_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_below__fold1__iff,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Osemilattice__inf(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) % 185.59/185.92 <=> ! [B_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__belowI,axiom, % 185.59/185.92 ! [V_a_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Osemilattice__inf(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__eta,axiom, % 185.59/185.92 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold1__in,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Groups_Oab__semigroup__mult(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff__singleton__if,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 185.59/185.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff__singleton,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_splitI,axiom, % 185.59/185.92 ! [T_c,T_b,V_ba_2,V_a_2,V_f_2] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_prod__caseI,axiom, % 185.59/185.92 ! [T_c,T_b,V_ba_2,V_a_2,V_f1_2] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_ba_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_mem__splitI,axiom, % 185.59/185.92 ! [T_d,T_c,V_ba_2,V_a_2,V_ca_2,V_z_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_ba_2))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_splitD,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) % 185.59/185.92 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_splitD_H,axiom, % 185.59/185.92 ! [V_ca_2,V_ba_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_ca_2)) % 185.59/185.92 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_ba_2),V_ca_2)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__UNIV__unit,axiom, % 185.59/185.92 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) ). % 185.59/185.92 % 185.59/185.92 fof(fact_one__reorient,axiom, % 185.59/185.92 ! [V_x_2,T_b] : % 185.59/185.92 ( class_Groups_Oone(T_b) % 185.59/185.92 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 185.59/185.92 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__paired__The,axiom, % 185.59/185.92 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_The__split__eq,axiom, % 185.59/185.92 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__Pair,axiom, % 185.59/185.92 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_swap__inj__on,axiom, % 185.59/185.92 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,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_A_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_mult__1__left,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Groups_Omonoid__mult(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_mult__1,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_mult__1__right,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Groups_Omonoid__mult(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_mult_Ocomm__neutral,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__mult__eq__1__iff,axiom, % 185.59/185.92 ! [V_n_2,V_m_2] : % 185.59/185.92 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.59/185.92 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.59/185.92 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__mult__1__right,axiom, % 185.59/185.92 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__1__eq__mult__iff,axiom, % 185.59/185.92 ! [V_n_2,V_m_2] : % 185.59/185.92 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 185.59/185.92 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.59/185.92 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__mult__1,axiom, % 185.59/185.92 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 185.59/185.92 % 185.59/185.92 fof(fact_Id__on__def_H,axiom, % 185.59/185.92 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),c_fequal))),V_A_2)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_less__1__mult,axiom, % 185.59/185.92 ! [V_n,V_m,T_a] : % 185.59/185.92 ( class_Rings_Olinordered__semidom(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 185.59/185.92 => 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))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_square__eq__1__iff,axiom, % 185.59/185.92 ! [V_x_2,T_b] : % 185.59/185.92 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.59/185.92 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 185.59/185.92 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 185.59/185.92 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_wf__less,axiom, % 185.59/185.92 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)))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inj__graph,axiom, % 185.59/185.92 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Pair__inject,axiom, % 185.59/185.92 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 185.59/185.92 ( 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) % 185.59/185.92 => ~ ( V_a = V_a_H % 185.59/185.92 => V_b != V_b_H ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Pair__eq,axiom, % 185.59/185.92 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 185.59/185.92 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) % 185.59/185.92 <=> ( V_a_2 = V_a_H_2 % 185.59/185.92 & V_ba_2 = V_b_H_2 ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__paired__All,axiom, % 185.59/185.92 ! [T_c,T_b,V_Pa_2] : % 185.59/185.92 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.59/185.92 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oidem,axiom, % 185.59/185.92 ! [V_x,T_a] : % 185.59/185.92 ( class_Lattices_Olattice(T_a) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oidem,axiom, % 185.59/185.92 ! [V_x,T_a] : % 185.59/185.92 ( class_Lattices_Olattice(T_a) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_wf,axiom, % 185.59/185.92 ! [T_b] : % 185.59/185.92 ( class_Orderings_Owellorder(T_b) % 185.59/185.92 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__weak__cong,axiom, % 185.59/185.92 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 185.59/185.92 ( V_p_2 = V_q_2 % 185.59/185.92 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_wfP__def,axiom, % 185.59/185.92 ! [V_r_2,T_b] : % 185.59/185.92 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.59/185.92 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_finite__psubset__def,axiom, % 185.59/185.92 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Domain__Collect__split,axiom, % 185.59/185.92 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Range__Collect__split,axiom, % 185.59/185.92 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inv__image__def,axiom, % 185.59/185.92 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__twice,axiom, % 185.59/185.92 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_rel__comp__def,axiom, % 185.59/185.92 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,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_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card__Diff__insert,axiom, % 185.59/185.92 ! [V_B_2,V_a_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_prod_Osimps_I2_J,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_split__conv,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_f_2,V_a_2),V_ba_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Nitpick_Oprod__def,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_semilattice__big_OF__eq,axiom, % 185.59/185.92 ! [V_A_2,V_F_2,V_f_2,T_b] : % 185.59/185.92 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 185.59/185.92 ! [V_x,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__ring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_prod_Orecs,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inf__Sup2__distrib,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Odistrib__lattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inf__Sup1__distrib,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Odistrib__lattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_sup__Inf2__distrib,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Odistrib__lattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__le__Sup,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Osingleton,axiom, % 185.59/185.92 ! [V_x_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Osingleton,axiom, % 185.59/185.92 ! [V_x_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 185.59/185.92 ! [V_ry,V_rx,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 185.59/185.92 ! [V_ry,V_rx,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 185.59/185.92 ! [V_rx,V_ly,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 185.59/185.92 ! [V_rx,V_ly,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 185.59/185.92 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 185.59/185.92 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 185.59/185.92 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oin__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_sup__Inf__absorb,axiom, % 185.59/185.92 ! [V_a_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oin__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inf__Sup__absorb,axiom, % 185.59/185.92 ! [V_a_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin__Inf,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_OF__eq,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_OF__eq,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oinsert__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oinsert__idem,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Osubset__idem,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Osubset__idem,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Ounion__idem,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Ounion__idem,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oinsert,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oinsert,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oinsert__remove,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.59/185.92 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oinsert__remove,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.59/185.92 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Ounion__inter,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,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__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Ounion__inter,axiom, % 185.59/185.92 ! [V_B_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 185.59/185.92 ! [V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oremove,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 185.59/185.92 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oremove,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 185.59/185.92 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_sup__Inf1__distrib,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Odistrib__lattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Oclosed,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Oclosed,axiom, % 185.59/185.92 ! [V_A_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_card_Oremove,axiom, % 185.59/185.92 ! [V_x_2,V_A_2,T_b] : % 185.59/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.59/185.92 => hAPP(c_Finite__Set_Ocard(T_b),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_b),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)))))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_fold__Un__disjoint,axiom, % 185.59/185.92 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.59/185.92 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.59/185.92 => ( 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)) % 185.59/185.92 => hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Inf__fin_Ohom__commute,axiom, % 185.59/185.92 ! [V_N_2,V_h_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.59/185.92 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_Sup__fin_Ohom__commute,axiom, % 185.59/185.92 ! [V_N_2,V_h_2,T_b] : % 185.59/185.92 ( class_Lattices_Olattice(T_b) % 185.59/185.92 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.59/185.92 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_hom__fold1__commute,axiom, % 185.59/185.92 ! [V_N_2,V_h_2,T_b] : % 185.59/185.92 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.59/185.92 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.59/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.59/185.92 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.59/185.92 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 185.59/185.92 ! [V_c,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 185.59/185.92 ! [V_d,V_c,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 185.59/185.92 ! [V_d,V_c,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 185.59/185.92 ! [V_d,V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_inj__on__add__nat,axiom, % 185.59/185.92 ! [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) ). % 185.59/185.92 % 185.59/185.92 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oab__semigroup__add(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__left__cancel,axiom, % 185.59/185.92 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.92 ( class_Groups_Ocancel__semigroup__add(T_b) % 185.59/185.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2) % 185.59/185.92 <=> V_ba_2 = V_ca_2 ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__right__cancel,axiom, % 185.59/185.92 ! [V_ca_2,V_a_2,V_ba_2,T_b] : % 185.59/185.92 ( class_Groups_Ocancel__semigroup__add(T_b) % 185.59/185.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2) % 185.59/185.92 <=> V_ba_2 = V_ca_2 ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__left__imp__eq,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 185.59/185.92 => ( 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) % 185.59/185.92 => V_b = V_c ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__imp__eq,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 185.59/185.92 => ( 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) % 185.59/185.92 => V_b = V_c ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__right__imp__eq,axiom, % 185.59/185.92 ! [V_c,V_a,V_b,T_a] : % 185.59/185.92 ( class_Groups_Ocancel__semigroup__add(T_a) % 185.59/185.92 => ( 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) % 185.59/185.92 => V_b = V_c ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__commute,axiom, % 185.59/185.92 ! [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) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__left__commute,axiom, % 185.59/185.92 ! [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)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__assoc,axiom, % 185.59/185.92 ! [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)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__left__cancel,axiom, % 185.59/185.92 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.92 ( 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) % 185.59/185.92 <=> V_m_2 = V_n_2 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__right__cancel,axiom, % 185.59/185.92 ! [V_n_2,V_k_2,V_m_2] : % 185.59/185.92 ( 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) % 185.59/185.92 <=> V_m_2 = V_n_2 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__imp__le__left,axiom, % 185.59/185.92 ! [V_b,V_a,V_c,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.59/185.92 => ( 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))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__imp__le__right,axiom, % 185.59/185.92 ! [V_b,V_c,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.59/185.92 => ( 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))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__mono,axiom, % 185.59/185.92 ! [V_d,V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.59/185.92 => 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))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__left__mono,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__right__mono,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__cancel__left,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__cancel__right,axiom, % 185.59/185.92 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__imp__less__left,axiom, % 185.59/185.92 ! [V_b,V_a,V_c,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.59/185.92 => ( 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))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__imp__less__right,axiom, % 185.59/185.92 ! [V_b,V_c,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.59/185.92 => ( 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))) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__strict__mono,axiom, % 185.59/185.92 ! [V_d,V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.59/185.92 => 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))) ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__strict__left__mono,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__strict__right__mono,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__cancel__left,axiom, % 185.59/185.92 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__cancel__right,axiom, % 185.59/185.92 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.59/185.92 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_combine__common__factor,axiom, % 185.59/185.92 ! [V_c,V_b,V_e,V_a,T_a] : % 185.59/185.92 ( class_Rings_Osemiring(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__class_Odistrib,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_crossproduct__eq,axiom, % 185.59/185.92 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 185.59/185.92 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.59/185.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) % 185.59/185.92 <=> ( V_w_2 = V_x_2 % 185.59/185.92 | V_y_2 = V_z_2 ) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 185.59/185.92 ! [V_b,V_m,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 185.59/185.92 ! [V_c,V_b,V_a,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_crossproduct__noteq,axiom, % 185.59/185.92 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.59/185.92 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.59/185.92 => ( ( V_a_2 != V_ba_2 % 185.59/185.92 & V_ca_2 != V_d_2 ) % 185.59/185.92 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 185.59/185.92 ! [V_z,V_y,V_x,T_a] : % 185.59/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__diff__cancel,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ogroup__add(T_a) % 185.59/185.92 => 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 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_diff__add__cancel,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ogroup__add(T_a) % 185.59/185.92 => 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 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_minus__add__cancel,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ogroup__add(T_a) % 185.59/185.92 => 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 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__minus__cancel,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ogroup__add(T_a) % 185.59/185.92 => 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 ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_minus__add,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Ogroup__add(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_minus__add__distrib,axiom, % 185.59/185.92 ! [V_b,V_a,T_a] : % 185.59/185.92 ( class_Groups_Oab__group__add(T_a) % 185.59/185.92 => 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)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_not__add__less1,axiom, % 185.59/185.92 ! [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)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_not__add__less2,axiom, % 185.59/185.92 ! [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)) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__left__cancel__less,axiom, % 185.59/185.92 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.92 ( 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))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_trans__less__add1,axiom, % 185.59/185.92 ! [V_m,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_trans__less__add2,axiom, % 185.59/185.92 ! [V_m,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__mono1,axiom, % 185.59/185.92 ! [V_k,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__less__mono,axiom, % 185.59/185.92 ! [V_l,V_k,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_less__add__eq__less,axiom, % 185.59/185.92 ! [V_n,V_m,V_l,V_k] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 185.59/185.92 => ( 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) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__lessD1,axiom, % 185.59/185.92 ! [V_k,V_j,V_i] : % 185.59/185.92 ( 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)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_termination__basic__simps_I1_J,axiom, % 185.59/185.92 ! [V_z,V_y,V_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_termination__basic__simps_I2_J,axiom, % 185.59/185.92 ! [V_y,V_z,V_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_le__add2,axiom, % 185.59/185.92 ! [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))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_le__add1,axiom, % 185.59/185.92 ! [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))) ). % 185.59/185.92 % 185.59/185.92 fof(fact_le__iff__add,axiom, % 185.59/185.92 ! [V_n_2,V_m_2] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.59/185.92 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_nat__add__left__cancel__le,axiom, % 185.59/185.92 ! [V_n_2,V_m_2,V_k_2] : % 185.59/185.92 ( 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))) % 185.59/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_trans__le__add1,axiom, % 185.59/185.92 ! [V_m,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_trans__le__add2,axiom, % 185.59/185.92 ! [V_m,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__mono1,axiom, % 185.59/185.92 ! [V_k,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => 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))) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__le__mono,axiom, % 185.59/185.92 ! [V_l,V_k,V_j,V_i] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.59/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 185.59/185.92 => 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))) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__leD2,axiom, % 185.59/185.92 ! [V_n,V_k,V_m] : % 185.59/185.92 ( 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)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__leD1,axiom, % 185.59/185.92 ! [V_n,V_k,V_m] : % 185.59/185.92 ( 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)) % 185.59/185.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_add__leE,axiom, % 185.59/185.92 ! [V_n,V_k,V_m] : % 185.59/185.92 ( 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)) % 185.59/185.92 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.59/185.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 185.59/185.92 % 185.59/185.92 fof(fact_termination__basic__simps_I3_J,axiom, % 185.59/185.92 ! [V_z,V_y,V_x] : % 185.59/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 185.87/185.92 => 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))) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_termination__basic__simps_I4_J,axiom, % 185.87/185.92 ! [V_y,V_z,V_x] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 185.87/185.92 => 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))) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__cancel2,axiom, % 185.87/185.92 ! [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) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__cancel,axiom, % 185.87/185.92 ! [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) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__diff__left,axiom, % 185.87/185.92 ! [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)) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__add__inverse,axiom, % 185.87/185.92 ! [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 ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__add__inverse2,axiom, % 185.87/185.92 ! [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 ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__mult__distrib,axiom, % 185.87/185.92 ! [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)) ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__mult__distrib2,axiom, % 185.87/185.92 ! [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)) ). % 185.87/185.92 % 185.87/185.92 fof(fact_fold__image__empty,axiom, % 185.87/185.92 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__less__le__mono,axiom, % 185.87/185.92 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.87/185.92 => 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))) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__le__less__mono,axiom, % 185.87/185.92 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.92 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.87/185.92 => 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))) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_less__add__one,axiom, % 185.87/185.92 ! [V_a,T_a] : % 185.87/185.92 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.92 => 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)))) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_eq__add__iff2,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oring(T_b) % 185.87/185.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2) % 185.87/185.92 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_eq__add__iff1,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oring(T_b) % 185.87/185.92 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2) % 185.87/185.92 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 185.87/185.92 ! [V_m,V_a,T_a] : % 185.87/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 185.87/185.92 ! [V_a,V_m,T_a] : % 185.87/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 185.87/185.92 ! [V_m,T_a] : % 185.87/185.92 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__minus__eq__add,axiom, % 185.87/185.92 ! [V_b,V_a,T_a] : % 185.87/185.92 ( class_Groups_Ogroup__add(T_a) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_ab__diff__minus,axiom, % 185.87/185.92 ! [V_b,V_a,T_a] : % 185.87/185.92 ( class_Groups_Oab__group__add(T_a) % 185.87/185.92 => 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)) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__def,axiom, % 185.87/185.92 ! [V_b,V_a,T_a] : % 185.87/185.92 ( class_Groups_Ogroup__add(T_a) % 185.87/185.92 => 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)) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 185.87/185.92 ! [V_y,V_x,T_a] : % 185.87/185.92 ( class_Rings_Ocomm__ring__1(T_a) % 185.87/185.92 => 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)) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_less__diff__conv,axiom, % 185.87/185.92 ! [V_k_2,V_j_2,V_i_2] : % 185.87/185.92 ( 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))) % 185.87/185.92 <=> 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)) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__diff__inverse,axiom, % 185.87/185.92 ! [V_n,V_m] : % 185.87/185.92 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.92 => 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 ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__add__assoc2,axiom, % 185.87/185.92 ! [V_i,V_j,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__diff__assoc2,axiom, % 185.87/185.92 ! [V_i,V_j,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__add__assoc,axiom, % 185.87/185.92 ! [V_i,V_j,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.92 => 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)) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__imp__diff__is__add,axiom, % 185.87/185.92 ! [V_k_2,V_j_2,V_i_2] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.87/185.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 185.87/185.92 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__add__diff__inverse2,axiom, % 185.87/185.92 ! [V_m,V_n] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.92 => 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 ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__diff__conv2,axiom, % 185.87/185.92 ! [V_i_2,V_j_2,V_k_2] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 185.87/185.92 => ( 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))) % 185.87/185.92 <=> 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)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_add__diff__assoc,axiom, % 185.87/185.92 ! [V_i,V_j,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__add__diff__inverse,axiom, % 185.87/185.92 ! [V_m,V_n] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.92 => 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 ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__add__diff,axiom, % 185.87/185.92 ! [V_m,V_n,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 185.87/185.92 => 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))) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__diff__conv,axiom, % 185.87/185.92 ! [V_i_2,V_k_2,V_j_2] : % 185.87/185.92 ( 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)) % 185.87/185.92 <=> 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))) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_diff__diff__right,axiom, % 185.87/185.92 ! [V_i,V_j,V_k] : % 185.87/185.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.92 => 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) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 185.87/185.92 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.92 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.92 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_folding__image_Oeq__fold,axiom, % 185.87/185.92 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.92 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.92 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__add__iff2,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oordered__ring(T_b) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.87/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_le__add__iff1,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oordered__ring(T_b) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.87/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_less__add__iff1,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oordered__ring(T_b) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.87/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_less__add__iff2,axiom, % 185.87/185.92 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 185.87/185.92 ( class_Rings_Oordered__ring(T_b) % 185.87/185.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2))) % 185.87/185.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_fold__image__distrib,axiom, % 185.87/185.92 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.92 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_card_Ounion__inter,axiom, % 185.87/185.92 ! [V_B_2,V_A_2,T_b] : % 185.87/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_card__Un__Int,axiom, % 185.87/185.92 ! [V_B_2,V_A_2,T_b] : % 185.87/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.92 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_fold__image__insert,axiom, % 185.87/185.92 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 185.87/185.92 ( class_Groups_Oab__semigroup__mult(T_c) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.92 => 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(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),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),V_A_2)) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_card__Un__disjoint,axiom, % 185.87/185.92 ! [V_B_2,V_A_2,T_b] : % 185.87/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.92 => ( 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)) % 185.87/185.92 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_card_Oinsert,axiom, % 185.87/185.92 ! [V_x_2,V_A_2,T_b] : % 185.87/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.92 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),V_A_2)) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_fold__image__Un__Int,axiom, % 185.87/185.92 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.92 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.92 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_fold__image__reindex,axiom, % 185.87/185.92 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 185.87/185.92 ( class_Groups_Oab__semigroup__mult(T_d) % 185.87/185.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 185.87/185.92 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 185.87/185.92 % 185.87/185.92 fof(fact_image__eq__fold__image,axiom, % 185.87/185.92 ! [V_f_2,T_c,V_A_2,T_b] : % 185.87/185.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.92 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card_Oinsert__remove,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),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)))))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__less__add__iff2,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.87/185.93 => ( 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))) % 185.87/185.93 <=> 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__less__add__iff1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.87/185.93 => ( 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))) % 185.87/185.93 <=> 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__eq__add__iff2,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.87/185.93 => ( 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) % 185.87/185.93 <=> 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) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__diff__add__eq2,axiom, % 185.87/185.93 ! [V_n,V_m,V_u,V_j,V_i] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__le__add__iff2,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.87/185.93 => ( 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))) % 185.87/185.93 <=> 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__eq__add__iff1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.87/185.93 => ( 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) % 185.87/185.93 <=> 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 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__diff__add__eq1,axiom, % 185.87/185.93 ! [V_n,V_m,V_u,V_i,V_j] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_left__add__mult__distrib,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__le__add__iff1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 185.87/185.93 => ( 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))) % 185.87/185.93 <=> 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__monoid__big_OF__eq,axiom, % 185.87/185.93 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.93 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.87/185.93 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.93 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) % 185.87/185.93 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.93 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_fold__image__Un__one,axiom, % 185.87/185.93 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.87/185.93 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.93 => ( ! [B_x] : % 185.87/185.93 ( 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_S_2),V_T_2))) % 185.87/185.93 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.93 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__Max__commute,axiom, % 185.87/185.93 ! [V_k_2,V_N_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__Min__commute,axiom, % 185.87/185.93 ! [V_k_2,V_N_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wfP__acyclicP,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.87/185.93 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__Suc__Diff1,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__mono,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_lessI,axiom, % 185.87/185.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_n__not__Suc__n,axiom, % 185.87/185.93 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__n__not__n,axiom, % 185.87/185.93 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat_Oinject,axiom, % 185.87/185.93 ! [V_nat_H_2,V_nat_2] : % 185.87/185.93 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 185.87/185.93 <=> V_nat_2 = V_nat_H_2 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__inject,axiom, % 185.87/185.93 ! [V_y,V_x] : % 185.87/185.93 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 185.87/185.93 => V_x = V_y ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__less__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__Suc__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 | V_m_2 = V_n_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__less__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__less__less__Suc__eq,axiom, % 185.87/185.93 ! [V_m_2,V_n_2] : % 185.87/185.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 185.87/185.93 <=> V_n_2 = V_m_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__antisym,axiom, % 185.87/185.93 ! [V_m,V_n] : % 185.87/185.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 185.87/185.93 => V_m = V_n ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__SucI,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__lessI,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__trans__Suc,axiom, % 185.87/185.93 ! [V_k,V_j,V_i] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__SucE,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 185.87/185.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => V_m = V_n ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__lessD,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__less__SucD,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__Suc__right,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__Suc,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__Suc__shift,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__n__not__le__n,axiom, % 185.87/185.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__less__eq__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__Suc__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__le__mono,axiom, % 185.87/185.93 ! [V_m_2,V_n_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__SucI,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__SucE,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 185.87/185.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__leD,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__diff__diff,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__Suc__Suc,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__mult__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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) % 185.87/185.93 <=> V_m_2 = V_n_2 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_inj__Suc,axiom, % 185.87/185.93 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wf__acyclic,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.93 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_acyclic__subset,axiom, % 185.87/185.93 ! [V_r_2,V_s_2,T_b] : % 185.87/185.93 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.93 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__iff__Suc__add,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__add__Suc2,axiom, % 185.87/185.93 ! [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)))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__add__Suc1,axiom, % 185.87/185.93 ! [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)))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__eq__Suc__le,axiom, % 185.87/185.93 ! [V_m_2,V_n_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__Suc__eq__le,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__le__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__imp__less__Suc,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__leI,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__less__Suc__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 185.87/185.93 <=> V_n_2 = V_m_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__le__lessD,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__less__Suc,axiom, % 185.87/185.93 ! [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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__mult__less__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__Suc__right,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__Suc,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__diff__le,axiom, % 185.87/185.93 ! [V_m,V_n] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__mult__le__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__Suc__1,axiom, % 185.87/185.93 ! [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 ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__Min__eq__Max,axiom, % 185.87/185.93 ! [V_S_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.93 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__Max__eq__Min,axiom, % 185.87/185.93 ! [V_S_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.93 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max_Osingleton,axiom, % 185.87/185.93 ! [V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min_Osingleton,axiom, % 185.87/185.93 ! [V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__eq__Suc__le__raw,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.93 <=> ~ ? [B_f] : % 185.87/185.93 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__Suc__diff__eq2,axiom, % 185.87/185.93 ! [V_m,V_j,V_k] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__Suc__diff__eq1,axiom, % 185.87/185.93 ! [V_m,V_j,V_k] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min__le,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max__ge,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max__in,axiom, % 185.87/185.93 ! [V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min__in,axiom, % 185.87/185.93 ! [V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_finite__acyclic__wf,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.87/185.93 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.87/185.93 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wf__iff__acyclic__if__finite,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.87/185.93 => ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.93 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__insert__disjoint,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__insert__if,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) % 185.87/185.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max__mono,axiom, % 185.87/185.93 ! [V_N_2,V_M_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 185.87/185.93 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min__antimono,axiom, % 185.87/185.93 ! [V_N_2,V_M_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 185.87/185.93 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__monoid__big_Oinfinite,axiom, % 185.87/185.93 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.93 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 185.87/185.93 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.93 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__insert,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_pred__nat__def,axiom, % 185.87/185.93 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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__Suc__eq__diff__pred,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__eq__plus1,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__eq__plus1__left,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Nitpick_Owf_H__def,axiom, % 185.87/185.93 ! [V_r_2,T_b] : % 185.87/185.93 ( c_Nitpick_Owf_H(T_b,V_r_2) % 185.87/185.93 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.87/185.93 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.87/185.93 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wf__pred__nat,axiom, % 185.87/185.93 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_finite__fun__UNIVD1,axiom, % 185.87/185.93 ! [T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) % 185.87/185.93 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_wf__if__measure,axiom, % 185.87/185.93 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 185.87/185.93 ( ! [B_x] : % 185.87/185.93 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.93 => 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))) ) % 185.87/185.93 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min_Oremove,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 185.87/185.93 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max_Oremove,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 185.87/185.93 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_image__split__eq__Sigma,axiom, % 185.87/185.93 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,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)))))),V_A_2))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_folding__one__idem_Ohom__commute,axiom, % 185.87/185.93 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 185.87/185.93 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.87/185.93 => ( ! [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)) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__zeroE,axiom, % 185.87/185.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le0,axiom, % 185.87/185.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__Suc,axiom, % 185.87/185.93 ! [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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_SigmaI,axiom, % 185.87/185.93 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_bot__nat__def,axiom, % 185.87/185.93 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Odistrib__sup__le,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Odistrib__inf__le,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__reorient,axiom, % 185.87/185.93 ! [V_x_2,T_b] : % 185.87/185.93 ( class_Groups_Ozero(T_b) % 185.87/185.93 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 185.87/185.93 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup_Oidem,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf_Oidem,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup_Ocommute,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__commute,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf_Ocommute,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__commute,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__inf__absorb,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__sup__absorb,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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 ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup_Oleft__idem,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__left__idem,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__left__idem,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup_Oleft__commute,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__left__commute,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__left__commute,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__inf__distrib1,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup_Oassoc,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__assoc,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf_Oassoc,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__assoc,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__inf__distrib2,axiom, % 185.87/185.93 ! [V_x,V_z,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 185.87/185.93 ! [V_x,V_z,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__min__eq__max,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__max__eq__min,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__0L,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__0L,axiom, % 185.87/185.93 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__0R,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__0R,axiom, % 185.87/185.93 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max_Oidem,axiom, % 185.87/185.93 ! [V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min_Oidem,axiom, % 185.87/185.93 ! [V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__max__iff__disj,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 185.87/185.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__supE,axiom, % 185.87/185.93 ! [V_x,V_b,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( 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)) % 185.87/185.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.87/185.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__mono,axiom, % 185.87/185.93 ! [V_d,V_b,V_c,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__least,axiom, % 185.87/185.93 ! [V_z,V_x,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 185.87/185.93 => 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)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__supI,axiom, % 185.87/185.93 ! [V_b,V_x,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.87/185.93 => 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)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__absorb1,axiom, % 185.87/185.93 ! [V_x,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Osup__absorb2,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__supI2,axiom, % 185.87/185.93 ! [V_a,V_b,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__supI1,axiom, % 185.87/185.93 ! [V_b,V_a,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__sup__iff,axiom, % 185.87/185.93 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__iff__sup,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.87/185.93 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__maxI2,axiom, % 185.87/185.93 ! [V_x,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__maxI1,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__le__iff__disj,axiom, % 185.87/185.93 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 185.87/185.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__infE,axiom, % 185.87/185.93 ! [V_b,V_a,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( 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))) % 185.87/185.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.87/185.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__mono,axiom, % 185.87/185.93 ! [V_d,V_b,V_c,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__greatest,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__infI,axiom, % 185.87/185.93 ! [V_b,V_a,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__absorb2,axiom, % 185.87/185.93 ! [V_x,V_y,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__absorb1,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__infI2,axiom, % 185.87/185.93 ! [V_a,V_x,V_b,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 185.87/185.93 => 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__infI1,axiom, % 185.87/185.93 ! [V_b,V_x,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 185.87/185.93 => 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__inf__iff,axiom, % 185.87/185.93 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ole__iff__inf,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 185.87/185.93 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__le2,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oinf__le1,axiom, % 185.87/185.93 ! [V_y,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__max__iff__disj,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 185.87/185.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__less__iff__conj,axiom, % 185.87/185.93 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oless__supI1,axiom, % 185.87/185.93 ! [V_b,V_a,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oless__supI2,axiom, % 185.87/185.93 ! [V_a,V_b,V_x,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__less__iff__conj,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,V_z_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__less__iff__disj,axiom, % 185.87/185.93 ! [V_z_2,V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 185.87/185.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oless__infI1,axiom, % 185.87/185.93 ! [V_b,V_x,V_a,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 185.87/185.93 => 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Oless__infI2,axiom, % 185.87/185.93 ! [V_a,V_x,V_b,T_a] : % 185.87/185.93 ( class_Orderings_Olinorder(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 185.87/185.93 => 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__add__distrib__left,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__add__distrib__left,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__diff__distrib__left,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__diff__distrib__left,axiom, % 185.87/185.93 ! [V_z,V_y,V_x,T_a] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_a) % 185.87/185.93 => 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)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_sup__max,axiom, % 185.87/185.93 ! [T_b] : % 185.87/185.93 ( ( class_Lattices_Osemilattice__sup(T_b) % 185.87/185.93 & class_Orderings_Olinorder(T_b) ) % 185.87/185.93 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_inf__min,axiom, % 185.87/185.93 ! [T_b] : % 185.87/185.93 ( ( class_Lattices_Osemilattice__inf(T_b) % 185.87/185.93 & class_Orderings_Olinorder(T_b) ) % 185.87/185.93 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_max__Suc__Suc,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__Suc__Suc,axiom, % 185.87/185.93 ! [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)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__diff,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__0__iff,axiom, % 185.87/185.93 ! [V_a_2,V_ba_2,T_b] : % 185.87/185.93 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 185.87/185.93 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) % 185.87/185.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__0__left,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Omonoid__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__0,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ocomm__monoid__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_double__zero__sym,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 185.87/185.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__0__right,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Omonoid__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add_Ocomm__neutral,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ocomm__monoid__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_divisors__zero,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Ono__zero__divisors(T_a) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_no__zero__divisors,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Ono__zero__divisors(T_a) % 185.87/185.93 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__eq__0__iff,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Rings_Oring__no__zero__divisors(T_b) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__zero__right,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Omult__zero(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__zero__left,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Omult__zero(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_right__minus__eq,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_b) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 <=> V_a_2 = V_ba_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_eq__iff__diff__eq__0,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oab__group__add(T_b) % 185.87/185.93 => ( V_a_2 = V_ba_2 % 185.87/185.93 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__self,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__0__right,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_one__neq__zero,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Ozero__neq__one(T_a) % 185.87/185.93 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__neq__one,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Ozero__neq__one(T_a) % 185.87/185.93 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__equal__zero,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 185.87/185.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__equal__0__iff__equal,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_b) % 185.87/185.93 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_equal__neg__zero,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 185.87/185.93 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__0__equal__iff__equal,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_b) % 185.87/185.93 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 185.87/185.93 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__zero,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Zero__not__Suc,axiom, % 185.87/185.93 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat_Osimps_I2_J,axiom, % 185.87/185.93 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__not__Zero,axiom, % 185.87/185.93 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat_Osimps_I3_J,axiom, % 185.87/185.93 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Zero__neq__Suc,axiom, % 185.87/185.93 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Suc__neq__Zero,axiom, % 185.87/185.93 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__less0,axiom, % 185.87/185.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neq0__conv,axiom, % 185.87/185.93 ! [V_n_2] : % 185.87/185.93 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__nat__zero__code,axiom, % 185.87/185.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_gr__implies__not0,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_gr0I,axiom, % 185.87/185.93 ! [V_n] : % 185.87/185.93 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__eq__cancel2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 185.87/185.93 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) % 185.87/185.93 <=> V_A_2 = V_B_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_plus__nat_Oadd__0,axiom, % 185.87/185.93 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 185.87/185.93 % 185.87/185.93 fof(fact_Nat_Oadd__0__right,axiom, % 185.87/185.93 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__is__0,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__eq__self__zero,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 185.87/185.93 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 185.87/185.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__0__eq,axiom, % 185.87/185.93 ! [V_n_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 185.87/185.93 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diffs0__imp__equal,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 => V_m = V_n ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__self__eq__0,axiom, % 185.87/185.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__nat_Odiff__0,axiom, % 185.87/185.93 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__0__eq__0,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__cancel2,axiom, % 185.87/185.93 ! [V_n_2,V_k_2,V_m_2] : % 185.87/185.93 ( 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) % 185.87/185.93 <=> ( V_m_2 = V_n_2 % 185.87/185.93 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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) % 185.87/185.93 <=> ( V_m_2 = V_n_2 % 185.87/185.93 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__is__0,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__0__right,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__0,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__mult__eq__cancel__disj,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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) % 185.87/185.93 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 | V_m_2 = V_n_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_UN__Times__distrib,axiom, % 185.87/185.93 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 185.87/185.93 ! [T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 185.87/185.93 ! [T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__empty1,axiom, % 185.87/185.93 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__minus__add__max,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__nonpos__nonpos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__increasing2,axiom, % 185.87/185.93 ! [V_a,V_b,V_c,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__increasing,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__nonneg__eq__0__iff,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__nonneg__nonneg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__le__square,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__ring(T_a) % 185.87/185.93 => 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__le__mult__iff,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2))) % 185.87/185.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__le__0__iff,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__nonneg__nonneg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__nonneg__nonpos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__nonneg__nonpos2,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__nonpos__nonneg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__nonpos__nonpos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__ring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__right__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__left__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__mult__left__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__comm__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__right__mono__neg,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Rings_Oordered__ring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__left__mono__neg,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Rings_Oordered__ring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__mono_H,axiom, % 185.87/185.93 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__mono,axiom, % 185.87/185.93 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__semiring(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_split__mult__pos__le,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__ring(T_a) % 185.87/185.93 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_split__mult__neg__le,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Oordered__cancel__semiring(T_a) % 185.87/185.93 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_pos__add__strict,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__neg__neg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__pos__pos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__strict__left__mono__neg,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__strict__right__mono__neg,axiom, % 185.87/185.93 ! [V_c,V_a,V_b,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_comm__mult__strict__left__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__strict__left__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__strict__right__mono,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__neg__neg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__neg__pos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel__left__neg,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__mult__pos2,axiom, % 185.87/185.93 ! [V_a,V_b,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( 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))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__mult__pos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( 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))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__pos__neg2,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__pos__neg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__pos__pos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel__left__pos,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel__left__disj,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.87/185.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel__right__disj,axiom, % 185.87/185.93 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2))) % 185.87/185.93 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 185.87/185.93 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__square__less__zero,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Rings_Olinordered__ring(T_a) % 185.87/185.93 => ~ 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__iff__diff__le__0,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__iff__diff__less__0,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__scale__eq__noteq,axiom, % 185.87/185.93 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 185.87/185.93 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 185.87/185.93 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 => ( ( V_a = V_b % 185.87/185.93 & V_c != V_d ) % 185.87/185.93 => 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)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_sum__squares__eq__zero__iff,axiom, % 185.87/185.93 ! [V_y_2,V_x_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.93 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__le__one,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.93 => 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__one__le__zero,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.93 => ~ 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))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__one,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_not__one__less__zero,axiom, % 185.87/185.93 ! [T_a] : % 185.87/185.93 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__0__le__iff__le,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_le__minus__self__iff,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__le__0__iff__le,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__le__self__iff,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__minus__self__iff,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__less__nonneg,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__less__0__iff__less,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_neg__0__less__iff__less,axiom, % 185.87/185.93 ! [V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__cartesian__product,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),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_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__empty2,axiom, % 185.87/185.93 ! [V_A_2,T_c,T_b] : 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),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__empty,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.93 ( 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)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) % 185.87/185.93 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.93 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_right__minus,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_eq__neg__iff__add__eq__0,axiom, % 185.87/185.93 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_b) % 185.87/185.93 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 185.87/185.93 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_left__minus,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_ab__left__minus,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Oab__group__add(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_minus__unique,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.93 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__0,axiom, % 185.87/185.93 ! [V_a,T_a] : % 185.87/185.93 ( class_Groups_Ogroup__add(T_a) % 185.87/185.93 => 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) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Compl__Times__UNIV1,axiom, % 185.87/185.93 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Compl__Times__UNIV2,axiom, % 185.87/185.93 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Un__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__Un__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Un__distrib2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__Suc__eq__0__disj,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.87/185.93 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 | ? [B_j] : % 185.87/185.93 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_less__Suc0,axiom, % 185.87/185.93 ! [V_n_2] : % 185.87/185.93 ( 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)))) % 185.87/185.93 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_gr0__conv__Suc,axiom, % 185.87/185.93 ! [V_n_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.87/185.93 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_one__is__add,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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) % 185.87/185.93 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.93 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.93 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__is__1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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)) % 185.87/185.93 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.93 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.93 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__gr__0,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.87/185.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_rel__comp__subset__Sigma,axiom, % 185.87/185.93 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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)))) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_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_C_2)))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card_Oempty,axiom, % 185.87/185.93 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__infinite,axiom, % 185.87/185.93 ! [V_A_2,T_b] : % 185.87/185.93 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__eq__1__iff,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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)) % 185.87/185.93 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.93 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_swap__product,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_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_A_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_zero__less__diff,axiom, % 185.87/185.93 ! [V_m_2,V_n_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__less,axiom, % 185.87/185.93 ! [V_m,V_n] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.87/185.93 => 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)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__mono2,axiom, % 185.87/185.93 ! [V_k,V_j,V_i] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__mono1,axiom, % 185.87/185.93 ! [V_k,V_j,V_i] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.87/185.93 => 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))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel2,axiom, % 185.87/185.93 ! [V_n_2,V_k_2,V_m_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__less__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__0__less__mult__iff,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( 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))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__mult__less__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.93 => ( 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))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_nat__mult__eq__cancel1,axiom, % 185.87/185.93 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.93 => ( 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) % 185.87/185.93 <=> V_m_2 = V_n_2 ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__add__0,axiom, % 185.87/185.93 ! [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) ). % 185.87/185.93 % 185.87/185.93 fof(fact_finite__cartesian__product,axiom, % 185.87/185.93 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.87/185.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__is__0__eq_H,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_diff__is__0__eq,axiom, % 185.87/185.93 ! [V_n_2,V_m_2] : % 185.87/185.93 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_equiv__type,axiom, % 185.87/185.93 ! [V_r_2,V_A_2,T_b] : % 185.87/185.93 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_One__nat__def,axiom, % 185.87/185.93 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Int__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__Int__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Int__distrib2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mult__eq__self__implies__10,axiom, % 185.87/185.93 ! [V_n,V_m] : % 185.87/185.93 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 185.87/185.93 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.87/185.93 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Id__on__subset__Times,axiom, % 185.87/185.93 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Diff__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__Diff__distrib1,axiom, % 185.87/185.93 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Sigma__Diff__distrib2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_UNIV__Times__UNIV,axiom, % 185.87/185.93 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ). % 185.87/185.93 % 185.87/185.93 fof(fact_SigmaE2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.87/185.93 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.93 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_SigmaD2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_SigmaD1,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_mem__Sigma__iff,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.87/185.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.93 & hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_card__cartesian__product__singleton,axiom, % 185.87/185.93 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Max_Oin__idem,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Min_Oin__idem,axiom, % 185.87/185.93 ! [V_x_2,V_A_2,T_b] : % 185.87/185.93 ( class_Orderings_Olinorder(T_b) % 185.87/185.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.93 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Times__subset__cancel2,axiom, % 185.87/185.93 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) % 185.87/185.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_Image__subset,axiom, % 185.87/185.93 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.87/185.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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)))) % 185.87/185.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__pos__nonneg,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__nonneg__pos,axiom, % 185.87/185.93 ! [V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__strict__increasing,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 185.87/185.93 => 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))) ) ) ) ). % 185.87/185.93 % 185.87/185.93 fof(fact_add__strict__increasing2,axiom, % 185.87/185.93 ! [V_c,V_b,V_a,T_a] : % 185.87/185.93 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 185.87/185.94 => 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))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_add__neg__nonpos,axiom, % 185.87/185.94 ! [V_b,V_a,T_a] : % 185.87/185.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.94 => 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))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_add__nonpos__neg,axiom, % 185.87/185.94 ! [V_b,V_a,T_a] : % 185.87/185.94 ( class_Groups_Oordered__comm__monoid__add(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.94 => 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))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__le__cancel__left__pos,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.94 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__le__cancel__left__neg,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.94 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__strict__mono,axiom, % 185.87/185.94 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => 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))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__strict__mono_H,axiom, % 185.87/185.94 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => 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))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__less__le__imp__less,axiom, % 185.87/185.94 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => 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))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__le__less__imp__less,axiom, % 185.87/185.94 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => 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))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__right__less__imp__less,axiom, % 185.87/185.94 ! [V_b,V_c,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__less__imp__less__right,axiom, % 185.87/185.94 ! [V_b,V_c,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__left__less__imp__less,axiom, % 185.87/185.94 ! [V_b,V_a,V_c,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__less__imp__less__left,axiom, % 185.87/185.94 ! [V_b,V_a,V_c,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__right__le__imp__le,axiom, % 185.87/185.94 ! [V_b,V_c,V_a,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__left__le__imp__le,axiom, % 185.87/185.94 ! [V_b,V_a,V_c,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__strict(T_a) % 185.87/185.94 => ( 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))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_sum__squares__le__zero__iff,axiom, % 185.87/185.94 ! [V_y_2,V_x_2,T_b] : % 185.87/185.94 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.94 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.94 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_sum__squares__ge__zero,axiom, % 185.87/185.94 ! [V_y,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__ring(T_a) % 185.87/185.94 => 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)))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_sum__squares__gt__zero__iff,axiom, % 185.87/185.94 ! [V_y_2,V_x_2,T_b] : % 185.87/185.94 ( class_Rings_Olinordered__ring__strict(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) % 185.87/185.94 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.94 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_not__sum__squares__lt__zero,axiom, % 185.87/185.94 ! [V_y,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__ring(T_a) % 185.87/185.94 => ~ 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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__cartesian__productD2,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__cartesian__productD1,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__right__le__one__le,axiom, % 185.87/185.94 ! [V_y,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.94 => 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)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__left__le__one__le,axiom, % 185.87/185.94 ! [V_y,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.94 => 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)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zero__less__two,axiom, % 185.87/185.94 ! [T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.94 => 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)))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_OF__eq,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_OF__eq,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_SetCompr__Sigma__eq,axiom, % 185.87/185.94 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Collect__split,axiom, % 185.87/185.94 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__eq__0__iff,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__ge__0__finite,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( 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_b),V_A_2))) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Suc__pred,axiom, % 185.87/185.94 ! [V_n] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.94 => 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 ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_diff__Suc__less,axiom, % 185.87/185.94 ! [V_i,V_n] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.94 => 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)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_n__less__m__mult__n,axiom, % 185.87/185.94 ! [V_m,V_n] : % 185.87/185.94 ( 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)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => 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))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_n__less__n__mult__m,axiom, % 185.87/185.94 ! [V_m,V_n] : % 185.87/185.94 ( 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)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => 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))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_one__less__mult,axiom, % 185.87/185.94 ! [V_m,V_n] : % 185.87/185.94 ( 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)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => 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))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat__diff__split__asm,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_Pa_2] : % 185.87/185.94 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 185.87/185.94 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.87/185.94 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.87/185.94 | ? [B_d] : % 185.87/185.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 185.87/185.94 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat__diff__split,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_Pa_2] : % 185.87/185.94 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 185.87/185.94 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 185.87/185.94 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.87/185.94 & ! [B_d] : % 185.87/185.94 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 185.87/185.94 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_one__le__mult__iff,axiom, % 185.87/185.94 ! [V_n_2,V_m_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> ( 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)) % 185.87/185.94 & 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)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__le__cancel2,axiom, % 185.87/185.94 ! [V_n_2,V_k_2,V_m_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__le__cancel1,axiom, % 185.87/185.94 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat__mult__le__cancel1,axiom, % 185.87/185.94 ! [V_n_2,V_m_2,V_k_2] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 185.87/185.94 => ( 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))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Ofold1__belowI,axiom, % 185.87/185.94 ! [V_a_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Obelow__fold1__iff,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 185.87/185.94 <=> ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_fold1__below__iff,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 185.87/185.94 <=> ? [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_strict__below__fold1__iff,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) % 185.87/185.94 <=> ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_fold1__strict__below__iff,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) % 185.87/185.94 <=> ? [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max__insert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min__insert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Osubset__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Osubset__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max__Un,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min__Un,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__less__Suc2,axiom, % 185.87/185.94 ! [V_i_2,V_M_2] : % 185.87/185.94 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.87/185.94 => 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))))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__less,axiom, % 185.87/185.94 ! [V_i_2,V_M_2] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.87/185.94 => 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) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__less__Suc,axiom, % 185.87/185.94 ! [V_i_2,V_M_2] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 185.87/185.94 => 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))))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_insert__times__insert,axiom, % 185.87/185.94 ! [V_B_2,V_ba_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_ba_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),hAPP(hAPP(c_Set_Oinsert(T_c),V_ba_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__equiv__class,axiom, % 185.87/185.94 ! [V_X_2,V_r_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_convex__bound__le,axiom, % 185.87/185.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__1(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 185.87/185.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 185.87/185.94 => 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)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Sigma__def,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,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_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__gt__0__iff,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( 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_b),V_A_2))) % 185.87/185.94 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__UNIV__card__ge__0,axiom, % 185.87/185.94 ! [T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 185.87/185.94 => 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_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__quotient,axiom, % 185.87/185.94 ! [V_r_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Suc__diff__1,axiom, % 185.87/185.94 ! [V_n] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.94 => 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 ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Suc__pred_H,axiom, % 185.87/185.94 ! [V_n] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.94 => 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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_add__eq__if,axiom, % 185.87/185.94 ! [V_n,V_m] : % 185.87/185.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 185.87/185.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 => 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)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_mult__eq__if,axiom, % 185.87/185.94 ! [V_n,V_m] : % 185.87/185.94 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.94 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 => 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)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Oinsert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Oinsert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_fold1__antimono,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__def,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card_Oeq__fold__g,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Oinsert__remove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Ounion__disjoint,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Ounion__inter,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Oinsert__remove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Ounion__disjoint,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Ounion__inter,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_convex__bound__lt,axiom, % 185.87/185.94 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 185.87/185.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 185.87/185.94 => 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)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_triple_Osize_I1_J,axiom, % 185.87/185.94 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.94 % 185.87/185.94 fof(fact_even__less__0__iff,axiom, % 185.87/185.94 ! [V_a_2,T_b] : % 185.87/185.94 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat_Osize_I2_J,axiom, % 185.87/185.94 ! [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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_dual__min,axiom, % 185.87/185.94 ! [T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_dual__max,axiom, % 185.87/185.94 ! [T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_triple_Osize_I2_J,axiom, % 185.87/185.94 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_fun1_2,V_com_2,V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.94 % 185.87/185.94 fof(fact_sup__nat__def,axiom, % 185.87/185.94 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 185.87/185.94 % 185.87/185.94 fof(fact_inf__nat__def,axiom, % 185.87/185.94 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat_Osize_I1_J,axiom, % 185.87/185.94 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.94 % 185.87/185.94 fof(fact_double__eq__0__iff,axiom, % 185.87/185.94 ! [V_a_2,T_b] : % 185.87/185.94 ( class_Groups_Olinordered__ab__group__add(T_b) % 185.87/185.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.94 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__ord__min,axiom, % 185.87/185.94 ! [T_b] : % 185.87/185.94 ( class_Orderings_Oord(T_b) % 185.87/185.94 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_max__ord__max,axiom, % 185.87/185.94 ! [T_b] : % 185.87/185.94 ( class_Orderings_Oord(T_b) % 185.87/185.94 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card_Ounion__inter__neutral,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( ( ? [B_x] : 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))) % 185.87/185.94 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 185.87/185.94 ! [V_A_2,V_I_2,T_c,T_b] : % 185.87/185.94 ? [B_f] : % 185.87/185.94 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) % 185.87/185.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__mult__setsum__if__inj,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.94 ( class_Rings_Osemiring__0(T_d) % 185.87/185.94 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_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))) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),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_d,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(T_b,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_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),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_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_fold__image__Sigma,axiom, % 185.87/185.94 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.87/185.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__cartesian__product,axiom, % 185.87/185.94 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__commute,axiom, % 185.87/185.94 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__0,axiom, % 185.87/185.94 ! [V_A_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__addf,axiom, % 185.87/185.94 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),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_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__product,axiom, % 185.87/185.94 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Rings_Osemiring__0(T_b) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__left__distrib,axiom, % 185.87/185.94 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Rings_Osemiring__0(T_b) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__right__distrib,axiom, % 185.87/185.94 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 185.87/185.94 ( class_Rings_Osemiring__0(T_b) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__subtractf,axiom, % 185.87/185.94 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Oab__group__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__negf,axiom, % 185.87/185.94 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Oab__group__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oempty,axiom, % 185.87/185.94 ! [V_g_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__empty,axiom, % 185.87/185.94 ! [V_f_2,T_c,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oinfinite,axiom, % 185.87/185.94 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__infinite,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__eq__0__iff,axiom, % 185.87/185.94 ! [V_f_2,V_F_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.87/185.94 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 <=> ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 185.87/185.94 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Odistrib,axiom, % 185.87/185.94 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__eq__setsum,axiom, % 185.87/185.94 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__eq__Suc0__iff,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.94 <=> ? [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.94 & ! [B_xa] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.87/185.94 => ( B_x != B_xa % 185.87/185.94 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__reindex,axiom, % 185.87/185.94 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_d) % 185.87/185.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__eq__1__iff,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.87/185.94 <=> ? [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.87/185.94 & ! [B_xa] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 185.87/185.94 => ( B_x != B_xa % 185.87/185.94 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__reindex__id,axiom, % 185.87/185.94 ! [V_B_2,V_f_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_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_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__delta_H,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__delta,axiom, % 185.87/185.94 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__setsum__restrict,axiom, % 185.87/185.94 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_d) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 185.87/185.94 ! [V_x_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oinsert,axiom, % 185.87/185.94 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__insert,axiom, % 185.87/185.94 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Un__Int,axiom, % 185.87/185.94 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff,axiom, % 185.87/185.94 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Oab__group__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oreindex,axiom, % 185.87/185.94 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oeq__fold,axiom, % 185.87/185.94 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_OF__eq,axiom, % 185.87/185.94 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff__nat,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,V_B_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__restrict__set_H,axiom, % 185.87/185.94 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__restrict__set,axiom, % 185.87/185.94 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__image__gen,axiom, % 185.87/185.94 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oinsert__remove,axiom, % 185.87/185.94 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Un__disjoint,axiom, % 185.87/185.94 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 185.87/185.94 ! [V_a_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Un,axiom, % 185.87/185.94 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Oab__group__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff1__nat,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,V_a_2,T_b] : % 185.87/185.94 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Un__nat,axiom, % 185.87/185.94 ! [V_f_2,V_B_2,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_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_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__cases,axiom, % 185.87/185.94 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_b),V_Pa_2))))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff1_H,axiom, % 185.87/185.94 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Oremove,axiom, % 185.87/185.94 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff1,axiom, % 185.87/185.94 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Oab__group__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 185.87/185.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__diff1__ring,axiom, % 185.87/185.94 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Rings_Oring(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oremove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__mono2,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Oordered__comm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.94 => ( ! [B_b] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat_Osize_I4_J,axiom, % 185.87/185.94 ! [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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat__size,axiom, % 185.87/185.94 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 185.87/185.94 % 185.87/185.94 fof(fact_nat_Osize_I3_J,axiom, % 185.87/185.94 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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 185.87/185.94 ! [V_x_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_Osup__Inf__absorb,axiom, % 185.87/185.94 ! [V_a_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 185.87/185.94 ! [V_B_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( 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)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oremove,axiom, % 185.87/185.94 ! [V_x_2,V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.94 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 185.87/185.94 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__le__Sup,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Sigma,axiom, % 185.87/185.94 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_d) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__multicount,axiom, % 185.87/185.94 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_T_2)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__SigmaI,axiom, % 185.87/185.94 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.87/185.94 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Max_Oclosed,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_Min_Oclosed,axiom, % 185.87/185.94 ! [V_A_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_arith__series__nat,axiom, % 185.87/185.94 ! [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)))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__Un__zero,axiom, % 185.87/185.94 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( 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_S_2),V_T_2))) % 185.87/185.94 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum_Ounion__inter__neutral,axiom, % 185.87/185.94 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( 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))) % 185.87/185.94 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__Suc__eq,axiom, % 185.87/185.94 ! [V_k_2,V_A_2,T_b] : % 185.87/185.94 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 185.87/185.94 <=> ? [B_b,B_B] : % 185.87/185.94 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 185.87/185.94 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 185.87/185.94 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 185.87/185.94 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__lessThan,axiom, % 185.87/185.94 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__eq__iff,axiom, % 185.87/185.94 ! [V_y_2,V_x_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 185.87/185.94 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__0,axiom, % 185.87/185.94 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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__Suc,axiom, % 185.87/185.94 ! [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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_card__lessThan,axiom, % 185.87/185.94 ! [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 ). % 185.87/185.94 % 185.87/185.94 fof(fact_UN__lessThan__UNIV,axiom, % 185.87/185.94 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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 185.87/185.94 ! [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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__lessThan__Suc,axiom, % 185.87/185.94 ! [V_n_2,V_f_2,T_b] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__iff,axiom, % 185.87/185.94 ! [V_k_2,V_i_2,T_b] : % 185.87/185.94 ( class_Orderings_Oord(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__subset__iff,axiom, % 185.87/185.94 ! [V_y_2,V_x_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_lessThan__strict__subset__iff,axiom, % 185.87/185.94 ! [V_n_2,V_m_2,T_b] : % 185.87/185.94 ( class_Orderings_Olinorder(T_b) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_single__Diff__lessThan,axiom, % 185.87/185.94 ! [V_k_2,T_b] : % 185.87/185.94 ( class_Orderings_Oorder(T_b) % 185.87/185.94 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_arith__series__general,axiom, % 185.87/185.94 ! [V_n_2,V_d_2,V_a_2,T_b] : % 185.87/185.94 ( class_Rings_Ocomm__semiring__1(T_b) % 185.87/185.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__mono3,axiom, % 185.87/185.94 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 185.87/185.94 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.94 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 185.87/185.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_setsum__reindex__nonzero,axiom, % 185.87/185.94 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 185.87/185.94 ( class_Groups_Ocomm__monoid__add(T_d) % 185.87/185.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.94 => ( ! [B_x] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.87/185.94 => ! [B_y] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 185.87/185.94 => ( B_x != B_y % 185.87/185.94 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 185.87/185.94 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 185.87/185.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_finite__SigmaI,axiom, % 185.87/185.94 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.94 => ( ! [B_a] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 185.87/185.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_equiv__intrel__iff,axiom, % 185.87/185.94 ! [V_y_2,V_x_2] : % 185.87/185.94 ( 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)))) % 185.87/185.94 <=> 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)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_negative__zless,axiom, % 185.87/185.94 ! [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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zadd__int,axiom, % 185.87/185.94 ! [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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zadd__int__left,axiom, % 185.87/185.94 ! [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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zle__int,axiom, % 185.87/185.94 ! [V_n_2,V_m_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__mult,axiom, % 185.87/185.94 ! [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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zmult__int,axiom, % 185.87/185.94 ! [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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__le__0__conv,axiom, % 185.87/185.94 ! [V_n_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__zle__neg,axiom, % 185.87/185.94 ! [V_m_2,V_n_2] : % 185.87/185.94 ( 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)))) % 185.87/185.94 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__eq__0__conv,axiom, % 185.87/185.94 ! [V_n_2] : % 185.87/185.94 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.94 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__0,axiom, % 185.87/185.94 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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_negative__eq__positive,axiom, % 185.87/185.94 ! [V_m_2,V_n_2] : % 185.87/185.94 ( 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) % 185.87/185.94 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.94 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_negative__zless__0,axiom, % 185.87/185.94 ! [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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_not__zle__0__negative,axiom, % 185.87/185.94 ! [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))))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__Suc,axiom, % 185.87/185.94 ! [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)) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zless__iff__Suc__zadd,axiom, % 185.87/185.94 ! [V_z_2,V_w_2] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 185.87/185.94 <=> ? [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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_equiv__intrel,axiom, % 185.87/185.94 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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_of__nat__eq__iff,axiom, % 185.87/185.94 ! [V_n_2,V_m_2,T_b] : % 185.87/185.94 ( class_Nat_Osemiring__char__0(T_b) % 185.87/185.94 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) % 185.87/185.94 <=> V_m_2 = V_n_2 ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zless__int,axiom, % 185.87/185.94 ! [V_n_2,V_m_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__1,axiom, % 185.87/185.94 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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_inj__int,axiom, % 185.87/185.94 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))) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__setsum,axiom, % 185.87/185.94 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 185.87/185.94 % 185.87/185.94 fof(fact_int__Suc0__eq__1,axiom, % 185.87/185.94 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) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zmult__zless__mono2__lemma,axiom, % 185.87/185.94 ! [V_k,V_j,V_i] : % 185.87/185.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.87/185.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.87/185.94 => 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))) ) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zero__less__int__conv,axiom, % 185.87/185.94 ! [V_n_2] : % 185.87/185.94 ( 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))) % 185.87/185.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zero__le__imp__of__nat,axiom, % 185.87/185.94 ! [V_m,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.94 => 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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_of__nat__0__le__iff,axiom, % 185.87/185.94 ! [V_n,T_a] : % 185.87/185.94 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.94 => 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))) ) ). % 185.87/185.94 % 185.87/185.94 fof(fact_zdiff__int,axiom, % 185.87/185.95 ! [V_m,V_n] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__less__0__iff,axiom, % 185.87/185.95 ! [V_m,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ~ 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__0,axiom, % 185.87/185.95 ! [T_a] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__less__iff,axiom, % 185.87/185.95 ! [V_n_2,V_m_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_less__imp__of__nat__less,axiom, % 185.87/185.95 ! [V_n,V_m,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__less__imp__less,axiom, % 185.87/185.95 ! [V_n,V_m,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ( 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))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__le__iff,axiom, % 185.87/185.95 ! [V_n_2,V_m_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__add,axiom, % 185.87/185.95 ! [V_n,V_m,T_a] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__mult,axiom, % 185.87/185.95 ! [V_n,V_m,T_a] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__1,axiom, % 185.87/185.95 ! [T_a] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__setsum,axiom, % 185.87/185.95 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_b) % 185.87/185.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_inj__of__nat,axiom, % 185.87/185.95 ! [T_b] : % 185.87/185.95 ( class_Nat_Osemiring__char__0(T_b) % 185.87/185.95 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__Suc,axiom, % 185.87/185.95 ! [V_m,T_a] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__diff,axiom, % 185.87/185.95 ! [V_m,V_n,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__constant,axiom, % 185.87/185.95 ! [V_A_2,V_y_2,T_c,T_b] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_b) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_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_c),V_A_2))),V_y_2) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__0__less__iff,axiom, % 185.87/185.95 ! [V_n_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_intrel__iff,axiom, % 185.87/185.95 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.87/185.95 ( 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)) % 185.87/185.95 <=> 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 185.87/185.95 ! [V_n_2,T_b] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_b) % 185.87/185.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zdiff__int__split,axiom, % 185.87/185.95 ! [V_y_2,V_x_2,V_Pa_2] : % 185.87/185.95 ( hBOOL(hAPP(V_Pa_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)))) % 185.87/185.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 185.87/185.95 => hBOOL(hAPP(V_Pa_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)))) ) % 185.87/185.95 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_One__int__def,axiom, % 185.87/185.95 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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_mult,axiom, % 185.87/185.95 ! [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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_le,axiom, % 185.87/185.95 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.87/185.95 ( 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))))))) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_negative__zle,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zero__zle__int,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_negative__zle__0,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__less__0__conv,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__int__eq,axiom, % 185.87/185.95 ! [V_n_2,V_m_2] : % 185.87/185.95 ( 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) % 185.87/185.95 <=> V_m_2 = V_n_2 ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_not__int__zless__negative,axiom, % 185.87/185.95 ! [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)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__iff__zadd,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 185.87/185.95 <=> ? [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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__add1__eq__le,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( 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)))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_add1__zle__eq,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( 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)) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__imp__add1__zle,axiom, % 185.87/185.95 ! [V_z,V_w] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__add1__eq,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( 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)))) % 185.87/185.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 185.87/185.95 | V_w_2 = V_z_2 ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__left__mono,axiom, % 185.87/185.95 ! [V_k,V_j,V_i] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__zless__mono,axiom, % 185.87/185.95 ! [V_z,V_z_H,V_w,V_w_H] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__zmult__distrib,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__zmult__distrib2,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__strict__right__mono,axiom, % 185.87/185.95 ! [V_k,V_j,V_i] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__assoc,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__left__commute,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__commute,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zminus__zadd__distrib,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_diff__int__def__symmetric,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_diff__int__def,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__diff1__eq,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( 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)))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__1__right,axiom, % 185.87/185.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__1,axiom, % 185.87/185.95 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__antisym,axiom, % 185.87/185.95 ! [V_w,V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 185.87/185.95 => V_z = V_w ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__trans,axiom, % 185.87/185.95 ! [V_k,V_j,V_i] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__linear,axiom, % 185.87/185.95 ! [V_w,V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 185.87/185.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zle__refl,axiom, % 185.87/185.95 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__le,axiom, % 185.87/185.95 ! [V_w_2,V_z_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 185.87/185.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 185.87/185.95 & V_z_2 != V_w_2 ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zdiff__zmult__distrib2,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zdiff__zmult__distrib,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__assoc,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__commute,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__zminus,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__linear,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 185.87/185.95 | V_x = V_y % 185.87/185.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zminus__zminus,axiom, % 185.87/185.95 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 185.87/185.95 % 185.87/185.95 fof(fact_less__bin__lemma,axiom, % 185.87/185.95 ! [V_l_2,V_k_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zminus__0,axiom, % 185.87/185.95 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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zmult__zless__mono2,axiom, % 185.87/185.95 ! [V_k,V_j,V_i] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__0__neq__1,axiom, % 185.87/185.95 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__0__less__1,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_pos__zmult__eq__1__iff,axiom, % 185.87/185.95 ! [V_n_2,V_m_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 185.87/185.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.95 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.95 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__one__le__iff__zero__less,axiom, % 185.87/185.95 ! [V_z_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__zminus__inverse2,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__0,axiom, % 185.87/185.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 185.87/185.95 % 185.87/185.95 fof(fact_zadd__0__right,axiom, % 185.87/185.95 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 185.87/185.95 % 185.87/185.95 fof(fact_odd__nonzero,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_odd__less__0,axiom, % 185.87/185.95 ! [V_z_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_le__imp__0__less,axiom, % 185.87/185.95 ! [V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 185.87/185.95 ! [V_i_2,V_inc_2,T_b] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_b) % 185.87/185.95 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 185.87/185.95 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 185.87/185.95 ( class_Rings_Osemiring__1(T_b) % 185.87/185.95 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_minus,axiom, % 185.87/185.95 ! [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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Zero__int__def,axiom, % 185.87/185.95 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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__def,axiom, % 185.87/185.95 ! [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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_add,axiom, % 185.87/185.95 ! [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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_less,axiom, % 185.87/185.95 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 185.87/185.95 ( 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))))))) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_self__quotient__aux1,axiom, % 185.87/185.95 ! [V_q,V_r,V_a] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.95 => ( 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)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_self__quotient__aux2,axiom, % 185.87/185.95 ! [V_q,V_r,V_a] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.95 => ( 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)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zdiv__mono2__neg__lemma,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 185.87/185.95 ( 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) % 185.87/185.95 => ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_unique__quotient__lemma__neg,axiom, % 185.87/185.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zdiv__mono2__lemma,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 185.87/185.95 ( 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) % 185.87/185.95 => ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_q__pos__lemma,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_b_H] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_q__neg__lemma,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_b_H] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_unique__quotient__lemma,axiom, % 185.87/185.95 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 185.87/185.95 ! [V_Pa_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_Pa_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_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_minus__int__def,axiom, % 185.87/185.95 ! [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))))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 185.87/185.95 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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Rep__Integ__inject,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 185.87/185.95 <=> V_x_2 = V_y_2 ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Rep__Integ__inverse,axiom, % 185.87/185.95 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( V_A_2 = V_B_2 % 185.87/185.95 <=> 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( 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) % 185.87/185.95 <=> V_x_2 = V_y_2 ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 185.87/185.95 ! [V_A_2,V_x_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 185.87/185.95 ! [V_A_2] : % 185.87/185.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 185.87/185.95 <=> 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 185.87/185.95 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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 185.87/185.95 ! [V_Pa_2] : % 185.87/185.95 ( ! [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.87/185.95 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 185.87/185.95 ! [V_Pa_2] : % 185.87/185.95 ( ? [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.95 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.87/185.95 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__ge__less__than__def,axiom, % 185.87/185.95 ! [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)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__ge__less__than2__def,axiom, % 185.87/185.95 ! [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)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int,axiom, % 185.87/185.95 ! [V_j_2,V_i_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__nat__if,axiom, % 185.87/185.95 ! [V_m_2,V_n_2] : % 185.87/185.95 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 185.87/185.95 => 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) ) % 185.87/185.95 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_eq__Abs__Integ,axiom, % 185.87/185.95 ! [V_z_2] : % 185.87/185.95 ~ ! [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))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_wf__int__ge__less__than2,axiom, % 185.87/185.95 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_wf__int__ge__less__than,axiom, % 185.87/185.95 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_infinite__UNIV__int,axiom, % 185.87/185.95 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__eq__iff,axiom, % 185.87/185.95 ! [V_z_2,V_w_2,T_b] : % 185.87/185.95 ( class_Int_Oring__char__0(T_b) % 185.87/185.95 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 185.87/185.95 <=> V_w_2 = V_z_2 ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__int__eq,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__0,axiom, % 185.87/185.95 ! [T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__0__eq__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Int_Oring__char__0(T_b) % 185.87/185.95 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 185.87/185.95 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__eq__0__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Int_Oring__char__0(T_b) % 185.87/185.95 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.95 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__le__iff,axiom, % 185.87/185.95 ! [V_z_2,V_w_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__less__iff,axiom, % 185.87/185.95 ! [V_z_2,V_w_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__add,axiom, % 185.87/185.95 ! [V_z,V_w,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__mult,axiom, % 185.87/185.95 ! [V_z,V_w,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__1,axiom, % 185.87/185.95 ! [T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__diff,axiom, % 185.87/185.95 ! [V_z,V_w,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__of__nat__eq,axiom, % 185.87/185.95 ! [V_n,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__minus,axiom, % 185.87/185.95 ! [V_z,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__setsum,axiom, % 185.87/185.95 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__nat__zero,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__le__0__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__0__le__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__0__less__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__less__0__iff,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__nat__base,axiom, % 185.87/185.95 ! [V_n,V_m] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nitpick_OFrac__def,axiom, % 185.87/185.95 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)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__int__rel__def,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_ba_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_ba_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_ba_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_ba_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_ba_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_ba_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))))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Integ__def,axiom, % 185.87/185.95 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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__bounded,axiom, % 185.87/185.95 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.95 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 185.87/185.95 & class_Rings_Osemiring__1(T_c) ) % 185.87/185.95 => ( ! [B_i] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__eq__id,axiom, % 185.87/185.95 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__int,axiom, % 185.87/185.95 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__int__rel__0,axiom, % 185.87/185.95 ! [V_b] : % 185.87/185.95 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.95 => 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)))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_self__remainder,axiom, % 185.87/185.95 ! [V_r,V_q,V_a] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.95 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_unique__quotient,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( 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))) % 185.87/185.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.95 => V_q = V_q_H ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_unique__remainder,axiom, % 185.87/185.95 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( 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))) % 185.87/185.95 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.95 => V_r = V_r_H ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 185.87/185.95 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__0,axiom, % 185.87/185.95 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ex__nat,axiom, % 185.87/185.95 ! [V_Pa_2] : % 185.87/185.95 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.87/185.95 <=> ? [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.95 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_all__nat,axiom, % 185.87/185.95 ! [V_Pa_2] : % 185.87/185.95 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.87/185.95 <=> ! [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.87/185.95 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 185.87/185.95 <=> V_x_2 = V_y_2 ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_eq__nat__nat__iff,axiom, % 185.87/185.95 ! [V_z_H_2,V_z_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 185.87/185.95 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 185.87/185.95 <=> V_z_2 = V_z_H_2 ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 185.87/185.95 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__return__embed,axiom, % 185.87/185.95 ! [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 ). % 185.87/185.95 % 185.87/185.95 fof(fact_self__quotient,axiom, % 185.87/185.95 ! [V_r,V_q,V_a] : % 185.87/185.95 ( 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))) % 185.87/185.95 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.95 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__0__iff,axiom, % 185.87/185.95 ! [V_i_2] : % 185.87/185.95 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__le__0,axiom, % 185.87/185.95 ! [V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__mono__iff,axiom, % 185.87/185.95 ! [V_w_2,V_z_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.87/185.95 => ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__nat__conj,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 185.87/185.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.87/185.95 => ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__1,axiom, % 185.87/185.95 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__0__le,axiom, % 185.87/185.95 ! [V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__eq__iff,axiom, % 185.87/185.95 ! [V_z_2,V_m_2] : % 185.87/185.95 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 185.87/185.95 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 185.87/185.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_int__nat__eq,axiom, % 185.87/185.95 ! [V_z] : % 185.87/185.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => 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) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zless__nat__eq__int__zless,axiom, % 185.87/185.95 ! [V_z_2,V_m_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 185.87/185.95 <=> 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__zminus__int,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Rep__Integ,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 185.87/185.95 ! [V_A_2,V_f_2,T_b] : % 185.87/185.95 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zero__less__nat__eq,axiom, % 185.87/185.95 ! [V_z_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 185.87/185.95 ! [V_y_2,V_x_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 185.87/185.95 => ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__less__eq__zless,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__eq__iff,axiom, % 185.87/185.95 ! [V_m_2,V_w_2] : % 185.87/185.95 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 185.87/185.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__eq__iff2,axiom, % 185.87/185.95 ! [V_w_2,V_m_2] : % 185.87/185.95 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 185.87/185.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__le__eq__zle,axiom, % 185.87/185.95 ! [V_z_2,V_w_2] : % 185.87/185.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 185.87/185.95 => ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_split__nat,axiom, % 185.87/185.95 ! [V_i_2,V_Pa_2] : % 185.87/185.95 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 185.87/185.95 <=> ( ! [B_n] : % 185.87/185.95 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 185.87/185.95 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__add__distrib,axiom, % 185.87/185.95 ! [V_z_H,V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__mult__distrib,axiom, % 185.87/185.95 ! [V_z_H,V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__diff__distrib,axiom, % 185.87/185.95 ! [V_z,V_z_H] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 185.87/185.95 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__nat__nat,axiom, % 185.87/185.95 ! [V_z,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => 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) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_one__less__nat__eq,axiom, % 185.87/185.95 ! [V_z_2] : % 185.87/185.95 ( 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))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__less__iff,axiom, % 185.87/185.95 ! [V_m_2,V_w_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 185.87/185.95 <=> 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 185.87/185.95 ! [V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__mult__distrib__neg,axiom, % 185.87/185.95 ! [V_z_H,V_z] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 185.87/185.95 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_2),c_Int_Onat)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__def,axiom, % 185.87/185.95 ! [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)))))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zminus1__lemma,axiom, % 185.87/185.95 ! [V_r_2,V_q_2,V_ba_2,V_a_2] : % 185.87/185.95 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_ba_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 185.87/185.95 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_ba_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_ba_2),V_r_2))))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__of__nat,axiom, % 185.87/185.95 ! [V_k,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => 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)))) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.95 => 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)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_divmod__int__relI,axiom, % 185.87/185.95 ! [V_r,V_q,V_b,V_a] : % 185.87/185.95 ( 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) % 185.87/185.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.87/185.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.87/185.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__aux__def,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__morphism__nat__int,axiom, % 185.87/185.95 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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__greaterThanLessThan__int,axiom, % 185.87/185.95 ! [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)))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__atLeastZeroLessThan__int,axiom, % 185.87/185.95 ! [V_u_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__atLeastLessThan__int,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__greaterThanLessThan__int,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__int_I9_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.87/185.95 => V_ba_2 = V_d_2 ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.87/185.95 => V_a_2 = V_ca_2 ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__eq__iff,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 185.87/185.95 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) % 185.87/185.95 <=> ( V_a_2 = V_ca_2 % 185.87/185.95 & V_ba_2 = V_d_2 ) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I15_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__empty,axiom, % 185.87/185.95 ! [V_a_2,V_ba_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 185.87/185.95 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__empty__iff2,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) % 185.87/185.95 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__empty__iff,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.95 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I3_J,axiom, % 185.87/185.95 ! [V_u_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__subset__iff,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 185.87/185.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.87/185.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I17_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__diff,axiom, % 185.87/185.95 ! [V_m_2,V_n_2,V_i_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 185.87/185.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__int_I11_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_greaterThanLessThan__empty,axiom, % 185.87/185.95 ! [V_k_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 185.87/185.95 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__uminus__greaterThanLessThan,axiom, % 185.87/185.95 ! [V_y_2,V_x_2,T_b] : % 185.87/185.95 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.95 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Int__atLeastLessThan,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I8_J,axiom, % 185.87/185.95 ! [V_u_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__int_I2_J,axiom, % 185.87/185.95 ! [V_u_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__add__int__atLeastLessThan,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__atLeastZeroLessThan__int,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__atLeastLessThan__int,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Int__greaterThanLessThan,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_tsub__eq,axiom, % 185.87/185.95 ! [V_x,V_y] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.87/185.95 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_tsub__def,axiom, % 185.87/185.95 ! [V_x,V_y] : % 185.87/185.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.87/185.95 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 185.87/185.95 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 185.87/185.95 ! [V_f_2,V_A_2,T_b] : % 185.87/185.95 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.95 <=> 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))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__atLeastLessThan,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__greaterThanLessThan,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan0,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeast0LessThan,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__atLeastLessThan,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 185.87/185.95 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__Suc__atLeastLessThan,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 185.87/185.95 ! [V_n_2,V_m_2,V_f_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 185.87/185.95 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_nat__set__def,axiom, % 185.87/185.95 ! [V_S_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_S_2) % 185.87/185.95 <=> ! [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__add__atLeastLessThan,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => ( V_A_2 = V_B_2 % 185.87/185.95 <=> 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) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__add__nat__ivl,axiom, % 185.87/185.95 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 185.87/185.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__diff__nat__ivl,axiom, % 185.87/185.95 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 185.87/185.95 ( class_Groups_Oab__group__add(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 185.87/185.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__singleton,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_UN__UN__finite__eq,axiom, % 185.87/185.95 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThan__add__Un,axiom, % 185.87/185.95 ! [V_k_2,V_j_2,V_i_2] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_subset__card__intvl__is__intvl,axiom, % 185.87/185.95 ! [V_k_2,V_A_2] : % 185.87/185.95 ( 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))))) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 185.87/185.95 ! [V_k_2,V_f_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__head__upt__Suc,axiom, % 185.87/185.95 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_atLeastLessThanSuc,axiom, % 185.87/185.95 ! [V_n_2,V_m_2] : % 185.87/185.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.95 => 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)) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.95 => 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)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 185.87/185.95 ! [V_x_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__greaterThanLessThan,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__op__ivl__Suc,axiom, % 185.87/185.95 ! [V_f_2,V_m_2,V_n_2,T_b] : % 185.87/185.95 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 185.87/185.95 ! [V_Pa_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_Pa_2))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__nat__int__set__return__embed,axiom, % 185.87/185.95 ! [V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => 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 ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 185.87/185.95 ! [V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 185.87/185.95 <=> 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))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 185.87/185.95 ! [V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 185.87/185.95 ! [V_x_2,V_y_2,V_ca_2] : % 185.87/185.95 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 185.87/185.95 => 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)) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 185.87/185.95 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.87/185.95 => 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))) ) % 185.87/185.95 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 185.87/185.95 => 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)) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 185.87/185.95 ! [V_B_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.95 <=> 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))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 185.87/185.95 ! [V_A_2,V_x_2] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.87/185.95 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.87/185.95 <=> 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))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_UN__finite2__subset,axiom, % 185.87/185.95 ! [V_B_2,V_k_2,V_A_2,T_b] : % 185.87/185.95 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ex__nat__less__eq,axiom, % 185.87/185.95 ! [V_Pa_2,V_n_2] : % 185.87/185.95 ( ? [B_m] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 185.87/185.95 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.87/185.95 <=> ? [B_x] : % 185.87/185.95 ( 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))) % 185.87/185.95 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_all__nat__less__eq,axiom, % 185.87/185.95 ! [V_Pa_2,V_n_2] : % 185.87/185.95 ( ! [B_m] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.87/185.95 <=> ! [B_x] : % 185.87/185.95 ( 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))) % 185.87/185.95 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 185.87/185.95 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 185.87/185.95 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 185.87/185.95 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 185.87/185.95 ! [V_y,V_x] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.95 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_is__nat__def,axiom, % 185.87/185.95 ! [V_x_2] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 185.87/185.95 ! [V_x_2,V_A_2] : % 185.87/185.95 ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 185.87/185.95 ! [V_f_2,V_A_2,T_b] : % 185.87/185.95 ( ! [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_wf__lenlex,axiom, % 185.87/185.95 ! [V_r_2,T_b] : % 185.87/185.95 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.95 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_UN__finite2__eq,axiom, % 185.87/185.95 ! [V_B_2,V_k_2,V_A_2,T_b] : % 185.87/185.95 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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) % 185.87/185.95 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_UN__finite__subset,axiom, % 185.87/185.95 ! [V_C_2,V_A_2,T_b] : % 185.87/185.95 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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)) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_wf__lex,axiom, % 185.87/185.95 ! [V_r_2,T_b] : % 185.87/185.95 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.95 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__odd__less__0,axiom, % 185.87/185.95 ! [V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_setsum__multicount__gen,axiom, % 185.87/185.95 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 185.87/185.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.87/185.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 185.87/185.95 => ( ! [B_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 185.87/185.95 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 185.87/185.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I4_J,axiom, % 185.87/185.95 ! [V_u_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__greaterThanAtMost,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_finite__greaterThanAtMost__int,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_greaterThanAtMost__empty,axiom, % 185.87/185.95 ! [V_k_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 185.87/185.95 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 185.87/185.95 ! [V_l_2,V_k_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) % 185.87/185.95 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_greaterThanAtMost__empty__iff,axiom, % 185.87/185.95 ! [V_l_2,V_k_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.95 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I20_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__int_I14_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__0,axiom, % 185.87/185.95 ! [T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__add,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__mult,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__diff,axiom, % 185.87/185.95 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__1,axiom, % 185.87/185.95 ! [T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__minus,axiom, % 185.87/185.95 ! [V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__of__nat,axiom, % 185.87/185.95 ! [V_n_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__greaterThanAtMost,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__of__int,axiom, % 185.87/185.95 ! [V_z_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Int__greaterThanAtMost,axiom, % 185.87/185.95 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__double__eq__0__iff,axiom, % 185.87/185.95 ! [V_a_2,T_b] : % 185.87/185.95 ( class_Int_Oring__char__0(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__uminus__greaterThanAtMost,axiom, % 185.87/185.95 ! [V_y_2,V_x_2,T_b] : % 185.87/185.95 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.95 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_image__uminus__atLeastLessThan,axiom, % 185.87/185.95 ! [V_y_2,V_x_2,T_b] : % 185.87/185.95 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.95 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__int_I10_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Oorder(T_b) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__greaterThanAtMost__int,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_ivl__disj__un_I16_J,axiom, % 185.87/185.95 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.95 ( class_Orderings_Olinorder(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 185.87/185.95 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__odd__nonzero,axiom, % 185.87/185.95 ! [V_a_2,T_b] : % 185.87/185.95 ( class_Int_Oring__char__0(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_lex__def,axiom, % 185.87/185.95 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_wf__lexn,axiom, % 185.87/185.95 ! [V_n_2,V_r_2,T_b] : % 185.87/185.95 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.95 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_com_Osize_I4_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_card__Pow,axiom, % 185.87/185.95 ! [V_A_2,T_b] : % 185.87/185.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.95 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),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_b),V_A_2)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 185.87/185.95 ! [V_q,V_p,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 185.87/185.95 ! [V_q,V_y,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 185.87/185.95 ! [V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_of__int__power,axiom, % 185.87/185.95 ! [V_n,V_z,T_a] : % 185.87/185.95 ( class_Rings_Oring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 185.87/185.95 ! [V_q,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 185.87/185.95 ! [V_q,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 185.87/185.95 ! [V_q,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 185.87/185.95 ! [V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 185.87/185.95 ! [V_q,V_p,V_x,T_a] : % 185.87/185.95 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.95 => 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)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Ints__power,axiom, % 185.87/185.95 ! [V_n_2,V_a_2,T_b] : % 185.87/185.95 ( class_Rings_Oring__1(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_lexn_Osimps_I1_J,axiom, % 185.87/185.95 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_com_Osize_I2_J,axiom, % 185.87/185.95 ! [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) ). % 185.87/185.95 % 185.87/185.95 fof(fact_com_Osize_I1_J,axiom, % 185.87/185.95 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.95 % 185.87/185.95 fof(fact_power__eq__if,axiom, % 185.87/185.95 ! [V_p,V_m] : % 185.87/185.95 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.95 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 185.87/185.95 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.95 => 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)))) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_com_Osize_I6_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_com_Osize_I5_J,axiom, % 185.87/185.95 ! [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))) ). % 185.87/185.95 % 185.87/185.95 fof(fact_power__strict__mono,axiom, % 185.87/185.95 ! [V_n,V_b,V_a,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.95 => 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))) ) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_one__less__power,axiom, % 185.87/185.95 ! [V_n,V_a,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.95 => 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))) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_power__increasing__iff,axiom, % 185.87/185.95 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2))) % 185.87/185.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_power__le__imp__le__exp,axiom, % 185.87/185.95 ! [V_n,V_m,V_a,T_a] : % 185.87/185.95 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.95 => ( 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))) % 185.87/185.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 185.87/185.95 ! [V_n,V_x] : % 185.87/185.95 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.95 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zpower__zpower,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 185.87/185.95 ! [V_n,V_x] : % 185.87/185.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.95 => 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))) ) ). % 185.87/185.95 % 185.87/185.95 fof(fact_zpower__zadd__distrib,axiom, % 185.87/185.95 ! [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)) ). % 185.87/185.95 % 185.87/185.95 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__power,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zpower__int,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__power__eq,axiom, % 185.87/185.96 ! [V_n,V_z] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 185.87/185.96 ! [V_n,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_field__power__not__zero,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 185.87/185.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__commutes,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__mult__distrib,axiom, % 185.87/185.96 ! [V_n,V_b,V_a,T_a] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__one,axiom, % 185.87/185.96 ! [V_n,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__mult,axiom, % 185.87/185.96 ! [V_n,V_m,V_a,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__one__right,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__mono,axiom, % 185.87/185.96 ! [V_n,V_b,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zero__le__power,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zero__less__power,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__eq__0__iff,axiom, % 185.87/185.96 ! [V_n_2,V_a_2,T_b] : % 185.87/185.96 ( ( class_Power_Opower(T_b) % 185.87/185.96 & class_Rings_Omult__zero(T_b) % 185.87/185.96 & class_Rings_Ono__zero__divisors(T_b) % 185.87/185.96 & class_Rings_Ozero__neq__one(T_b) ) % 185.87/185.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_one__le__power,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__0__Suc,axiom, % 185.87/185.96 ! [V_n,T_a] : % 185.87/185.96 ( ( class_Power_Opower(T_a) % 185.87/185.96 & class_Rings_Osemiring__0(T_a) ) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__inject__exp,axiom, % 185.87/185.96 ! [V_n_2,V_m_2,V_a_2,T_b] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 185.87/185.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) % 185.87/185.96 <=> V_m_2 = V_n_2 ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__Suc,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Power_Opower(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__Suc2,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__0,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Power_Opower(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__add,axiom, % 185.87/185.96 ! [V_n,V_m,V_a,T_a] : % 185.87/185.96 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 185.87/185.96 ! [V_m_2,V_x_2] : % 185.87/185.96 ( 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)) % 185.87/185.96 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__Suc__0,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__power__less__imp__less,axiom, % 185.87/185.96 ! [V_n,V_m,V_i] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 185.87/185.96 => ( 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))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__zero__less__power__iff,axiom, % 185.87/185.96 ! [V_n_2,V_x_2] : % 185.87/185.96 ( 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))) % 185.87/185.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 185.87/185.96 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_of__nat__power,axiom, % 185.87/185.96 ! [V_n,V_m,T_a] : % 185.87/185.96 ( class_Rings_Osemiring__1(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__less__imp__less__base,axiom, % 185.87/185.96 ! [V_b,V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( 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))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__le__imp__le__base,axiom, % 185.87/185.96 ! [V_b,V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( 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)))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__inject__base,axiom, % 185.87/185.96 ! [V_b,V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( 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)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.96 => V_a = V_b ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__gt1__lemma,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__less__power__Suc,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__0__left,axiom, % 185.87/185.96 ! [V_n,T_a] : % 185.87/185.96 ( ( class_Power_Opower(T_a) % 185.87/185.96 & class_Rings_Osemiring__0(T_a) ) % 185.87/185.96 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__gt1,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__strict__increasing__iff,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_b) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__less__imp__less__exp,axiom, % 185.87/185.96 ! [V_n,V_m,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => ( 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))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__strict__increasing,axiom, % 185.87/185.96 ! [V_a,V_N,V_n,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__increasing,axiom, % 185.87/185.96 ! [V_a,V_N,V_n,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__minus,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Oring__1(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__one__le__power,axiom, % 185.87/185.96 ! [V_n,V_i] : % 185.87/185.96 ( 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)) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__Suc__less,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__eq__imp__eq__base,axiom, % 185.87/185.96 ! [V_b,V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( 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) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => V_a = V_b ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__Suc__less__one,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__strict__decreasing,axiom, % 185.87/185.96 ! [V_a,V_N,V_n,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.96 => 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))) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__decreasing,axiom, % 185.87/185.96 ! [V_a,V_N,V_n,T_a] : % 185.87/185.96 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.96 => 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))) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__power__power,axiom, % 185.87/185.96 ! [T_b] : % 185.87/185.96 ( class_Power_Opower(T_b) % 185.87/185.96 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__power__div__base,axiom, % 185.87/185.96 ! [V_k,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_card__Plus__conv__if,axiom, % 185.87/185.96 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.96 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 185.87/185.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) % 185.87/185.96 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 185.87/185.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition__Integ,axiom, % 185.87/185.96 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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.96 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.87/185.96 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zminus__zminus,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zminus2,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__0,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zero,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__by__0,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__by__1,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__neg__pos__less0,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 185.87/185.96 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__self,axiom, % 185.87/185.96 ! [V_a] : % 185.87/185.96 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__mult1__if,axiom, % 185.87/185.96 ! [V_b,V_a,V_c,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self2__is__id,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self1__is__id,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__mult2,axiom, % 185.87/185.96 ! [V_b,V_a,V_c,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__mult1,axiom, % 185.87/185.96 ! [V_b,V_a,V_c,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__self,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__mono1__neg,axiom, % 185.87/185.96 ! [V_b,V_a_H,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__mono1,axiom, % 185.87/185.96 ! [V_b,V_a_H,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__neg__neg__trivial,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__mono2__neg,axiom, % 185.87/185.96 ! [V_b,V_b_H,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__nonpos__pos__le0,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( 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_ba_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__pos__pos__trivial,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__nonneg__neg__le0,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__mono2,axiom, % 185.87/185.96 ! [V_b,V_b_H,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 185.87/185.96 ! [V_ba_2,V_a_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 185.87/185.96 => ( 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_ba_2))) % 185.87/185.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),V_a_2)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 185.87/185.96 ! [V_i_2,V_k_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.96 => ( 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))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 185.87/185.96 => ( 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_ba_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__eq__0__iff,axiom, % 185.87/185.96 ! [V_k_2,V_i_2] : % 185.87/185.96 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 185.87/185.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__div__less__self,axiom, % 185.87/185.96 ! [V_k,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zmult2__eq,axiom, % 185.87/185.96 ! [V_b,V_a,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power_Opower_Opower__0,axiom, % 185.87/185.96 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 185.87/185.96 % 185.87/185.96 fof(fact_power_Opower_Opower__Suc,axiom, % 185.87/185.96 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,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_b,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__div,axiom, % 185.87/185.96 ! [V_r,V_q,V_b,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self2,axiom, % 185.87/185.96 ! [V_c,V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self1,axiom, % 185.87/185.96 ! [V_c,V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__add__self2,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__add__self1,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_finite__PlusD_I2_J,axiom, % 185.87/185.96 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 185.87/185.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_finite__PlusD_I1_J,axiom, % 185.87/185.96 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 185.87/185.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_finite__Plus,axiom, % 185.87/185.96 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.87/185.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_finite__Plus__iff,axiom, % 185.87/185.96 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 185.87/185.96 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__div__eq,axiom, % 185.87/185.96 ! [V_r_1,V_y,V_b_1,V_a_1] : % 185.87/185.96 ( 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) % 185.87/185.96 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.87/185.96 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__zdiv,axiom, % 185.87/185.96 ! [V_k_2,V_n_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 185.87/185.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.96 => ! [B_i] : % 185.87/185.96 ( ? [B_j] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 185.87/185.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ! [B_i] : % 185.87/185.96 ( ? [B_j] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_card__Plus,axiom, % 185.87/185.96 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.87/185.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_norm__frac_Osimps,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) ) % 185.87/185.96 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_UNIV__Plus__UNIV,axiom, % 185.87/185.96 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_OAbs__image,axiom, % 185.87/185.96 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_ORep__range,axiom, % 185.87/185.96 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__le__mono,axiom, % 185.87/185.96 ! [V_k,V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__le__dividend,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult2__eq,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__1,axiom, % 185.87/185.96 ! [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 ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__less,axiom, % 185.87/185.96 ! [V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__mult__div__cancel__disj,axiom, % 185.87/185.96 ! [V_n,V_m,V_k] : % 185.87/185.96 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__int,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__le__mono2,axiom, % 185.87/185.96 ! [V_k,V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self__is__m,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => 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 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult__self1__is__m,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => 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 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__mult__div__cancel1,axiom, % 185.87/185.96 ! [V_n,V_m,V_k] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__less__dividend,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__geq,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__if,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__div,axiom, % 185.87/185.96 ! [V_k_2,V_n_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 185.87/185.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.87/185.96 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => ! [B_i,B_j] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 185.87/185.96 => ( 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) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__div__distrib,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_ORep__inject,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 185.87/185.96 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_ORep__inverse,axiom, % 185.87/185.96 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_le__div__geq,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__div_H,axiom, % 185.87/185.96 ! [V_n_2,V_m_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 185.87/185.96 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 185.87/185.96 | ? [B_q] : % 185.87/185.96 ( 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)) % 185.87/185.96 & 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)))) % 185.87/185.96 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__div__lemma,axiom, % 185.87/185.96 ! [V_m_2,V_q_2,V_n_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.87/185.96 => ( ( 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)) % 185.87/185.96 & 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)))) ) % 185.87/185.96 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_OAbs__inject,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 185.87/185.96 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 185.87/185.96 <=> V_x_2 = V_y_2 ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_OAbs__inverse,axiom, % 185.87/185.96 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 185.87/185.96 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_type__definition_ORep,axiom, % 185.87/185.96 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 185.87/185.96 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Plus__eq__empty__conv,axiom, % 185.87/185.96 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.96 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) % 185.87/185.96 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.96 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_z3div__def,axiom, % 185.87/185.96 ! [V_k,V_l] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_norm__frac_Opsimps,axiom, % 185.87/185.96 ! [V_ba_2,V_a_2] : % 185.87/185.96 ( 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_ba_2))) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) ) % 185.87/185.96 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.96 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult2__lemma,axiom, % 185.87/185.96 ! [V_c,V_r,V_q,V_b,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => 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)))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__step,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__add1__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__mod__distrib,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zpower__zmod,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( c_Nat__Transfer_Ois__nat(V_x) % 185.87/185.96 => ( c_Nat__Transfer_Ois__nat(V_y) % 185.87/185.96 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__less__eq__dividend,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__less,axiom, % 185.87/185.96 ! [V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__int,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__diff__cong,axiom, % 185.87/185.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__diff__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__diff__left__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__diff__right__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiff__zmod__left,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiff__zmod__right,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__distrib2,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__distrib,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__right__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zmult1__eq,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__left__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__mult1,axiom, % 185.87/185.96 ! [V_b,V_a,V_c,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__mult2,axiom, % 185.87/185.96 ! [V_b,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__simps_I3_J,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__simps_I4_J,axiom, % 185.87/185.96 ! [V_b,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__cong,axiom, % 185.87/185.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__self2,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__self1,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__right__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__left__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__eq,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__simps_I2_J,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__simps_I1_J,axiom, % 185.87/185.96 ! [V_b,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__add__cong,axiom, % 185.87/185.96 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__minus__eq,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__minus__cong,axiom, % 185.87/185.96 ! [V_a_H,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Oring__div(T_a) % 185.87/185.96 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zminus__zmod,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus__zminus,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus2,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__0,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zero,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__by__0,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__self,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__self,axiom, % 185.87/185.96 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mod__trivial,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_accp__downward,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2,V_r_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_ba_2)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 185.87/185.96 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_accp_Oequations,axiom, % 185.87/185.96 ! [V_a_2,V_r_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 185.87/185.96 <=> ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 185.87/185.96 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_accp_Osimps,axiom, % 185.87/185.96 ! [V_a_2,V_r_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 185.87/185.96 <=> ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 185.87/185.96 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_accp__wfPD,axiom, % 185.87/185.96 ! [V_x_2,V_r_2,T_b] : % 185.87/185.96 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.87/185.96 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_wfP__accp__iff,axiom, % 185.87/185.96 ! [V_r_2,T_b] : % 185.87/185.96 ( c_Wellfounded_OwfP(T_b,V_r_2) % 185.87/185.96 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self2__is__0,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self1__is__0,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self2,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self1,axiom, % 185.87/185.96 ! [V_b,V_c,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__by__1,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__div__trivial,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__Suc,axiom, % 185.87/185.96 ! [V_n,V_m] : % 185.87/185.96 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.96 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__1,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__less__divisor,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__eq__0__iff,axiom, % 185.87/185.96 ! [V_d_2,V_m_2] : % 185.87/185.96 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__le__nonneg__dividend,axiom, % 185.87/185.96 ! [V_k,V_m] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 185.87/185.96 ! [V_y,V_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_neg__mod__bound,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__mod__bound,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__geq,axiom, % 185.87/185.96 ! [V_n,V_m] : % 185.87/185.96 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__if,axiom, % 185.87/185.96 ! [V_n,V_m] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self3,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mult1__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult2__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_le__mod__geq,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__eq__0__iff,axiom, % 185.87/185.96 ! [V_d_2,V_m_2] : % 185.87/185.96 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Divides_Omod__div__equality_H,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mult__div__cancel,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mod__equality_H,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus2__not__zero,axiom, % 185.87/185.96 ! [V_l,V_k] : % 185.87/185.96 ( 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) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus1__not__zero,axiom, % 185.87/185.96 ! [V_l,V_k] : % 185.87/185.96 ( 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) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_DIVISION__BY__ZERO,axiom, % 185.87/185.96 ! [V_a] : % 185.87/185.96 ( 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) % 185.87/185.96 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zdiv__trivial,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zadd1__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__div__mod,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__div__equality2,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__div__equality,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mod__equality2,axiom, % 185.87/185.96 ! [V_c,V_a,V_b,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__mod__equality,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Divides_Osemiring__div(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__le__divisor,axiom, % 185.87/185.96 ! [V_m,V_n] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__mult__self4,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__neg__neg__trivial,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_neg__mod__conj,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( 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))) % 185.87/185.96 & 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_neg__mod__sign,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__pos__trivial,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__mod__conj,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => ( 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))) % 185.87/185.96 & 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pos__mod__sign,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus2__eq__if,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zminus1__eq__if,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zdiv__equality,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zmult1__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zmod__equality,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zmod__equality2,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_accp__subset,axiom, % 185.87/185.96 ! [V_R2_2,V_R1_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult__div__cancel,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zdiv__equality_H,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__mod,axiom, % 185.87/185.96 ! [V_r,V_q,V_b,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__lemma,axiom, % 185.87/185.96 ! [V_q,V_b,V_r,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 185.87/185.96 => 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__mod,axiom, % 185.87/185.96 ! [V_k_2,V_n_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 185.87/185.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 185.87/185.96 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => ! [B_i,B_j] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 185.87/185.96 => ( 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) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__neg__trivial,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( 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))) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Suc__times__mod__eq,axiom, % 185.87/185.96 ! [V_m,V_k] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__div__mod,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__mod__eq,axiom, % 185.87/185.96 ! [V_y,V_q_1,V_b_1,V_a_1] : % 185.87/185.96 ( 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) % 185.87/185.96 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 185.87/185.96 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult2__lemma__aux2,axiom, % 185.87/185.96 ! [V_q,V_r,V_b,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult2__lemma__aux1,axiom, % 185.87/185.96 ! [V_q,V_r,V_b,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult2__lemma__aux4,axiom, % 185.87/185.96 ! [V_q,V_b,V_r,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult2__lemma__aux3,axiom, % 185.87/185.96 ! [V_q,V_b,V_r,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__zmod,axiom, % 185.87/185.96 ! [V_k_2,V_n_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 185.87/185.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 185.87/185.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.96 => ! [B_i,B_j] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 185.87/185.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ! [B_i,B_j] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmod__zmult2__eq,axiom, % 185.87/185.96 ! [V_b,V_a,V_c] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zminus2__eq__if,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) % 185.87/185.96 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zdiv__zminus1__eq__if,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) % 185.87/185.96 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zadd1__lemma,axiom, % 185.87/185.96 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( 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))) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__neg__lemma,axiom, % 185.87/185.96 ! [V_n_2,V_Pa_2,V_k_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(V_Pa_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))) % 185.87/185.96 <=> ! [B_i,B_j] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__pos__lemma,axiom, % 185.87/185.96 ! [V_n_2,V_Pa_2,V_k_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(V_Pa_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))) % 185.87/185.96 <=> ! [B_i,B_j] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 185.87/185.96 & 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) ) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zmult1__lemma,axiom, % 185.87/185.96 ! [V_a,V_r,V_q,V_c,V_b] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_z3mod__def,axiom, % 185.87/185.96 ! [V_k,V_l] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 185.87/185.96 ! [V_a,V_r,V_q,V_c,V_b] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 185.87/185.96 ! [V_c,V_r,V_q,V_b,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.87/185.96 => 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)))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__add1__eq,axiom, % 185.87/185.96 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( 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))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 185.87/185.96 => 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)))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__unique,axiom, % 185.87/185.96 ! [V_qr_H,V_qr,V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 185.87/185.96 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 185.87/185.96 => V_qr = V_qr_H ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 185.87/185.96 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__eq,axiom, % 185.87/185.96 ! [V_qr,V_n,V_m] : % 185.87/185.96 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 185.87/185.96 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__eq,axiom, % 185.87/185.96 ! [V_r,V_q,V_n,V_m] : % 185.87/185.96 ( 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))) % 185.87/185.96 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__eq,axiom, % 185.87/185.96 ! [V_r,V_q,V_n,V_m] : % 185.87/185.96 ( 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))) % 185.87/185.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel,axiom, % 185.87/185.96 ! [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)))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_norm__frac_Opinduct,axiom, % 185.87/185.96 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( ! [B_a,B_b] : % 185.87/185.96 ( 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))) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_negDivAlg__div__mod,axiom, % 185.87/185.96 ! [V_l,V_k] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_posDivAlg__div__mod,axiom, % 185.87/185.96 ! [V_l,V_k] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__mod__div,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_posDivAlg__0,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_negDivAlg__correct,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__correct,axiom, % 185.87/185.96 ! [V_a,V_b] : % 185.87/185.96 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_posDivAlg__correct,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__def,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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)) ) % 185.87/185.96 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.96 => 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))) ) ) ) ) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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))) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_com_Osize_I12_J,axiom, % 185.87/185.96 ! [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))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_com_Osize_I13_J,axiom, % 185.87/185.96 ! [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))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__gen__delta,axiom, % 185.87/185.96 ! [V_ca_2,V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_ba_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__timesf,axiom, % 185.87/185.96 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_of__int__setprod,axiom, % 185.87/185.96 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.96 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 & class_Rings_Oring__1(T_b) ) % 185.87/185.96 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 185.87/185.96 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__setprod,axiom, % 185.87/185.96 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 185.87/185.96 % 185.87/185.96 fof(fact_of__nat__setprod,axiom, % 185.87/185.96 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.96 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 & class_Rings_Osemiring__1(T_b) ) % 185.87/185.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__cartesian__product,axiom, % 185.87/185.96 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__1,axiom, % 185.87/185.96 ! [V_A_2,T_c,T_b] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 185.87/185.96 ! [V_A_2,V_f_2,T_b] : % 185.87/185.96 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.96 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__zero,axiom, % 185.87/185.96 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Rings_Ocomm__semiring__1(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( ? [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.96 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__zero__iff,axiom, % 185.87/185.96 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( ( class_Rings_Ocomm__semiring__1(T_c) % 185.87/185.96 & class_Rings_Ono__zero__divisors(T_c) ) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) % 185.87/185.96 <=> ? [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.96 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__empty,axiom, % 185.87/185.96 ! [V_f_2,T_c,T_b] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oempty,axiom, % 185.87/185.96 ! [V_g_2,T_c,T_b] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_b) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__infinite,axiom, % 185.87/185.96 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oinfinite,axiom, % 185.87/185.96 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__eq__1__iff,axiom, % 185.87/185.96 ! [V_f_2,V_F_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 185.87/185.96 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 185.87/185.96 <=> ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 185.87/185.96 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 185.87/185.96 ! [V_f_2,V_A_2,T_b] : % 185.87/185.96 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.96 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.96 => ( c_Nat__Transfer_Onat__set(V_A_2) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Odistrib,axiom, % 185.87/185.96 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__pos__nat__iff,axiom, % 185.87/185.96 ! [V_f_2,V_S_2,T_b] : % 185.87/185.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.96 => ( 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_b,tc_Nat_Onat),V_f_2),V_S_2))) % 185.87/185.96 <=> ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.87/185.96 => 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))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__reindex__cong,axiom, % 185.87/185.96 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.87/185.96 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.87/185.96 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.87/185.96 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__reindex,axiom, % 185.87/185.96 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.87/185.96 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__reindex__id,axiom, % 185.87/185.96 ! [V_B_2,V_f_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__delta_H,axiom, % 185.87/185.96 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__delta,axiom, % 185.87/185.96 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__constant,axiom, % 185.87/185.96 ! [V_y_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oinsert,axiom, % 185.87/185.96 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__insert,axiom, % 185.87/185.96 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Ounion__inter,axiom, % 185.87/185.96 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__Un__Int,axiom, % 185.87/185.96 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_com_Osize_I10_J,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_com_Osize_I9_J,axiom, % 185.87/185.96 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oreindex,axiom, % 185.87/185.96 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_OF__eq,axiom, % 185.87/185.96 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oeq__fold,axiom, % 185.87/185.96 ! [V_g_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_negateSnd__eq,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__int__rel__neg,axiom, % 185.87/185.96 ! [V_qr,V_b,V_a] : % 185.87/185.96 ( 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)) % 185.87/185.96 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oinsert__remove,axiom, % 185.87/185.96 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Ounion__disjoint,axiom, % 185.87/185.96 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.96 => ( 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)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__Un__disjoint,axiom, % 185.87/185.96 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.96 => ( 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)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Oremove,axiom, % 185.87/185.96 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_com_Osize_I14_J,axiom, % 185.87/185.96 ! [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))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__neg__neg,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__neg__neg,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod_Ounion__inter__neutral,axiom, % 185.87/185.96 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.96 => ( ! [B_x] : % 185.87/185.96 ( 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))) % 185.87/185.96 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__Un__one,axiom, % 185.87/185.96 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.96 => ( ! [B_x] : % 185.87/185.96 ( 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_S_2),V_T_2))) % 185.87/185.96 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_snd__conv,axiom, % 185.87/185.96 ! [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 ). % 185.87/185.96 % 185.87/185.96 fof(fact_snd__eqD,axiom, % 185.87/185.96 ! [V_a,V_y,V_x,T_a,T_b] : % 185.87/185.96 ( 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 % 185.87/185.96 => V_y = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_fst__conv,axiom, % 185.87/185.96 ! [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 ). % 185.87/185.96 % 185.87/185.96 fof(fact_fst__eqD,axiom, % 185.87/185.96 ! [V_a,V_y,V_x,T_b,T_a] : % 185.87/185.96 ( 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 % 185.87/185.96 => V_x = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_pair__collapse,axiom, % 185.87/185.96 ! [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 ). % 185.87/185.96 % 185.87/185.96 fof(fact_surjective__pairing,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__beta,axiom, % 185.87/185.96 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_prod__case__beta,axiom, % 185.87/185.96 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__comp__eq,axiom, % 185.87/185.96 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__def,axiom, % 185.87/185.96 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_split__comp,axiom, % 185.87/185.96 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_prod__eqI,axiom, % 185.87/185.96 ! [V_q,V_p,T_b,T_a] : % 185.87/185.96 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 185.87/185.96 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 185.87/185.96 => V_p = V_q ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Pair__fst__snd__eq,axiom, % 185.87/185.96 ! [T_c,T_b,V_t_2,V_s_2] : % 185.87/185.96 ( V_s_2 = V_t_2 % 185.87/185.96 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 185.87/185.96 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_The__split,axiom, % 185.87/185.96 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_fst__def,axiom, % 185.87/185.96 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ). % 185.87/185.96 % 185.87/185.96 fof(fact_snd__def,axiom, % 185.87/185.96 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ). % 185.87/185.96 % 185.87/185.96 fof(fact_vimage__Times,axiom, % 185.87/185.96 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_fst__eq__Domain,axiom, % 185.87/185.96 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__int__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__int__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_snd__eq__Range,axiom, % 185.87/185.96 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ). % 185.87/185.96 % 185.87/185.96 fof(fact_fst__image__times,axiom, % 185.87/185.96 ! [V_A_2,T_c,T_b,V_B_2] : % 185.87/185.96 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.96 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.96 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.96 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_snd__image__times,axiom, % 185.87/185.96 ! [V_B_2,T_c,T_b,V_A_2] : % 185.87/185.96 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.96 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.96 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.96 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = V_B_2 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__neg__pos,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__neg__pos,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__pos__pos,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__pos,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__pos__neg,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__neg,axiom, % 185.87/185.96 ! [V_b,V_a] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.96 => 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)))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_prod__size__simp,axiom, % 185.87/185.96 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,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_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_conjI__realizer,axiom, % 185.87/185.96 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 185.87/185.96 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 185.87/185.96 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) % 185.87/185.96 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_exI__realizer,axiom, % 185.87/185.96 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 185.87/185.96 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 185.87/185.96 ! [V_f_2,V_A_2,T_b] : % 185.87/185.96 ( ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.96 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_reduction__pair__def,axiom, % 185.87/185.96 ! [V_Pa_2,T_b] : % 185.87/185.96 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.87/185.96 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)) % 185.87/185.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_reduction__pair__lemma,axiom, % 185.87/185.96 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 185.87/185.96 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) % 185.87/185.96 => ( c_Wellfounded_Owf(T_b,V_S_2) % 185.87/185.96 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__nat__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__nat__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divmod__nat__rel__def,axiom, % 185.87/185.96 ! [V_qr_2,V_n_2,V_m_2] : % 185.87/185.96 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 185.87/185.96 <=> ( 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)) % 185.87/185.96 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.96 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.87/185.96 => ( 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))) % 185.87/185.96 & 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)) ) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 185.87/185.96 => ( 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))) % 185.87/185.96 & 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))) ) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__pos__neg__1__number__of,axiom, % 185.87/185.96 ! [V_w] : % 185.87/185.96 ( 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))) % 185.87/185.96 => 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))))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__neg__1__number__of,axiom, % 185.87/185.96 ! [V_w] : % 185.87/185.96 ( 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))) % 185.87/185.96 => 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))))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__Sigma,axiom, % 185.87/185.96 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 185.87/185.96 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( ! [B_x] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_div__pos__pos__1__number__of,axiom, % 185.87/185.96 ! [V_w] : % 185.87/185.96 ( 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))) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__eq__number__of__int__code,axiom, % 185.87/185.96 ! [V_l_2,V_k_2] : % 185.87/185.96 ( 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))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__number__of__int__code,axiom, % 185.87/185.96 ! [V_l_2,V_k_2] : % 185.87/185.96 ( 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))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_of__nat__number__of__lemma,axiom, % 185.87/185.96 ! [V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => ( ( 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))) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_minus__numeral__code_I5_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_eq__number__of,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,T_b] : % 185.87/185.96 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.96 & class_Int_Oring__char__0(T_b) ) % 185.87/185.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.87/185.96 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__reorient,axiom, % 185.87/185.96 ! [V_x_2,V_w_2,T_b] : % 185.87/185.96 ( class_Int_Onumber(T_b) % 185.87/185.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 185.87/185.96 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__is__id,axiom, % 185.87/185.96 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 185.87/185.96 % 185.87/185.96 fof(fact_times__numeral__code_I5_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_plus__numeral__code_I9_J,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_of__int__number__of__eq,axiom, % 185.87/185.96 ! [V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__eq,axiom, % 185.87/185.96 ! [V_k,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__number__of__def,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_le__number__of__eq__not__less,axiom, % 185.87/185.96 ! [V_w_2,V_v_2,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Orderings_Olinorder(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_right__distrib__number__of,axiom, % 185.87/185.96 ! [V_c,V_b,V_v,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Rings_Osemiring(T_b) ) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_left__distrib__number__of,axiom, % 185.87/185.96 ! [V_v,V_b,V_a,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Rings_Osemiring(T_b) ) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_left__diff__distrib__number__of,axiom, % 185.87/185.96 ! [V_v,V_b,V_a,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Rings_Oring(T_b) ) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_right__diff__distrib__number__of,axiom, % 185.87/185.96 ! [V_c,V_b,V_v,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Rings_Oring(T_b) ) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_le__number__of,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,T_b] : % 185.87/185.96 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.96 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__number__of,axiom, % 185.87/185.96 ! [V_y_2,V_x_2,T_b] : % 185.87/185.96 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.96 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_min__number__of,axiom, % 185.87/185.96 ! [V_v,V_u,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Orderings_Oord(T_b) ) % 185.87/185.96 => ( ( 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))) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_max__number__of,axiom, % 185.87/185.96 ! [V_v,V_u,T_b] : % 185.87/185.96 ( ( class_Int_Onumber(T_b) % 185.87/185.96 & class_Orderings_Oord(T_b) ) % 185.87/185.96 => ( ( 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))) % 185.87/185.96 => 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) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => 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) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_add__number__of__left,axiom, % 185.87/185.96 ! [V_z,V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_add__number__of__eq,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__add,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mult__number__of__left,axiom, % 185.87/185.96 ! [V_z,V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_arith__simps_I32_J,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__mult,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__diff,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_arith__simps_I30_J,axiom, % 185.87/185.96 ! [V_w,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__minus,axiom, % 185.87/185.96 ! [V_w,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Ints__number__of,axiom, % 185.87/185.96 ! [V_w_2,T_b] : % 185.87/185.96 ( class_Int_Onumber__ring(T_b) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_add__number__of__diff1,axiom, % 185.87/185.96 ! [V_c,V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_minus__number__of__mult,axiom, % 185.87/185.96 ! [V_z,V_w,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_diff__number__of__eq,axiom, % 185.87/185.96 ! [V_w,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_minus__numeral__code_I6_J,axiom, % 185.87/185.96 ! [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))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_add__number__of__diff2,axiom, % 185.87/185.96 ! [V_w,V_c,V_v,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_int__eq__iff__number__of,axiom, % 185.87/185.96 ! [V_v_2,V_m_2] : % 185.87/185.96 ( 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) % 185.87/185.96 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 185.87/185.96 & 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))) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_mod__pos__pos__1__number__of,axiom, % 185.87/185.96 ! [V_w] : % 185.87/185.96 ( 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))) % 185.87/185.96 => 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))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_one__div__nat__number__of,axiom, % 185.87/185.96 ! [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))) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__number__of__odd__number__of,axiom, % 185.87/185.96 ! [V_v_2,V_w_2,T_b] : % 185.87/185.96 ( class_Int_Onumber__ring(T_b) % 185.87/185.96 => ( ( 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))) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__diff1,axiom, % 185.87/185.96 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Fields_Ofield(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setsum__nonneg__0,axiom, % 185.87/185.96 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 185.87/185.96 ( class_Groups_Oordered__ab__group__add(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.87/185.96 => ( ! [B_i] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 185.87/185.96 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 185.87/185.96 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_minus__divide__left,axiom, % 185.87/185.96 ! [V_b,V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__1,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_diff__divide__distrib,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_times__divide__eq__right,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_add__divide__distrib,axiom, % 185.87/185.96 ! [V_c,V_b,V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__zero__left,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__zero,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_rel__simps_I51_J,axiom, % 185.87/185.96 ! [V_l_2,V_k_2] : % 185.87/185.96 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 185.87/185.96 <=> V_k_2 = V_l_2 ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__int__code_I16_J,axiom, % 185.87/185.96 ! [V_k2_2,V_k1_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_rel__simps_I17_J,axiom, % 185.87/185.96 ! [V_l_2,V_k_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_rel__simps_I34_J,axiom, % 185.87/185.96 ! [V_l_2,V_k_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__eq__int__code_I16_J,axiom, % 185.87/185.96 ! [V_k2_2,V_k1_2] : % 185.87/185.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__divide,axiom, % 185.87/185.96 ! [V_n,V_b,V_a,T_a] : % 185.87/185.96 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setsum__divide__distrib,axiom, % 185.87/185.96 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.96 ( class_Fields_Ofield(T_b) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonzero__eq__divide__eq,axiom, % 185.87/185.96 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_b) % 185.87/185.96 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.87/185.96 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonzero__divide__eq__eq,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_b) % 185.87/185.96 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 185.87/185.96 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__eq__imp,axiom, % 185.87/185.96 ! [V_a,V_b,V_c,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_eq__divide__imp,axiom, % 185.87/185.96 ! [V_b,V_a,V_c,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 185.87/185.96 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__self__if,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 185.87/185.96 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 185.87/185.96 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__self,axiom, % 185.87/185.96 ! [V_a,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_right__inverse__eq,axiom, % 185.87/185.96 ! [V_a_2,V_ba_2,T_b] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_b) % 185.87/185.96 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2) = c_Groups_Oone__class_Oone(T_b) % 185.87/185.96 <=> V_a_2 = V_ba_2 ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonzero__minus__divide__right,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonzero__minus__divide__divide,axiom, % 185.87/185.96 ! [V_a,V_b,T_a] : % 185.87/185.96 ( class_Rings_Odivision__ring(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nonzero__power__divide,axiom, % 185.87/185.96 ! [V_n,V_a,V_b,T_a] : % 185.87/185.96 ( class_Fields_Ofield(T_a) % 185.87/185.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.96 => 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)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__one__over,axiom, % 185.87/185.96 ! [V_n,V_a,T_a] : % 185.87/185.96 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.96 => 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) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_bin__less__0__simps_I4_J,axiom, % 185.87/185.96 ! [V_w_2] : % 185.87/185.96 ( 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))) % 185.87/185.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_Bit1__def,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__number__of,axiom, % 185.87/185.96 ! [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) ). % 185.87/185.96 % 185.87/185.96 fof(fact_nat__number__of__def,axiom, % 185.87/185.96 ! [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)) ). % 185.87/185.96 % 185.87/185.96 fof(fact_setprod__dividef,axiom, % 185.87/185.96 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.96 ( class_Fields_Ofield__inverse__zero(T_c) % 185.87/185.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_eq__divide__eq__number__of1,axiom, % 185.87/185.96 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.87/185.96 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) % 185.87/185.96 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_ba_2 ) % 185.87/185.96 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_eq__divide__eq__number__of,axiom, % 185.87/185.96 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.87/185.96 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.87/185.96 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_ba_2 ) % 185.87/185.96 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__eq__eq__number__of,axiom, % 185.87/185.96 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.96 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 185.87/185.96 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) ) % 185.87/185.96 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__eq__eq__number__of1,axiom, % 185.87/185.96 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.87/185.96 ( ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 % 185.87/185.96 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) % 185.87/185.96 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.96 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_number__of__Bit1,axiom, % 185.87/185.96 ! [V_w,T_a] : % 185.87/185.96 ( class_Int_Onumber__ring(T_a) % 185.87/185.96 => 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)) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__number__of__odd,axiom, % 185.87/185.96 ! [V_z_2,V_w_2,T_b] : % 185.87/185.96 ( class_Int_Onumber__ring(T_b) % 185.87/185.96 => ( ( 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))) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_zpower__number__of__odd,axiom, % 185.87/185.96 ! [V_z_2,V_w_2] : % 185.87/185.96 ( ( 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))) % 185.87/185.96 => 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))) ) % 185.87/185.96 & ( ~ 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))) % 185.87/185.96 => 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) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__less__eq__number__of1,axiom, % 185.87/185.96 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.87/185.96 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 185.87/185.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_divide__less__eq__number__of,axiom, % 185.87/185.96 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.96 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__divide__eq__number__of,axiom, % 185.87/185.96 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.87/185.96 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_less__divide__eq__number__of1,axiom, % 185.87/185.96 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.87/185.96 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.96 & class_Int_Onumber(T_b) ) % 185.87/185.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 185.87/185.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_ba_2)) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 185.87/185.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.96 % 185.87/185.96 fof(fact_power__diff,axiom, % 185.87/185.96 ! [V_m,V_n,V_a,T_a] : % 185.87/185.96 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 185.87/185.97 => 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)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__divide__eq__number__of1,axiom, % 185.87/185.97 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 & class_Int_Onumber(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__divide__eq__number__of,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 & class_Int_Onumber(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__le__eq__number__of,axiom, % 185.87/185.97 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 & class_Int_Onumber(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__le__eq__number__of1,axiom, % 185.87/185.97 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 & class_Int_Onumber(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_expand__Suc,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( 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))) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_geometric__sum,axiom, % 185.87/185.97 ! [V_n_2,V_x_2,T_b] : % 185.87/185.97 ( class_Fields_Ofield(T_b) % 185.87/185.97 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),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_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__left__mono__neg,axiom, % 185.87/185.97 ! [V_c,V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__left__mono,axiom, % 185.87/185.97 ! [V_c,V_a,V_b,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__divide__le__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__le__divide__eq,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_times__divide__times__eq,axiom, % 185.87/185.97 ! [V_w,V_z,V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__divide__divide,axiom, % 185.87/185.97 ! [V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__divide__right,axiom, % 185.87/185.97 ! [V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__le__divide__iff,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__le__0__iff,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__right__mono,axiom, % 185.87/185.97 ! [V_c,V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__right__mono__neg,axiom, % 185.87/185.97 ! [V_c,V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__strict__right__mono__neg,axiom, % 185.87/185.97 ! [V_c,V_a,V_b,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__strict__right__mono,axiom, % 185.87/185.97 ! [V_c,V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__neg__neg,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__neg__pos,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__pos__neg,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__pos__pos,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__less__0__iff,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__less__divide__iff,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_frac__eq__eq,axiom, % 185.87/185.97 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 185.87/185.97 ( class_Fields_Ofield(T_b) % 185.87/185.97 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) % 185.87/185.97 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__divide__mult__cancel__left,axiom, % 185.87/185.97 ! [V_b,V_a,V_c,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__divide__mult__cancel__right,axiom, % 185.87/185.97 ! [V_b,V_a,V_c,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__eq__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.97 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 185.87/185.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) % 185.87/185.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__divide__eq,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_b) % 185.87/185.97 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 185.87/185.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) % 185.87/185.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__nonneg__pos,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__nonneg__neg,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_frac__less2,axiom, % 185.87/185.97 ! [V_z,V_w,V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 185.87/185.97 => 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))) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_frac__less,axiom, % 185.87/185.97 ! [V_z,V_w,V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 185.87/185.97 => 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))) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_frac__le,axiom, % 185.87/185.97 ! [V_z,V_w,V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 185.87/185.97 => 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))) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__nonpos__pos,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__nonpos__neg,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__strict__left__mono__neg,axiom, % 185.87/185.97 ! [V_c,V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__strict__left__mono,axiom, % 185.87/185.97 ! [V_c,V_a,V_b,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__divide__less__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__less__divide__eq,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__imp__less__div__pos,axiom, % 185.87/185.97 ! [V_x,V_z,V_y,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__imp__div__pos__less,axiom, % 185.87/185.97 ! [V_z,V_x,V_y,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__divide__less__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__less__divide__eq,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__less__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__divide__eq,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__num__frac,axiom, % 185.87/185.97 ! [V_x,V_z,V_y,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__divide__eq__iff,axiom, % 185.87/185.97 ! [V_y,V_x,V_z,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__frac__num,axiom, % 185.87/185.97 ! [V_z,V_x,V_y,T_a] : % 185.87/185.97 ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__add__eq__iff,axiom, % 185.87/185.97 ! [V_y,V_x,V_z,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__frac__eq,axiom, % 185.87/185.97 ! [V_w,V_x,V_z,V_y,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__frac__eq,axiom, % 185.87/185.97 ! [V_w,V_x,V_z,V_y,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__diff__eq__iff,axiom, % 185.87/185.97 ! [V_y,V_x,V_z,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__divide__eq__iff,axiom, % 185.87/185.97 ! [V_y,V_x,V_z,T_a] : % 185.87/185.97 ( class_Fields_Ofield(T_a) % 185.87/185.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_gt__half__sum,axiom, % 185.87/185.97 ! [V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__half__sum,axiom, % 185.87/185.97 ! [V_b,V_a,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 185.87/185.97 => 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))))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__divide__eq,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__le__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__le__divide__eq,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__divide__le__eq,axiom, % 185.87/185.97 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__imp__div__pos__le,axiom, % 185.87/185.97 ! [V_z,V_x,V_y,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__imp__le__div__pos,axiom, % 185.87/185.97 ! [V_x,V_z,V_y,T_a] : % 185.87/185.97 ( class_Fields_Olinordered__field(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_one__mod__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setprod__Un,axiom, % 185.87/185.97 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.97 ( class_Fields_Ofield(T_c) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 185.87/185.97 => ( ! [B_x] : % 185.87/185.97 ( 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))) % 185.87/185.97 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__nat__number__of__number__of,axiom, % 185.87/185.97 ! [V_w,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__int,axiom, % 185.87/185.97 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__1,axiom, % 185.87/185.97 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__0,axiom, % 185.87/185.97 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__eq__ge__0,axiom, % 185.87/185.97 ! [V_x_2] : % 185.87/185.97 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__def,axiom, % 185.87/185.97 ! [V_Z_2] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__nat,axiom, % 185.87/185.97 ! [V_z] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 185.87/185.97 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__number__of__Bit1,axiom, % 185.87/185.97 ! [V_w_2] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 185.87/185.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__nat,axiom, % 185.87/185.97 ! [V_z] : % 185.87/185.97 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 185.87/185.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__imp__number__of__eq__0,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__zminus__int,axiom, % 185.87/185.97 ! [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))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H_2,V_v_2] : % 185.87/185.97 ( 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) % 185.87/185.97 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 185.87/185.97 => 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))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 185.87/185.97 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 185.87/185.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 185.87/185.97 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__add__left,axiom, % 185.87/185.97 ! [V_k,V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_int__nat__number__of,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__nat__eq__if,axiom, % 185.87/185.97 ! [V_z_2,V_z_H_2] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_of__nat__number__of__eq,axiom, % 185.87/185.97 ! [V_v,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mod__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__Bit1,axiom, % 185.87/185.97 ! [V_w_2] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 185.87/185.97 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 185.87/185.97 => 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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__nat__number__of,axiom, % 185.87/185.97 ! [V_n,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__nat__number__of__add,axiom, % 185.87/185.97 ! [V_n,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__nat__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_v_H_2] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__number__of__Suc,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__Pls,axiom, % 185.87/185.97 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I39_J,axiom, % 185.87/185.97 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I46_J,axiom, % 185.87/185.97 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I19_J,axiom, % 185.87/185.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I2_J,axiom, % 185.87/185.97 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Pls,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Pls__right,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__Pls,axiom, % 185.87/185.97 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__pred,axiom, % 185.87/185.97 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 185.87/185.97 % 185.87/185.97 fof(fact_Pls__def,axiom, % 185.87/185.97 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__Pls,axiom, % 185.87/185.97 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I1_J,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 185.87/185.97 % 185.87/185.97 fof(fact_semiring__norm_I112_J,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of__Pls,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__numeral__0__right,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__numeral__0,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bin__less__0__simps_I1_J,axiom, % 185.87/185.97 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__Pls,axiom, % 185.87/185.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.97 % 185.87/185.97 fof(fact_semiring__norm_I113_J,axiom, % 185.87/185.97 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__is__num__zero,axiom, % 185.87/185.97 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I22_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I12_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__diff__number__of,axiom, % 185.87/185.97 ! [V_m,V_v] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__neg__number__of__Pls,axiom, % 185.87/185.97 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__add__1,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__1__add__number__of,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__iff__pred__less,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__Bit1,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pred__def,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__diff__1,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__numeral__1,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__numeral__1__right,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__Numeral0,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_semiring__norm_I110_J,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_numeral__1__eq__1,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__0__number__of,axiom, % 185.87/185.97 ! [V_v_2] : % 185.87/185.97 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__number__of__0,axiom, % 185.87/185.97 ! [V_v_2] : % 185.87/185.97 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of2,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I5_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I29_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H_2,V_v_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__numeral__1,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( ( class_Fields_Ofield(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__Numeral1,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( ( class_Fields_Ofield(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => 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 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H_2,V_v_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_one__is__num__one,axiom, % 185.87/185.97 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__numeral__1__eq__1,axiom, % 185.87/185.97 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Numeral1__eq1__nat,axiom, % 185.87/185.97 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 185.87/185.97 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__def,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__special_I3_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__special_I1_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__special_I1_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__special_I3_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__0__number__of,axiom, % 185.87/185.97 ! [V_v_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_numeral__1__eq__Suc__0,axiom, % 185.87/185.97 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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_numeral__3__eq__3,axiom, % 185.87/185.97 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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power3__eq__cube,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 185.87/185.97 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))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc3__eq__add__3,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 185.87/185.97 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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 185.87/185.97 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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of__succ,axiom, % 185.87/185.97 ! [V_k,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of__pred,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__special_I4_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__special_I2_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__special_I2_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__special_I4_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Rings_Olinordered__idom(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__special_I2_J,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__special_I3_J,axiom, % 185.87/185.97 ! [V_v,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__diff__eq__diff__pred,axiom, % 185.87/185.97 ! [V_m,V_n] : % 185.87/185.97 ( 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)) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__mult__left,axiom, % 185.87/185.97 ! [V_k,V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__nat__number__of,axiom, % 185.87/185.97 ! [V_v_H,V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__number__of__pred__iff__0,axiom, % 185.87/185.97 ! [V_v_2] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 185.87/185.97 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mod__Suc__eq__mod__add3,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__mod__eq__add3__mod,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__div__eq__add3__div,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__Suc__eq__div__add3,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__special_I1_J,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__special_I2_J,axiom, % 185.87/185.97 ! [V_v,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__number__of__Suc,axiom, % 185.87/185.97 ! [V_n_2,V_v_2] : % 185.87/185.97 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 185.87/185.97 <=> 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))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__eq__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_n_2] : % 185.87/185.97 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 185.87/185.97 <=> 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))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__Suc__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_n_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> 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))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__number__of__Suc,axiom, % 185.87/185.97 ! [V_n_2,V_v_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__Suc__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_n_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> 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))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_le__number__of__Suc,axiom, % 185.87/185.97 ! [V_n_2,V_v_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__nat__number__of,axiom, % 185.87/185.97 ! [V_v] : % 185.87/185.97 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_max__number__of__Suc,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_max__Suc__number__of,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__Suc__number__of,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__case__add__eq__if,axiom, % 185.87/185.97 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_of__int__num,axiom, % 185.87/185.97 ! [V_k_2,T_b] : % 185.87/185.97 ( class_Rings_Oring__1(T_b) % 185.87/185.97 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 185.87/185.97 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),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_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),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))))) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__case__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I44_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 185.87/185.97 <=> V_k_2 = c_Int_OPls ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I38_J,axiom, % 185.87/185.97 ! [V_l_2] : % 185.87/185.97 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 185.87/185.97 <=> c_Int_OPls = V_l_2 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Bit0__Pls,axiom, % 185.87/185.97 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Bit0__Bit0,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Bit0__def,axiom, % 185.87/185.97 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__Bit0,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__Bit0,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I7_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I48_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 185.87/185.97 <=> V_k_2 = V_l_2 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__int__code_I13_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I14_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I31_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__eq__int__code_I13_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I50_J,axiom, % 185.87/185.97 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I49_J,axiom, % 185.87/185.97 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bin__less__0__simps_I3_J,axiom, % 185.87/185.97 ! [V_w_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I21_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I27_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I32_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__eq__int__code_I14_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I10_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I4_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__int__code_I15_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I16_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Bit1__Bit0,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Bit0__Bit1,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I3_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I9_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I10_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zdiv__number__of__Bit0,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__number__of__Bit0,axiom, % 185.87/185.97 ! [V_w_2] : % 185.87/185.97 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 185.87/185.97 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pred__Bit0,axiom, % 185.87/185.97 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pred__Bit1,axiom, % 185.87/185.97 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__Bit1,axiom, % 185.87/185.97 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__Bit0,axiom, % 185.87/185.97 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__number__of__Bit0,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__case__0,axiom, % 185.87/185.97 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__case__Suc,axiom, % 185.87/185.97 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of__Bit0,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__eq__int__code_I15_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I33_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__int__code_I14_J,axiom, % 185.87/185.97 ! [V_k2_2,V_k1_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I15_J,axiom, % 185.87/185.97 ! [V_l_2,V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_card__UNIV__bool,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__Bit1,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I8_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Bit1__Bit1,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__number__of__even,axiom, % 185.87/185.97 ! [V_w_2,V_z_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zpower__number__of__even,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_double__number__of__Bit0,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of1,axiom, % 185.87/185.97 ! [V_n] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( 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)))) % 185.87/185.97 & 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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 185.87/185.97 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__number__of__even__number__of,axiom, % 185.87/185.97 ! [V_w_2,V_v_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_max__Suc2,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_max__Suc1,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__2__right,axiom, % 185.87/185.97 ! [V_z,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__2,axiom, % 185.87/185.97 ! [V_z,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_one__add__one__is__two,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__power2,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__eq__power2,axiom, % 185.87/185.97 ! [V_a_2,T_b] : % 185.87/185.97 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.87/185.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) % 185.87/185.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_numeral__2__eq__2,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_semiring__norm_I115_J,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__eq__square,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 185.87/185.97 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))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__2__eq__Suc,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__2__eq__Suc_H,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_one__power2,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__minus,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Rings_Oring__1(T_a) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__mult__2__right,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__mult__2,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__even__eq,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 185.87/185.97 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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 185.87/185.97 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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__1__add__1,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mod2__Suc__Suc,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div2__Suc__Suc,axiom, % 185.87/185.97 ! [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))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zmod__number__of__Bit0,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__self__div__2,axiom, % 185.87/185.97 ! [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 ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 185.87/185.97 ! [V_n_2,V_m_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 185.87/185.97 <=> 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_half__gt__zero,axiom, % 185.87/185.97 ! [V_r,T_a] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 185.87/185.97 => 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)))))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_half__gt__zero__iff,axiom, % 185.87/185.97 ! [V_r_2,T_b] : % 185.87/185.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 185.87/185.97 & class_Int_Onumber__ring(T_b) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__Suc,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__eq__imp__eq,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.97 => ( 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)))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => V_x = V_y ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__le__imp__le,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.97 => ( 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)))))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__le__power2,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => 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)))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__less__0,axiom, % 185.87/185.97 ! [V_a,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => ~ 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__less__power2,axiom, % 185.87/185.97 ! [V_a_2,T_b] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 185.87/185.97 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_sum__power2__eq__zero__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b) % 185.87/185.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__eq__square__number__of,axiom, % 185.87/185.97 ! [V_w,T_b] : % 185.87/185.97 ( ( class_Groups_Omonoid__mult(T_b) % 185.87/185.97 & class_Int_Onumber(T_b) ) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_less__2__cases,axiom, % 185.87/185.97 ! [V_n] : % 185.87/185.97 ( 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))))) % 185.87/185.97 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.97 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__2,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__eq__1__iff,axiom, % 185.87/185.97 ! [V_a_2,T_b] : % 185.87/185.97 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 185.87/185.97 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) % 185.87/185.97 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 185.87/185.97 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 185.87/185.97 ! [V_n,V_x,T_a] : % 185.87/185.97 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__minus__even,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Rings_Oring__1(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__Suc2,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__Suc1,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__less__imp__less,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__semidom(T_a) % 185.87/185.97 => ( 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)))))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_sum__power2__le__zero__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b))) % 185.87/185.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_sum__power2__ge__zero,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => 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))))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__sum__power2__lt__zero,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => ~ 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_sum__power2__gt__zero__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 185.87/185.97 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__sum,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__le__even__power_H,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => 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)))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__odd__eq,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Groups_Omonoid__mult(T_a) % 185.87/185.97 => 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))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 185.87/185.97 ! [V_n,V_x,T_a] : % 185.87/185.97 ( class_Rings_Ocomm__semiring__1(T_a) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__minus1__even,axiom, % 185.87/185.97 ! [V_n,T_a] : % 185.87/185.97 ( class_Rings_Oring__1(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zdiv__number__of__Bit1,axiom, % 185.87/185.97 ! [V_v,V_w] : % 185.87/185.97 ( ( 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))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ 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))) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mod2__gr__0,axiom, % 185.87/185.97 ! [V_m_2] : % 185.87/185.97 ( 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)))))) % 185.87/185.97 <=> 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__2__gt__zero,axiom, % 185.87/185.97 ! [V_n] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 185.87/185.97 => 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)))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power2__diff,axiom, % 185.87/185.97 ! [V_y,V_x,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_odd__0__le__power__imp__0__le,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => ( 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))))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_odd__power__less__zero,axiom, % 185.87/185.97 ! [V_n,V_a,T_a] : % 185.87/185.97 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__minus1__odd,axiom, % 185.87/185.97 ! [V_n,T_a] : % 185.87/185.97 ( class_Rings_Oring__1(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__n__div__2__gt__zero,axiom, % 185.87/185.97 ! [V_n] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 185.87/185.97 => 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)))))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_of__nat__double,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_a) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__zmod__mult__2,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.97 => 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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__zdiv__mult__2,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__zdiv__mult__2,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_arith__series__int,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zmod__number__of__Bit1,axiom, % 185.87/185.97 ! [V_v,V_w] : % 185.87/185.97 ( ( 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))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ 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))) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__zmod__mult__2,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_adjust__def,axiom, % 185.87/185.97 ! [V_ba_2] : c_Divides_Oadjust(V_ba_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_ba_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_ba_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))))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_adjust__eq,axiom, % 185.87/185.97 ! [V_r_2,V_q_2,V_ba_2] : hAPP(c_Divides_Oadjust(V_ba_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_ba_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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 185.87/185.97 ! [V_w] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( 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))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ 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))) % 185.87/185.97 => 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)))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg__eqn__number__of,axiom, % 185.87/185.97 ! [V_w,V_v] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( 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))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ 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))) % 185.87/185.97 => 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)))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg__eqn,axiom, % 185.87/185.97 ! [V_a,V_b] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg_Osimps,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => 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) ) % 185.87/185.97 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg_Opsimps,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2] : % 185.87/185.97 ( 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_ba_2))) % 185.87/185.97 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 185.87/185.97 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 185.87/185.97 ! [V_w] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( 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)))) % 185.87/185.97 => 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))) ) % 185.87/185.97 & ( ~ 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)))) % 185.87/185.97 => 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)))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg__eqn__number__of,axiom, % 185.87/185.97 ! [V_w,V_v] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( 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)))) % 185.87/185.97 => 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))) ) % 185.87/185.97 & ( ~ 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)))) % 185.87/185.97 => 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)))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I37_J,axiom, % 185.87/185.97 c_Int_OPls != c_Int_OMin ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I40_J,axiom, % 185.87/185.97 c_Int_OMin != c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I7_J,axiom, % 185.87/185.97 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I24_J,axiom, % 185.87/185.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I47_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 185.87/185.97 <=> V_k_2 = c_Int_OMin ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I43_J,axiom, % 185.87/185.97 ! [V_l_2] : % 185.87/185.97 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 185.87/185.97 <=> c_Int_OMin = V_l_2 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Bit1__Min,axiom, % 185.87/185.97 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I45_J,axiom, % 185.87/185.97 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I42_J,axiom, % 185.87/185.97 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bin__less__0__simps_I2_J,axiom, % 185.87/185.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I23_J,axiom, % 185.87/185.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I20_J,axiom, % 185.87/185.97 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I26_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I30_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I3_J,axiom, % 185.87/185.97 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I6_J,axiom, % 185.87/185.97 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I13_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I9_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I28_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I8_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__number__of__Pls__Min,axiom, % 185.87/185.97 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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int_OMin__def,axiom, % 185.87/185.97 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__Min,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_neg__number__of__Min,axiom, % 185.87/185.97 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pred__Pls,axiom, % 185.87/185.97 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Min__right,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_add__Min,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pred__Min,axiom, % 185.87/185.97 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 185.87/185.97 % 185.87/185.97 fof(fact_succ__Min,axiom, % 185.87/185.97 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I2_J,axiom, % 185.87/185.97 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__minus1,axiom, % 185.87/185.97 ! [V_z,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_mult__minus1__right,axiom, % 185.87/185.97 ! [V_z,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_number__of__Min,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_arith__simps_I31_J,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_divide__minus1,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I11_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_rel__simps_I25_J,axiom, % 185.87/185.97 ! [V_k_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zmod__minus1__right,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I4_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus__Min,axiom, % 185.87/185.97 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 185.87/185.97 % 185.87/185.97 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 185.87/185.97 ! [V_n,V_m] : % 185.87/185.97 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.97 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.97 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zmult__eq__1__iff,axiom, % 185.87/185.97 ! [V_n_2,V_m_2] : % 185.87/185.97 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.97 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 185.87/185.97 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 185.87/185.97 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 185.87/185.97 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I6_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_diff__bin__simps_I5_J,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_of__int__m1,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zdiv__minus1__right,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_minus1__divide,axiom, % 185.87/185.97 ! [V_x,T_a] : % 185.87/185.97 ( ( class_Fields_Ofield__inverse__zero(T_a) % 185.87/185.97 & class_Int_Onumber__ring(T_a) ) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__eq__minus1,axiom, % 185.87/185.97 ! [V_b] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg__minus1,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__pos__neg__trivial,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 185.87/185.97 => ( 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))) % 185.87/185.97 => 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) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zmod__minus1,axiom, % 185.87/185.97 ! [V_b] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__m1__even,axiom, % 185.87/185.97 ! [V_n,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_power__m1__odd,axiom, % 185.87/185.97 ! [V_n,T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => 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) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg_Osimps,axiom, % 185.87/185.97 ! [V_b,V_a] : % 185.87/185.97 ( ( ( 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))) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ ( 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))) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg__eqn,axiom, % 185.87/185.97 ! [V_a,V_b] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 185.87/185.97 => ( ( 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))) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ 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))) % 185.87/185.97 => 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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg_Opsimps,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2] : % 185.87/185.97 ( 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_ba_2))) % 185.87/185.97 => ( ( ( 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_ba_2))) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => c_Divides_OnegDivAlg(V_a_2,V_ba_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_ba_2)) ) % 185.87/185.97 & ( ~ ( 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_ba_2))) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => c_Divides_OnegDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_posDivAlg_Opinduct,axiom, % 185.87/185.97 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ! [B_a,B_b] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_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))) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__rec__add__eq__if,axiom, % 185.87/185.97 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),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_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,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))))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__rec__0,axiom, % 185.87/185.97 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__rec__Suc,axiom, % 185.87/185.97 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b,V_f1_2,V_f2_2),V_nat_2)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__rec__number__of,axiom, % 185.87/185.97 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_negDivAlg_Opinduct,axiom, % 185.87/185.97 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ! [B_a,B_b] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ( ( ~ ( 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))) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_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))) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 185.87/185.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__special_I4_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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))))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__special_I2_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_iszero__0,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_a) % 185.87/185.97 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_iszero__def,axiom, % 185.87/185.97 ! [V_z_2,T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => ( c_Int_Oiszero(T_b,V_z_2) % 185.87/185.97 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__iszero__1,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_a) % 185.87/185.97 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_iszero__Numeral0,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_iszero__number__of__Bit1,axiom, % 185.87/185.97 ! [V_w,T_a] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_a) % 185.87/185.97 & class_Int_Oring__char__0(T_a) ) % 185.87/185.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_iszero__number__of__Bit0,axiom, % 185.87/185.97 ! [V_w_2,T_b] : % 185.87/185.97 ( ( class_Int_Onumber__ring(T_b) % 185.87/185.97 & class_Int_Oring__char__0(T_b) ) % 185.87/185.97 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nonzero__number__of__Min,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_not__iszero__Numeral1,axiom, % 185.87/185.97 ! [T_a] : % 185.87/185.97 ( class_Int_Onumber__ring(T_a) % 185.87/185.97 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__number__of__eq,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__special_I1_J,axiom, % 185.87/185.97 ! [V_y_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_eq__special_I3_J,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.97 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_int__of__code,axiom, % 185.87/185.97 ! [V_k] : % 185.87/185.97 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.97 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.97 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.97 => ( ( 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) % 185.87/185.97 => 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)))))) ) % 185.87/185.97 & ( 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) % 185.87/185.97 => 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)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nats__number__of,axiom, % 185.87/185.97 ! [V_w_2,T_b] : % 185.87/185.97 ( class_Int_Onumber__ring(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_one__code__numeral__code,axiom, % 185.87/185.97 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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral__zero__minus__one,axiom, % 185.87/185.97 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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_zero__code__numeral__code,axiom, % 185.87/185.97 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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nats__0,axiom, % 185.87/185.97 ! [T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nats__add,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nats__mult,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Nats__1,axiom, % 185.87/185.97 ! [T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_of__nat__in__Nats,axiom, % 185.87/185.97 ! [V_n_2,T_b] : % 185.87/185.97 ( class_Rings_Osemiring__1(T_b) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_div__mod__code__numeral__def,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_nat__of__aux__code,axiom, % 185.87/185.97 ! [V_n,V_i] : % 185.87/185.97 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.97 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 185.87/185.97 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osize_I1_J,axiom, % 185.87/185.97 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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osize_I2_J,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__nonneg__leq__bound,axiom, % 185.87/185.97 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_c) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 185.87/185.97 => ( ! [B_i] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 185.87/185.97 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 185.87/185.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_greaterThan__0,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_greaterThan__eq__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 185.87/185.97 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Oinject,axiom, % 185.87/185.97 ! [V_code__numeral_H_2,V_code__numeral_2] : % 185.87/185.97 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 185.87/185.97 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osimps_I3_J,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osimps_I2_J,axiom, % 185.87/185.97 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 185.87/185.97 % 185.87/185.97 fof(fact_greaterThan__iff,axiom, % 185.87/185.97 ! [V_k_2,V_i_2,T_b] : % 185.87/185.97 ( class_Orderings_Oord(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_greaterThan__subset__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Suc__code__numeral__minus__one,axiom, % 185.87/185.97 ! [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 ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I11_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__uminus__greaterThan,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.97 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__uminus__lessThan,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.97 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I5_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_greaterThan__Suc,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osize_I4_J,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_sum__diff__distrib,axiom, % 185.87/185.97 ! [V_n_2,V_Pa_2,V_Q_2] : % 185.87/185.97 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x))) % 185.87/185.97 => 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_Pa_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_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 185.87/185.97 ! [V_N_2,V_h_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.97 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_code__numeral_Osize_I3_J,axiom, % 185.87/185.97 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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__Suc,axiom, % 185.87/185.97 ! [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)))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 185.87/185.97 ! [V_N_2,V_h_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.97 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__natinterval__difff,axiom, % 185.87/185.97 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.87/185.97 ( class_Groups_Oab__group__add(T_b) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b),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)))) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_finite__atLeastAtMost,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int__atLeastAtMostR2,axiom, % 185.87/185.97 ! [V_d_2,V_ca_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int__atLeastAtMostL2,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_ba_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__eq__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 185.87/185.97 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I13_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ex__nat__less,axiom, % 185.87/185.97 ! [V_Pa_2,V_n_2] : % 185.87/185.97 ( ? [B_m] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 185.87/185.97 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.87/185.97 <=> ? [B_x] : % 185.87/185.97 ( 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))) % 185.87/185.97 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_all__nat__less,axiom, % 185.87/185.97 ! [V_Pa_2,V_n_2] : % 185.87/185.97 ( ! [B_m] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 185.87/185.97 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 185.87/185.97 <=> ! [B_x] : % 185.87/185.97 ( 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))) % 185.87/185.97 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastatMost__empty__iff,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastatMost__empty__iff2,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) % 185.87/185.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastatMost__empty,axiom, % 185.87/185.97 ! [V_a_2,V_ba_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) % 185.87/185.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastatMost__subset__iff,axiom, % 185.87/185.97 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 185.87/185.97 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastAtMost__singleton_H,axiom, % 185.87/185.97 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( V_a_2 = V_ba_2 % 185.87/185.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastAtMost__singleton__iff,axiom, % 185.87/185.97 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 185.87/185.97 <=> ( V_a_2 = V_ba_2 % 185.87/185.97 & V_ba_2 = V_ca_2 ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastAtMost__singleton,axiom, % 185.87/185.97 ! [V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__uminus__atLeastAtMost,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.97 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__Suc__atLeastAtMost,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 185.87/185.97 ! [V_n_2,V_m_2,V_f_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 185.87/185.97 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__add__atLeastAtMost,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__iff,axiom, % 185.87/185.97 ! [V_k_2,V_i_2,T_b] : % 185.87/185.97 ( class_Orderings_Oord(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__subset__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__0,axiom, % 185.87/185.97 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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_card__atLeastAtMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastAtMostSuc__conv,axiom, % 185.87/185.97 ! [V_n_2,V_m_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Compl__atLeast,axiom, % 185.87/185.97 ! [V_k_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Compl__lessThan,axiom, % 185.87/185.97 ! [V_k_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 185.87/185.97 ! [V_k_2,V_f_2] : % 185.87/185.97 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.97 => 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)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast__Suc__greaterThan,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I21_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I15_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int__atLeastAtMost,axiom, % 185.87/185.97 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastatMost__psubset__iff,axiom, % 185.87/185.97 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) % 185.87/185.97 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.87/185.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) % 185.87/185.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) % 185.87/185.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_d_2)) ) ) ) % 185.87/185.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I22_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I4_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I16_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I12_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I13_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I7_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__head__Suc,axiom, % 185.87/185.97 ! [V_f_2,V_n_2,V_m_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I14_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I8_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_UN__atLeast__UNIV,axiom, % 185.87/185.97 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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I6_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__cl__ivl__Suc,axiom, % 185.87/185.97 ! [V_f_2,V_m_2,V_n_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__head,axiom, % 185.87/185.97 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__ub__add__nat,axiom, % 185.87/185.97 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => ( 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)))) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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)))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I6_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I5_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I18_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I1_J,axiom, % 185.87/185.97 ! [V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I19_J,axiom, % 185.87/185.97 ! [V_u_2,V_m_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I12_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_gauss__sum,axiom, % 185.87/185.97 ! [V_n_2,T_b] : % 185.87/185.97 ( class_Rings_Ocomm__semiring__1(T_b) % 185.87/185.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_UN__le__eq__Un0,axiom, % 185.87/185.97 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Max_Ohom__commute,axiom, % 185.87/185.97 ! [V_N_2,V_h_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.97 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Min_Ohom__commute,axiom, % 185.87/185.97 ! [V_N_2,V_h_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 185.87/185.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 185.87/185.97 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.97 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_finite__atLeastAtMost__int,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_finite__atMost,axiom, % 185.87/185.97 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__eq__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 185.87/185.97 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 185.87/185.97 ! [V_y_2,V_x_2] : % 185.87/185.97 ( c_Nat__Transfer_Ois__nat(V_x_2) % 185.87/185.97 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeast0AtMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_lessThan__Suc__atMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_card__atMost,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__Suc,axiom, % 185.87/185.97 ! [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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__iff,axiom, % 185.87/185.97 ! [V_k_2,V_i_2,T_b] : % 185.87/185.97 ( class_Orderings_Oord(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__subset__iff,axiom, % 185.87/185.97 ! [V_y_2,V_x_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) % 185.87/185.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 185.87/185.97 ! [V_y_2,V_x_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 185.87/185.97 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Compl__greaterThan,axiom, % 185.87/185.97 ! [V_k_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Compl__atMost,axiom, % 185.87/185.97 ! [V_k_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 185.87/185.97 ! [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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_UN__atMost__UNIV,axiom, % 185.87/185.97 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)) ). % 185.87/185.97 % 185.87/185.97 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_setsum__atMost__Suc,axiom, % 185.87/185.97 ! [V_n_2,V_f_2,T_b] : % 185.87/185.97 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__0,axiom, % 185.87/185.97 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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_simp__from__to,axiom, % 185.87/185.97 ! [V_i_2,V_j_2] : % 185.87/185.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 185.87/185.97 => 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)) ) % 185.87/185.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 185.87/185.97 => 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)) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int__atLeastAtMostL1,axiom, % 185.87/185.97 ! [V_d_2,V_ba_2,V_a_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_Int__atLeastAtMostR1,axiom, % 185.87/185.97 ! [V_d_2,V_ca_2,V_ba_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I9_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_UN__le__add__shift,axiom, % 185.87/185.97 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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_b,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) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I3_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__int_I1_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__uminus__atLeast,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.97 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_image__uminus__atMost,axiom, % 185.87/185.97 ! [V_x_2,T_b] : % 185.87/185.97 ( class_Groups_Oordered__ab__group__add(T_b) % 185.87/185.97 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_card__atLeastAtMost__int,axiom, % 185.87/185.97 ! [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))) ). % 185.87/185.97 % 185.87/185.97 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 185.87/185.97 ! [V_n_2,V_m_2] : % 185.87/185.97 ( c_Nat__Transfer_Ois__nat(V_m_2) % 185.87/185.97 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 185.87/185.97 => 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))) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I2_J,axiom, % 185.87/185.97 ! [V_u_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I10_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_atMost__Int__atLeast,axiom, % 185.87/185.97 ! [V_n_2,T_b] : % 185.87/185.97 ( class_Orderings_Oorder(T_b) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_ivl__disj__un_I7_J,axiom, % 185.87/185.97 ! [V_u_2,V_l_2,T_b] : % 185.87/185.97 ( class_Orderings_Olinorder(T_b) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 185.87/185.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bset_I8_J,axiom, % 185.87/185.97 ! [V_B_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_aset_I6_J,axiom, % 185.87/185.97 ! [V_A_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 185.87/185.97 => 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)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bset_I3_J,axiom, % 185.87/185.97 ! [V_B_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => ( ! [B_x] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xa] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 185.87/185.97 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 185.87/185.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_aset_I4_J,axiom, % 185.87/185.97 ! [V_A_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( B_x != V_t_2 % 185.87/185.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bset_I4_J,axiom, % 185.87/185.97 ! [V_B_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( B_x != V_t_2 % 185.87/185.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_bset_I7_J,axiom, % 185.87/185.97 ! [V_B_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 185.87/185.97 => 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))) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_aset_I3_J,axiom, % 185.87/185.97 ! [V_A_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( 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)) % 185.87/185.97 => ( ! [B_x] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xa] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 185.87/185.97 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 185.87/185.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_aset_I5_J,axiom, % 185.87/185.97 ! [V_A_2,V_t_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.97 ( 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))) % 185.87/185.97 => ! [B_xb] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.87/185.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 185.87/185.97 => 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)) ) ) ) ) ). % 185.87/185.97 % 185.87/185.97 fof(fact_aset_I8_J,axiom, % 185.87/185.97 ! [V_t_2,V_A_2,V_D_2] : % 185.87/185.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.97 => ! [B_x] : % 185.87/185.97 ( ! [B_xa] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ! [B_xb] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.87/185.98 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 185.87/185.98 => 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))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_bset_I6_J,axiom, % 185.87/185.98 ! [V_t_2,V_B_2,V_D_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.98 => ! [B_x] : % 185.87/185.98 ( ! [B_xa] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ! [B_xb] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.87/185.98 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 185.87/185.98 => 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)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_periodic__finite__ex,axiom, % 185.87/185.98 ! [V_Pa_2,V_d_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.87/185.98 => ( ! [B_x,B_k] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.98 <=> hBOOL(hAPP(V_Pa_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)))) ) % 185.87/185.98 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.87/185.98 <=> ? [B_x] : % 185.87/185.98 ( 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))) % 185.87/185.98 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_aset_I7_J,axiom, % 185.87/185.98 ! [V_t_2,V_A_2,V_D_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.98 => ! [B_x] : % 185.87/185.98 ( ! [B_xa] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ! [B_xb] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 185.87/185.98 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 185.87/185.98 => 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))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_bset_I5_J,axiom, % 185.87/185.98 ! [V_t_2,V_B_2,V_D_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 185.87/185.98 => ! [B_x] : % 185.87/185.98 ( ! [B_xa] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ! [B_xb] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 185.87/185.98 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 185.87/185.98 => 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)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_decr__mult__lemma,axiom, % 185.87/185.98 ! [V_k_2,V_Pa_2,V_d_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.98 => ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_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)))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_negD,axiom, % 185.87/185.98 ! [V_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.98 => ? [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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_incr__mult__lemma,axiom, % 185.87/185.98 ! [V_k_2,V_Pa_2,V_d_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 185.87/185.98 => ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_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)))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_ex__least__nat__less,axiom, % 185.87/185.98 ! [V_n_2,V_Pa_2] : % 185.87/185.98 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 185.87/185.98 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 185.87/185.98 => ? [B_k] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 185.87/185.98 & ! [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 185.87/185.98 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 185.87/185.98 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_strong__setprod__reindex__cong,axiom, % 185.87/185.98 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__mult(T_d) % 185.87/185.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.87/185.98 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setprod__mono__one__right,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.87/185.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setprod__mono__one__left,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.87/185.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_SigmaE,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 185.87/185.98 => ~ ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 185.87/185.98 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zero__less__imp__eq__int,axiom, % 185.87/185.98 ! [V_k] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 185.87/185.98 => ? [B_n] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 185.87/185.98 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__surj,axiom, % 185.87/185.98 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 185.87/185.98 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) % 185.87/185.98 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__mono__zero__right,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.87/185.98 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__imageI,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_R_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_ba_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fst__map__pair,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fst__comp__map__pair,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_snd__comp__map__pair,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_snd__prod__fun,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__ident,axiom, % 185.87/185.98 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair_Ocomp,axiom, % 185.87/185.98 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__compose,axiom, % 185.87/185.98 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair_Ocompositionality,axiom, % 185.87/185.98 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__simp,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_ba_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_ba_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair_Oidentity,axiom, % 185.87/185.98 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair_Oid,axiom, % 185.87/185.98 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__def,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__surj__on,axiom, % 185.87/185.98 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 185.87/185.98 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 185.87/185.98 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 185.87/185.98 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__map__pair__image,axiom, % 185.87/185.98 ! [V_f_2,T_c,V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.87/185.98 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_map__pair__inj__on,axiom, % 185.87/185.98 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.87/185.98 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 185.87/185.98 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,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))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_prod__fun__imageE,axiom, % 185.87/185.98 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) % 185.87/185.98 => ~ ! [B_x,B_y] : % 185.87/185.98 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__mono__zero__left,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 185.87/185.98 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__strict__mono,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.98 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_A_2))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_field__le__mult__one__interval,axiom, % 185.87/185.98 ! [V_y,V_x,T_a] : % 185.87/185.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.98 => ( ! [B_z] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 185.87/185.98 => 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)) ) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 185.87/185.98 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.98 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.98 => ( V_A_2 = V_B_2 % 185.87/185.98 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__1__neg,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn0,axiom, % 185.87/185.98 ! [T_a] : % 185.87/185.98 ( class_Groups_Osgn__if(T_a) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__0__0,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__sgn,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__times,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__less,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__greater,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__pos,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__1__pos,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zsgn__def,axiom, % 185.87/185.98 ! [V_i] : % 185.87/185.98 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 185.87/185.98 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 185.87/185.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 185.87/185.98 => 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)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__if,axiom, % 185.87/185.98 ! [V_x,T_a] : % 185.87/185.98 ( class_Groups_Osgn__if(T_a) % 185.87/185.98 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 185.87/185.98 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 185.87/185.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sgn__neg,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.98 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_code__numeral_Osimps_I5_J,axiom, % 185.87/185.98 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_decr__lemma,axiom, % 185.87/185.98 ! [V_z,V_x,V_d] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_incr__lemma,axiom, % 185.87/185.98 ! [V_x,V_z,V_d] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__abs,axiom, % 185.87/185.98 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__abs__ge__zero,axiom, % 185.87/185.98 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => 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__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nonzero__abs__divide,axiom, % 185.87/185.98 ! [V_a,V_b,T_a] : % 185.87/185.98 ( class_Fields_Olinordered__field(T_a) % 185.87/185.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__power__minus,axiom, % 185.87/185.98 ! [V_n,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__minus__commute,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__triangle__ineq3,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__triangle__ineq2,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__triangle__ineq2__sym,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__less__iff,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 185.87/185.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_power__abs,axiom, % 185.87/185.98 ! [V_n,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__le__D1,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__ge__self,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__idempotent,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__add__abs,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__mult__self,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__mult,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__minus__cancel,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__of__nat,axiom, % 185.87/185.98 ! [V_n,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__int__eq,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__setprod,axiom, % 185.87/185.98 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( class_Fields_Olinordered__field(T_b) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__divide,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__setsum__abs,axiom, % 185.87/185.98 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__mult__less,axiom, % 185.87/185.98 ! [V_d,V_b,V_c,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 185.87/185.98 => 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))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__triangle__ineq,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__ge__minus__self,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__le__iff,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 185.87/185.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__leI,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__le__D2,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__ge__zero,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__le__zero__iff,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) % 185.87/185.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__of__nonneg,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__of__pos,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zero__less__abs__iff,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) % 185.87/185.98 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__not__less__zero,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ~ 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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__one,axiom, % 185.87/185.98 ! [T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__zero,axiom, % 185.87/185.98 ! [T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__eq__0,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.98 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 185.87/185.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__zmult__eq__1,axiom, % 185.87/185.98 ! [V_n,V_m] : % 185.87/185.98 ( 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) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__sgn,axiom, % 185.87/185.98 ! [V_k,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_mult__sgn__abs,axiom, % 185.87/185.98 ! [V_x,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__mult__pos,axiom, % 185.87/185.98 ! [V_y,V_x,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__eq__mult,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Rings_Oordered__ring__abs(T_a) % 185.87/185.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 185.87/185.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__diff__triangle__ineq,axiom, % 185.87/185.98 ! [V_d,V_c,V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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))))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__triangle__ineq4,axiom, % 185.87/185.98 ! [V_b,V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__of__nonpos,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__minus__le__zero,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => 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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__if,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oabs__if(T_a) % 185.87/185.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 185.87/185.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__of__neg,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zero__le__power__abs,axiom, % 185.87/185.98 ! [V_n,V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__div__pos,axiom, % 185.87/185.98 ! [V_x,V_y,T_a] : % 185.87/185.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__minus__one,axiom, % 185.87/185.98 ! [T_a] : % 185.87/185.98 ( ( class_Int_Onumber__ring(T_a) % 185.87/185.98 & class_Rings_Olinordered__idom(T_a) ) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zabs__less__one__iff,axiom, % 185.87/185.98 ! [V_z_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zabs__def,axiom, % 185.87/185.98 ! [V_i] : % 185.87/185.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 185.87/185.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 185.87/185.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__abs__mult__distrib,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zero__le__zpower__abs,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__number__of,axiom, % 185.87/185.98 ! [V_x,T_a] : % 185.87/185.98 ( ( class_Int_Onumber__ring(T_a) % 185.87/185.98 & class_Rings_Olinordered__idom(T_a) ) % 185.87/185.98 => ( ( 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))) % 185.87/185.98 => 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)) ) % 185.87/185.98 & ( ~ 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))) % 185.87/185.98 => 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) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__power__minus__one,axiom, % 185.87/185.98 ! [V_n,T_a] : % 185.87/185.98 ( ( class_Int_Onumber__ring(T_a) % 185.87/185.98 & class_Rings_Olinordered__idom(T_a) ) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_zero__less__zpower__abs__iff,axiom, % 185.87/185.98 ! [V_n_2,V_x_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_power2__abs,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_abs__power2,axiom, % 185.87/185.98 ! [V_a,T_a] : % 185.87/185.98 ( class_Rings_Olinordered__idom(T_a) % 185.87/185.98 => 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)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_code__numeral_Osimps_I4_J,axiom, % 185.87/185.98 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_divmod__int__pdivmod,axiom, % 185.87/185.98 ! [V_l_2,V_k_2] : % 185.87/185.98 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)) ) % 185.87/185.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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) ) % 185.87/185.98 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Oint__gcd__def,axiom, % 185.87/185.98 ! [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)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_divmod__int__code,axiom, % 185.87/185.98 ! [V_l_2,V_k_2] : % 185.87/185.98 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)) ) % 185.87/185.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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) ) % 185.87/185.98 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__compose,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__eq__conv,axiom, % 185.87/185.98 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 185.87/185.98 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) % 185.87/185.98 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_snd__apsnd,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fst__apsnd,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__conv,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_negateSnd__def,axiom, % 185.87/185.98 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__def,axiom, % 185.87/185.98 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__id,axiom, % 185.87/185.98 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__gcd_Osimps,axiom, % 185.87/185.98 ! [V_x,V_y] : % 185.87/185.98 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 185.87/185.98 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_pdivmod__def,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_pdivmod__posDivAlg,axiom, % 185.87/185.98 ! [V_k,V_l] : % 185.87/185.98 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)) ) % 185.87/185.98 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__gcd_Opsimps,axiom, % 185.87/185.98 ! [V_y_2,V_x_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 185.87/185.98 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => 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)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Onat__lcm__def,axiom, % 185.87/185.98 ! [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)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Oint__lcm__def,axiom, % 185.87/185.98 ! [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)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__gcd_Opinduct,axiom, % 185.87/185.98 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ( ! [B_x,B_y] : % 185.87/185.98 ( 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))) % 185.87/185.98 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__apfst,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__apsnd,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apsnd__apfst__commute,axiom, % 185.87/185.98 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__compose,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_snd__apfst,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__eq__conv,axiom, % 185.87/185.98 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.98 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) % 185.87/185.98 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fst__apfst,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__conv,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__def,axiom, % 185.87/185.98 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_apfst__id,axiom, % 185.87/185.98 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 185.87/185.98 ( ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.98 & class_Groups_Ocomm__monoid__mult(T_b) ) % 185.87/185.98 => ( V_A_2 = V_B_2 % 185.87/185.98 => ( c_Nat__Transfer_Onat__set(V_B_2) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_accp__acc__eq,axiom, % 185.87/185.98 ! [V_x_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Ozero__frac__def,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc__wfD,axiom, % 185.87/185.98 ! [V_x_2,V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__acc__iff,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc__subset,axiom, % 185.87/185.98 ! [V_R2_2,V_R1_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc_Osimps,axiom, % 185.87/185.98 ! [V_r_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc__downward,axiom, % 185.87/185.98 ! [V_a_2,V_r_2,V_ba_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Oone__frac__def,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Nitpick_Ofrac__def,axiom, % 185.87/185.98 ! [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)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__def,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.98 & ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat0__intermed__int__val,axiom, % 185.87/185.98 ! [V_k_2,V_f_2,V_n_2] : % 185.87/185.98 ( ! [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 185.87/185.98 => 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))) ) % 185.87/185.98 => ( 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)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.87/185.98 => ? [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.87/185.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_int__val__lemma,axiom, % 185.87/185.98 ! [V_k_2,V_f_2,V_n_2] : % 185.87/185.98 ( ! [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 185.87/185.98 => 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))) ) % 185.87/185.98 => ( 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)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.87/185.98 => ? [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.87/185.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__Id__on,axiom, % 185.87/185.98 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__empty,axiom, % 185.87/185.98 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__Un,axiom, % 185.87/185.98 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 185.87/185.98 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__Id,axiom, % 185.87/185.98 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__Int,axiom, % 185.87/185.98 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 185.87/185.98 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__onD,axiom, % 185.87/185.98 ! [V_a_2,V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__onD1,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__onD2,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__reflcl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_reflp__def,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Predicate_Oreflp(T_b,V_r_2) % 185.87/185.98 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__onI,axiom, % 185.87/185.98 ! [V_A_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) % 185.87/185.98 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setprod__pos__nat,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.87/185.98 => 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))) ) % 185.87/185.98 => 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_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_reflpE,axiom, % 185.87/185.98 ! [V_x_2,V_r_2,T_b] : % 185.87/185.98 ( c_Predicate_Oreflp(T_b,V_r_2) % 185.87/185.98 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Rep__Integ__cases,axiom, % 185.87/185.98 ! [V_y_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 185.87/185.98 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Rep__Integ__induct,axiom, % 185.87/185.98 ! [V_Pa_2,V_y_2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 185.87/185.98 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) % 185.87/185.98 => hAPP(V_g_2,B_x) = V_z_2 ) % 185.87/185.98 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_pigeonhole__infinite,axiom, % 185.87/185.98 ! [V_f_2,T_c,V_A_2,T_b] : % 185.87/185.98 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 185.87/185.98 => ? [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__def_H,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 <=> ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_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(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) % 185.87/185.98 & ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Abs__Integ__cases,axiom, % 185.87/185.98 ! [V_x_2] : % 185.87/185.98 ~ ! [B_y] : % 185.87/185.98 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Powp__def,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 185.87/185.98 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_ball__empty,axiom, % 185.87/185.98 ! [V_Pa_2,T_b,B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_congruent__def,axiom, % 185.87/185.98 ! [V_f_2,V_r_2,T_c,T_b] : % 185.87/185.98 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__Inf,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inf__Sup,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Abs__Integ__induct,axiom, % 185.87/185.98 ! [V_x_2,V_Pa_2] : % 185.87/185.98 ( ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UnionI,axiom, % 185.87/185.98 ! [V_A_2,V_C_2,V_X_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__upper,axiom, % 185.87/185.98 ! [V_A_2,V_B_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__disjoint,axiom, % 185.87/185.98 ! [V_A_2,V_C_2,T_b] : % 185.87/185.98 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_less__Sup__iff,axiom, % 185.87/185.98 ! [V_S_2,V_a_2,T_b] : % 185.87/185.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 & class_Orderings_Olinorder(T_b) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 185.87/185.98 <=> ? [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_vimage__Union,axiom, % 185.87/185.98 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Domain__Union,axiom, % 185.87/185.98 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_image__Union,axiom, % 185.87/185.98 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Int__Union,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Int__Union2,axiom, % 185.87/185.98 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UN__simps_I8_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UN__extend__simps_I8_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__Pow__eq,axiom, % 185.87/185.98 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_Field__Union,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sigma__Union,axiom, % 185.87/185.98 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__le__iff,axiom, % 185.87/185.98 ! [V_ba_2,V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_ba_2)) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Range__Union,axiom, % 185.87/185.98 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__empty,axiom, % 185.87/185.98 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__mono,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__quotient,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__insert,axiom, % 185.87/185.98 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__UnionD,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_subset__Pow__Union,axiom, % 185.87/185.98 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__UNIV,axiom, % 185.87/185.98 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__Un__distrib,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UNION__eq__Union__image,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__image__eq,axiom, % 185.87/185.98 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__upper,axiom, % 185.87/185.98 ! [V_A_2,V_x_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__empty,axiom, % 185.87/185.98 ! [T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__singleton,axiom, % 185.87/185.98 ! [V_a_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__insert,axiom, % 185.87/185.98 ! [V_A_2,V_a_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__UNIV,axiom, % 185.87/185.98 ! [T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inter__eq,axiom, % 185.87/185.98 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Un__eq__Union,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Un__Union__image,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__Int__subset,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__binary,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_ba_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__fin__Sup,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_card__partition,axiom, % 185.87/185.98 ! [V_k_2,V_C_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 185.87/185.98 => ( ! [B_c] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 185.87/185.98 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 185.87/185.98 => ( ! [B_c1] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 185.87/185.98 => ! [B_c2] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 185.87/185.98 => ( B_c1 != B_c2 % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 185.87/185.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__Union,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 185.87/185.98 => ( ! [B_M] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_insert__partition,axiom, % 185.87/185.98 ! [V_F_2,V_x_2,T_b] : % 185.87/185.98 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 185.87/185.98 => ! [B_xa] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) % 185.87/185.98 => ( B_x != B_xa % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Union__def,axiom, % 185.87/185.98 ! [V_S_2,T_b] : 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_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__UN__I,axiom, % 185.87/185.98 ! [V_B_2,T_c,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ! [B_a] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 185.87/185.98 ! [V_M_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 185.87/185.98 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_inj__on__diff__nat,axiom, % 185.87/185.98 ! [V_k_2,V_N_2] : % 185.87/185.98 ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 185.87/185.98 => 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) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_ex__bij__betw__nat__finite,axiom, % 185.87/185.98 ! [V_M_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 185.87/185.98 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,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_b),V_M_2)),V_M_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_mem__splitI2,axiom, % 185.87/185.98 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 185.87/185.98 ( ! [B_a,B_b] : % 185.87/185.98 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_mem__splitE,axiom, % 185.87/185.98 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2))) % 185.87/185.98 => ~ ! [B_x,B_y] : % 185.87/185.98 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__SucD,axiom, % 185.87/185.98 ! [V_n_2,V_A_2,V_f_2,T_b] : % 185.87/185.98 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 185.87/185.98 => ? [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 & 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))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Eps__split,axiom, % 185.87/185.98 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__mod__eq__lemma,axiom, % 185.87/185.98 ! [V_y,V_n,V_x] : % 185.87/185.98 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 185.87/185.98 => ? [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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_someI,axiom, % 185.87/185.98 ! [T_b,V_x_2,V_Pa_2] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_tfl__some,axiom, % 185.87/185.98 ! [T_b,B_P] : % 185.87/185.98 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 185.87/185.98 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_someI__ex,axiom, % 185.87/185.98 ! [T_b,V_Pa_2] : % 185.87/185.98 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_some__eq__ex,axiom, % 185.87/185.98 ! [T_b,V_Pa_2] : % 185.87/185.98 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 185.87/185.98 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_some__eq__trivial,axiom, % 185.87/185.98 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_some__sym__eq__trivial,axiom, % 185.87/185.98 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_exE__some,axiom, % 185.87/185.98 ! [T_b,V_ca_2,V_Pa_2] : % 185.87/185.98 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 185.87/185.98 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_split__paired__Eps,axiom, % 185.87/185.98 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Eps__split__eq,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_inv__into__def,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(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(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_inv__def,axiom, % 185.87/185.98 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_ex__bij__betw__finite__nat,axiom, % 185.87/185.98 ! [V_M_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 185.87/185.98 => ? [B_h] : c_Fun_Obij__betw(T_b,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_b),V_M_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sigma__mono,axiom, % 185.87/185.98 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc_OaccI,axiom, % 185.87/185.98 ! [V_r_2,V_x_2,T_b] : % 185.87/185.98 ( ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_not__acc__down,axiom, % 185.87/185.98 ! [V_R_2,V_x_2,T_b] : % 185.87/185.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 185.87/185.98 => ~ ! [B_z] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__image__1,axiom, % 185.87/185.98 ! [V_f_2,V_S_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 185.87/185.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 185.87/185.98 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_card_Oneutral,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 185.87/185.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_max__ext_Osimps,axiom, % 185.87/185.98 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) % 185.87/185.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 185.87/185.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 185.87/185.98 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 & ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 185.87/185.98 => ? [B_xa] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_mod__induct__0,axiom, % 185.87/185.98 ! [V_i_2,V_Pa_2,V_p_2] : % 185.87/185.98 ( ! [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 185.87/185.98 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 185.87/185.98 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 185.87/185.98 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__image__cong,axiom, % 185.87/185.98 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( class_Groups_Oab__semigroup__mult(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.98 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 185.87/185.98 => 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),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__subset__Sigma__aux,axiom, % 185.87/185.98 ! [V_A_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.98 => ( V_a_2 = V_ba_2 % 185.87/185.98 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Min__eqI,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Max__eqI,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_r__into__rtrancl,axiom, % 185.87/185.98 ! [V_r_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl_Ortrancl__refl,axiom, % 185.87/185.98 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__Un__subset,axiom, % 185.87/185.98 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Range__rtrancl,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Domain__rtrancl,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Image__closed__trancl,axiom, % 185.87/185.98 ! [V_X_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) % 185.87/185.98 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_in__rtrancl__UnI,axiom, % 185.87/185.98 ! [V_S_2,V_R_2,V_x_2,T_b] : % 185.87/185.98 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__trans,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__Un__rtrancl,axiom, % 185.87/185.98 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__subset__rtrancl,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__subset,axiom, % 185.87/185.98 ! [V_S_2,V_R_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__mono,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__idemp,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_r__comp__rtrancl__eq,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__idemp__self__comp,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__rtrancl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__empty,axiom, % 185.87/185.98 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__reflcl__absorb,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__reflcl,axiom, % 185.87/185.98 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__r__diff__Id,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__unfold,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Not__Domain__rtrancl,axiom, % 185.87/185.98 ! [V_y_2,V_R_2,V_x_2,T_b] : % 185.87/185.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 <=> V_x_2 = V_y_2 ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc__downwards,axiom, % 185.87/185.98 ! [V_ba_2,V_r_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acc__downwards__aux,axiom, % 185.87/185.98 ! [V_r_2,V_a_2,V_ba_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__insert,axiom, % 185.87/185.98 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 185.87/185.98 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acyclic__insert,axiom, % 185.87/185.98 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) % 185.87/185.98 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.87/185.98 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__Int__subset,axiom, % 185.87/185.98 ! [V_r_2,V_s_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_pred__nat__trancl__eq__le,axiom, % 185.87/185.98 ! [V_n_2,V_m_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__insert,axiom, % 185.87/185.98 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sequence__trans,axiom, % 185.87/185.98 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 185.87/185.98 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => 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,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_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 185.87/185.98 ! [V_R_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl_Or__into__trancl,axiom, % 185.87/185.98 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__into__rtrancl,axiom, % 185.87/185.98 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__rtrancl__absorb,axiom, % 185.87/185.98 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__trancl__absorb,axiom, % 185.87/185.98 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_r__r__into__trancl,axiom, % 185.87/185.98 ! [V_ca_2,V_R_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_R_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_R_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__into__trancl2,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__trans,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_comp__funpow,axiom, % 185.87/185.98 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__power,axiom, % 185.87/185.98 ! [V_R_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 185.87/185.98 <=> ? [B_n] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__1,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__empty,axiom, % 185.87/185.98 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__trancl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__commute,axiom, % 185.87/185.98 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__trancl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__range,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow__swap1,axiom, % 185.87/185.98 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__domain,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_r__into__trancl_H,axiom, % 185.87/185.98 ! [V_r_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__exp,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) % 185.87/185.98 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow__mult,axiom, % 185.87/185.98 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__mono,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__unfold__left,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__unfold__right,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__unfold,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__imp__rtrancl,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__power,axiom, % 185.87/185.98 ! [V_R_2,V_p_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_relpow_Osimps_I2_J,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__add,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),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_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_relpow_Osimps_I1_J,axiom, % 185.87/185.98 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__subset__Sigma,axiom, % 185.87/185.98 ! [V_A_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_less__than__def,axiom, % 185.87/185.98 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__eq__or__trancl,axiom, % 185.87/185.98 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 <=> ( V_x_2 = V_y_2 % 185.87/185.98 | ( V_x_2 != V_y_2 % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__into__trancl2,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtranclD,axiom, % 185.87/185.98 ! [V_R_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 => ( V_a_2 = V_ba_2 % 185.87/185.98 | ( V_a_2 != V_ba_2 % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__into__trancl1,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__rtrancl__trancl,axiom, % 185.87/185.98 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__trancl__trancl,axiom, % 185.87/185.98 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acyclic__def,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.87/185.98 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__0__E,axiom, % 185.87/185.98 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 185.87/185.98 => V_x_2 = V_y_2 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__0__I,axiom, % 185.87/185.98 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__Suc__I,axiom, % 185.87/185.98 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__Suc__I2,axiom, % 185.87/185.98 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow_Osimps_I2_J,axiom, % 185.87/185.98 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow__add,axiom, % 185.87/185.98 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_reflcl__trancl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__reflcl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow_Osimps_I1_J,axiom, % 185.87/185.98 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__Int__subset,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__subset__Field2,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 185.87/185.98 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_less__eq,axiom, % 185.87/185.98 ! [V_n_2,V_m_2] : % 185.87/185.98 ( 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))) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_funpow__code__def,axiom, % 185.87/185.98 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_irrefl__tranclI,axiom, % 185.87/185.98 ! [V_x_2,V_r_2,T_b] : % 185.87/185.98 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__E2,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => V_x_2 != V_z_2 ) % 185.87/185.98 => ~ ! [B_y,B_m] : % 185.87/185.98 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__UNION,axiom, % 185.87/185.98 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__iff,axiom, % 185.87/185.98 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converseI,axiom, % 185.87/185.98 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converseD,axiom, % 185.87/185.98 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_total__on__converse,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.87/185.98 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acyclic__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.87/185.98 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__Id__on,axiom, % 185.87/185.98 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Field__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__inv__image,axiom, % 185.87/185.98 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__Id,axiom, % 185.87/185.98 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__Un,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__rel__comp,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__converse,axiom, % 185.87/185.98 ! [V_r_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.87/185.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__Int,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__converse,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.87/185.98 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__converse__trancl,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 185.87/185.98 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_equiv__comp__eq,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.87/185.98 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Range__def,axiom, % 185.87/185.98 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Domain__converse,axiom, % 185.87/185.98 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Range__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__converseD,axiom, % 185.87/185.98 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__converseI,axiom, % 185.87/185.98 ! [V_r_2,V_x_2,V_y_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__converseI,axiom, % 185.87/185.98 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_trancl__converseD,axiom, % 185.87/185.98 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Image__subset__eq,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_refl__on__comp__subset,axiom, % 185.87/185.98 ! [V_r_2,V_A_2,T_b] : % 185.87/185.98 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_comp__equivI,axiom, % 185.87/185.98 ! [V_A_2,V_r_2,T_b] : % 185.87/185.98 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 % 185.87/185.98 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 185.87/185.98 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__acyclic__wf__converse,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 185.87/185.98 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 185.87/185.98 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__def,axiom, % 185.87/185.98 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),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_r_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__E,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.98 => V_x_2 != V_z_2 ) % 185.87/185.98 => ~ ! [B_y,B_m] : % 185.87/185.98 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_acyclicI,axiom, % 185.87/185.98 ! [V_r_2,T_b] : % 185.87/185.98 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 185.87/185.98 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Image__Int__eq,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 185.87/185.98 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__Un__separatorE,axiom, % 185.87/185.98 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 185.87/185.98 => ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) % 185.87/185.98 => B_x = B_y ) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__subset,axiom, % 185.87/185.98 ! [V_s_2,V_r_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.98 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 185.87/185.98 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__rel__comp,axiom, % 185.87/185.98 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.87/185.98 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 185.87/185.98 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__Id,axiom, % 185.87/185.98 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__rel__pow,axiom, % 185.87/185.98 ! [V_n_2,V_R_2,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 185.87/185.98 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__Id__on,axiom, % 185.87/185.98 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valuedD,axiom, % 185.87/185.98 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.87/185.98 => ( 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)),V_r_2)) % 185.87/185.98 => ( 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_z_2)),V_r_2)) % 185.87/185.98 => V_y_2 = V_z_2 ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__def,axiom, % 185.87/185.98 ! [V_r_2,T_c,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 185.87/185.98 <=> ! [B_x,B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) % 185.87/185.98 => ! [B_z] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) % 185.87/185.98 => B_y = B_z ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_single__valued__confluent,axiom, % 185.87/185.98 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 185.87/185.98 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rtrancl__Un__separator__converseE,axiom, % 185.87/185.98 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 185.87/185.98 => ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) % 185.87/185.98 => B_y = B_x ) ) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__Suc__E,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 185.87/185.98 => ~ ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__Suc__D2,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 185.87/185.98 => ? [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_rel__pow__Suc__E2,axiom, % 185.87/185.98 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 185.87/185.98 => ~ ! [B_y] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_tranclD,axiom, % 185.87/185.98 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 185.87/185.98 => ? [B_z] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_tranclD2,axiom, % 185.87/185.98 ! [V_R_2,V_y_2,V_x_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 185.87/185.98 => ? [B_z] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_wf__no__infinite__down__chainE,axiom, % 185.87/185.98 ! [V_f_2,V_r_2,T_b] : % 185.87/185.98 ( c_Wellfounded_Owf(T_b,V_r_2) % 185.87/185.98 => ~ ! [B_k] : 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,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osize_I11_J,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I34_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I35_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I11_J,axiom, % 185.87/185.98 ! [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 ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I10_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I2_J,axiom, % 185.87/185.98 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 185.87/185.98 ( 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) % 185.87/185.98 <=> ( V_loc_2 = V_loc_H_2 % 185.87/185.98 & V_fun_2 = V_fun_H_2 % 185.87/185.98 & V_com_2 = V_com_H_2 ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I38_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I39_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I23_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I22_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I36_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osimps_I37_J,axiom, % 185.87/185.98 ! [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) ). % 185.87/185.98 % 185.87/185.98 fof(fact_com_Osize_I3_J,axiom, % 185.87/185.98 ! [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))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__reindex__cong,axiom, % 185.87/185.98 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 185.87/185.98 ( class_Groups_Ocomm__monoid__add(T_d) % 185.87/185.98 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 185.87/185.98 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 185.87/185.98 => ( ! [B_a] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.87/185.98 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_scomp__unfold,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Pair__scomp,axiom, % 185.87/185.98 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_scomp__scomp,axiom, % 185.87/185.98 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_scomp__Pair,axiom, % 185.87/185.98 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_scomp__apply,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_scomp__def,axiom, % 185.87/185.98 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_iterate_Osimps,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 185.87/185.98 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.98 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) % 185.87/185.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.98 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_setsum__ivl__cong,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,V_d_2,V_ba_2,V_ca_2,V_a_2,T_b,T_c] : % 185.87/185.98 ( ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.98 & class_Orderings_Oord(T_b) ) % 185.87/185.98 => ( V_a_2 = V_ca_2 % 185.87/185.98 => ( V_ba_2 = V_d_2 % 185.87/185.98 => ( ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 185.87/185.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 185.87/185.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_log_Osimps,axiom, % 185.87/185.98 ! [V_i,V_b] : % 185.87/185.98 ( ( ( 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))) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 185.87/185.98 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 185.87/185.98 & ( ~ ( 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))) % 185.87/185.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 185.87/185.98 => 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))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_minus__shift__def,axiom, % 185.87/185.98 ! [V_r,V_l,V_k] : % 185.87/185.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.87/185.98 => 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) ) % 185.87/185.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 185.87/185.98 => 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) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_inc__shift__def,axiom, % 185.87/185.98 ! [V_k,V_v] : % 185.87/185.98 ( ( V_v = V_k % 185.87/185.98 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 185.87/185.98 & ( V_v != V_k % 185.87/185.98 => 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)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_range,axiom, % 185.87/185.98 ! [V_s,V_k] : % 185.87/185.98 ( 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)) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_nat__intermed__int__val,axiom, % 185.87/185.98 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 185.87/185.98 ( ! [B_i] : % 185.87/185.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 185.87/185.98 => 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))) ) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 185.87/185.98 => ? [B_i] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 185.87/185.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 185.87/185.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__empty,axiom, % 185.87/185.98 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__image__def,axiom, % 185.87/185.98 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_folding_Oeq__fold,axiom, % 185.87/185.98 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__def,axiom, % 185.87/185.98 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_union__fold__insert,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__sup__insert,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Osemilattice__sup(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__inf__insert,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Osemilattice__inf(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ba_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_Ofold__inf__insert,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ba_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_Ofold__sup__insert,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sup__Sup__fold__sup,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_inf__Inf__fold__inf,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 185.87/185.98 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 185.87/185.98 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sup__SUPR__fold__sup,axiom, % 185.87/185.98 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_sup__le__fold__sup,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Osemilattice__sup(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_2),V_A_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold__inf__le__inf,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Osemilattice__inf(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ba_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_ba_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ba_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_ba_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_Osup__le__fold__sup,axiom, % 185.87/185.98 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_2),V_A_2))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__fold__sup,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inf__fold__inf,axiom, % 185.87/185.98 ! [V_A_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold1__eq__fold__idem,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Olattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Olattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Min_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Max_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_minus__fold__remove,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))),V_B_2),V_A_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_folding__one_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_SUPR__fold__sup,axiom, % 185.87/185.98 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fold1__eq__fold,axiom, % 185.87/185.98 ! [V_a_2,V_A_2,T_b] : % 185.87/185.98 ( class_Groups_Oab__semigroup__mult(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Olattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Lattices_Olattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Min_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Max_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 185.87/185.98 ! [V_x_2,V_A_2,T_b] : % 185.87/185.98 ( class_Orderings_Olinorder(T_b) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__rec,axiom, % 185.87/185.98 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 185.87/185.98 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.87/185.98 => V_y_2 = V_x_2 ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 185.87/185.98 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => 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)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 185.87/185.98 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm,axiom, % 185.87/185.98 ! [T_b] : % 185.87/185.98 ( class_Groups_Oab__semigroup__mult(T_b) % 185.87/185.98 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 185.87/185.98 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__equality,axiom, % 185.87/185.98 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 185.87/185.98 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 185.87/185.98 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__insert,axiom, % 185.87/185.98 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 185.87/185.98 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.98 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => ? [B_y_H] : % 185.87/185.98 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 185.87/185.98 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INFI__fold__inf,axiom, % 185.87/185.98 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF1__D,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_ba_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF1__E,axiom, % 185.87/185.98 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_ba_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__D,axiom, % 185.87/185.98 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__E,axiom, % 185.87/185.98 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF2__E,axiom, % 185.87/185.98 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) % 185.87/185.98 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 185.87/185.98 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF2__D,axiom, % 185.87/185.98 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_finite__INT,axiom, % 185.87/185.98 ! [V_A_2,T_c,V_I_2,T_b] : % 185.87/185.98 ( ? [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 185.87/185.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 185.87/185.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Compl__INT,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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_OSUPR(T_c,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_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Compl__UN,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,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)) = 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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_converse__INTER,axiom, % 185.87/185.98 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UN__extend__simps_I7_J,axiom, % 185.87/185.98 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_UN__simps_I7_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I2_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 185.87/185.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I1_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.98 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 185.87/185.98 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__insert__distrib,axiom, % 185.87/185.98 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I5_J,axiom, % 185.87/185.98 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I5_J,axiom, % 185.87/185.98 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : % 185.87/185.98 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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)) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.87/185.98 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b] : % 185.87/185.98 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.87/185.98 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Un__INT__distrib2,axiom, % 185.87/185.98 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I6_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Un__INT__distrib,axiom, % 185.87/185.98 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I7_J,axiom, % 185.87/185.98 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I6_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I7_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__Int__distrib,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Pow__INT__eq,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INFI__apply,axiom, % 185.87/185.98 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF__commute,axiom, % 185.87/185.98 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__iff,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Inter__def,axiom, % 185.87/185.98 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_vimage__INT,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF__INT__eq2,axiom, % 185.87/185.98 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__empty,axiom, % 185.87/185.98 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__constant,axiom, % 185.87/185.98 ! [V_ca_2,T_c,T_b,V_A_2] : % 185.87/185.98 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.98 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF__const,axiom, % 185.87/185.98 ! [V_M_2,T_b,V_A_2,T_c] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.98 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__absorb,axiom, % 185.87/185.98 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 185.87/185.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF__INT__eq,axiom, % 185.87/185.98 ! [V_x_2,V_r_2,T_c,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) % 185.87/185.98 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I10_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I10_J,axiom, % 185.87/185.98 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : 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(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I8_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I8_J,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INFI__bool__eq,axiom, % 185.87/185.98 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__insert,axiom, % 185.87/185.98 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_Collect__ball__eq,axiom, % 185.87/185.98 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__Un,axiom, % 185.87/185.98 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__extend__simps_I9_J,axiom, % 185.87/185.98 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__simps_I9_J,axiom, % 185.87/185.98 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__lower,axiom, % 185.87/185.98 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_le__INF__iff,axiom, % 185.87/185.98 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 185.87/185.98 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INT__subset__iff,axiom, % 185.87/185.98 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) % 185.87/185.98 <=> ! [B_x] : % 185.87/185.98 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 185.87/185.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 185.87/185.98 % 185.87/185.98 fof(fact_INF__less__iff,axiom, % 185.87/185.98 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 185.87/185.98 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.98 & class_Orderings_Olinorder(T_b) ) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) % 185.87/185.99 <=> ? [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Image__INT__subset,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Un__Inter,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Inter__image__eq,axiom, % 185.87/185.99 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INTER__eq__Inter__image,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INF__subset,axiom, % 185.87/185.99 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INTER__def,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b,T_c] : 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(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__simps_I2_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__simps_I1_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__simps_I3_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__extend__simps_I3_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__extend__simps_I4_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_bij__image__INT,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Obij__betw(T_b,T_c,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))) % 185.87/185.99 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INF__leI,axiom, % 185.87/185.99 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Int__Inter__image,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__greaterThan__UNIV,axiom, % 185.87/185.99 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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INT__simps_I4_J,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 185.87/185.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 185.87/185.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Image__INT__eq,axiom, % 185.87/185.99 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 185.87/185.99 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 185.87/185.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 185.87/185.99 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inf__INFI__fold__inf,axiom, % 185.87/185.99 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 185.87/185.99 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2)) % 185.87/185.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.99 => ~ ! [B_y] : % 185.87/185.99 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 185.87/185.99 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_image__INT,axiom, % 185.87/185.99 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 185.87/185.99 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INF1__iff,axiom, % 185.87/185.99 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_ba_2)) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INF2__iff,axiom, % 185.87/185.99 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__on__INTER,axiom, % 185.87/185.99 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 185.87/185.99 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 => ( ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 185.87/185.99 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 185.87/185.99 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 185.87/185.99 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_ba_2),V_ca_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 185.87/185.99 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inf__le__fold__inf,axiom, % 185.87/185.99 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.87/185.99 ( class_Lattices_Osemilattice__inf(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_fold__sup__le__sup,axiom, % 185.87/185.99 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 185.87/185.99 ( class_Lattices_Osemilattice__sup(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_ba_2),V_ca_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_mod__div__decomp,axiom, % 185.87/185.99 ! [V_b,V_a,T_a] : % 185.87/185.99 ( class_Divides_Osemiring__div(T_a) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 185.87/185.99 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_transfer__nat__int__set__cong,axiom, % 185.87/185.99 ! [V_P_H_2,V_Pa_2] : % 185.87/185.99 ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 185.87/185.99 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 185.87/185.99 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 185.87/185.99 => 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_Pa_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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_folding__image__simple__idem_Oidem,axiom, % 185.87/185.99 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.99 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 185.87/185.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 185.87/185.99 => 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) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 185.87/185.99 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.99 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 185.87/185.99 => 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) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_UnionE,axiom, % 185.87/185.99 ! [V_C_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 185.87/185.99 => ~ ! [B_X] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_converseE,axiom, % 185.87/185.99 ! [V_r_2,V_yx_2,T_c,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 185.87/185.99 => ~ ! [B_x,B_y] : % 185.87/185.99 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rel__compE,axiom, % 185.87/185.99 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) % 185.87/185.99 => ~ ! [B_x,B_y,B_z] : % 185.87/185.99 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2)) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Oplus__frac__def,axiom, % 185.87/185.99 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),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_b),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_b),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_b),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_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Otimes__frac__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Oof__frac__def,axiom, % 185.87/185.99 ! [V_q,T_a,T_b] : % 185.87/185.99 ( ( class_Rings_Oinverse(T_b) % 185.87/185.99 & class_Rings_Oring__1(T_b) ) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Oless__frac__def,axiom, % 185.87/185.99 ! [V_r_2,V_q_2,T_b] : % 185.87/185.99 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 185.87/185.99 ! [V_r_2,V_q_2,T_b] : % 185.87/185.99 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Onum__def,axiom, % 185.87/185.99 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Odenom__def,axiom, % 185.87/185.99 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_setprod__pos,axiom, % 185.87/185.99 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.99 ( class_Rings_Olinordered__semidom(T_c) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_internal__split__def,axiom, % 185.87/185.99 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ). % 185.87/185.99 % 185.87/185.99 fof(fact_internal__split__conv,axiom, % 185.87/185.99 ! [V_ba_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_ba_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_setprod__nonneg,axiom, % 185.87/185.99 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.99 ( class_Rings_Olinordered__semidom(T_c) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_bool_Osize_I1_J,axiom, % 185.87/185.99 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.99 % 185.87/185.99 fof(fact_bool_Osize_I2_J,axiom, % 185.87/185.99 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.99 % 185.87/185.99 fof(fact_finite__less__ub,axiom, % 185.87/185.99 ! [V_u_2,V_f_2] : % 185.87/185.99 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 185.87/185.99 => 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)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lenlex__def,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexn__length,axiom, % 185.87/185.99 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) % 185.87/185.99 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 185.87/185.99 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_neq__if__length__neq,axiom, % 185.87/185.99 ! [V_ys,V_xs,T_a] : % 185.87/185.99 ( 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) % 185.87/185.99 => V_xs != V_ys ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lenlex__conv,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__sublist,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,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_b)),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)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexn_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,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_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_impossible__Cons,axiom, % 185.87/185.99 ! [V_x,V_ys,V_xs,T_a] : % 185.87/185.99 ( 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))) % 185.87/185.99 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Oinject,axiom, % 185.87/185.99 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) % 185.87/185.99 <=> ( V_a_2 = V_a_H_2 % 185.87/185.99 & V_list_2 = V_list_H_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_not__Cons__self2,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 185.87/185.99 % 185.87/185.99 fof(fact_not__Cons__self,axiom, % 185.87/185.99 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osize_I4_J,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__in__lex,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) % 185.87/185.99 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.99 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) % 185.87/185.99 | ( V_x_2 = V_y_2 % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__Cons__def,axiom, % 185.87/185.99 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),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_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_pick_Osimps,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_i] : % 185.87/185.99 ( ( 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))) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( ~ 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))) % 185.87/185.99 => 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))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select__weight__cons__zero,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__cons__cons,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_ba_2,V_x_2,V_a_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_ba_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.99 | ( V_a_2 = V_ba_2 % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__lex,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osize_I2_J,axiom, % 185.87/185.99 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),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_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__acc__listrel1I,axiom, % 185.87/185.99 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__converse,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 185.87/185.99 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__mono,axiom, % 185.87/185.99 ! [V_s_2,V_r_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 185.87/185.99 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1I2,axiom, % 185.87/185.99 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rtrancl__listrel1__eq__len,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__eq__len,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__listrel1__converse,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__listrel1__Cons,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.99 & V_xs_2 = V_ys_2 ) % 185.87/185.99 | ( V_x_2 = V_y_2 % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1I1,axiom, % 185.87/185.99 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Cons,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__linear,axiom, % 185.87/185.99 ! [V_y_2,V_x_2,V_r_2,T_b] : % 185.87/185.99 ( ! [B_a,B_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) % 185.87/185.99 | B_a = B_b % 185.87/185.99 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) ) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 | V_x_2 = V_y_2 % 185.87/185.99 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__rtrancl__refl,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__mono,axiom, % 185.87/185.99 ! [V_s_2,V_r_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 185.87/185.99 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__eq__len,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__rtrancl__trans,axiom, % 185.87/185.99 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__reflcl__if__listrel1,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__subset__listrel,axiom, % 185.87/185.99 ! [V_r_H_2,V_r_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 185.87/185.99 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel_OCons,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrelp__listrel__eq,axiom, % 185.87/185.99 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 185.87/185.99 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Cons1,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => ~ ! [B_y,B_ys] : % 185.87/185.99 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2)) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrelp_Oequations_I2_J,axiom, % 185.87/185.99 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 185.87/185.99 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 185.87/185.99 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrelp_OCons,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 185.87/185.99 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 185.87/185.99 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Cons2,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => ~ ! [B_x,B_xs] : % 185.87/185.99 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2)) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__subset,axiom, % 185.87/185.99 ! [V_A_2,V_r_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__UNIV,axiom, % 185.87/185.99 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__mono,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_equiv__listrel,axiom, % 185.87/185.99 ! [V_r_2,V_A_2,T_b] : % 185.87/185.99 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 185.87/185.99 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__refl__on,axiom, % 185.87/185.99 ! [V_r_2,V_A_2,T_b] : % 185.87/185.99 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 185.87/185.99 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__in__lists__iff,axiom, % 185.87/185.99 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__accD,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__accI,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__iff__nth,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 185.87/185.99 & ! [B_n] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__irreflexive,axiom, % 185.87/185.99 ! [V_y_2,V_r_2,T_b] : % 185.87/185.99 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_infinite__UNIV__listI,axiom, % 185.87/185.99 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__eq__iff__nth__eq,axiom, % 185.87/185.99 ! [T_b,V_ys_2,V_xs_2] : % 185.87/185.99 ( V_xs_2 = V_ys_2 % 185.87/185.99 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 185.87/185.99 & ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__Cons__0,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__Cons__Suc,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth_Osimps,axiom, % 185.87/185.99 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__Cons_H,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_n] : % 185.87/185.99 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 185.87/185.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__Cons__number__of,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_v] : % 185.87/185.99 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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 ) % 185.87/185.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__take__index__conv,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) % 185.87/185.99 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 ) % 185.87/185.99 | ? [B_i] : % 185.87/185.99 ( 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_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) % 185.87/185.99 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__sublist,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),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))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_finite__set,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__subset__Cons,axiom, % 185.87/185.99 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__all,axiom, % 185.87/185.99 ! [V_n,V_xs,T_a] : % 185.87/185.99 ( 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)) % 185.87/185.99 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__take__subset,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__take__subset__set__take,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__sublist__subset,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__take,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n,V_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__upt__eq__take,axiom, % 185.87/185.99 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Suc__Cons,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__ConsD,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) % 185.87/185.99 => ( V_y_2 = V_x_2 % 185.87/185.99 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__sublistD,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__takeD,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_notin__set__sublistI,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__take,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__take,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Oset_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_card__length,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_all__set__conv__all__nth,axiom, % 185.87/185.99 ! [V_Pa_2,V_xs_2,T_b] : % 185.87/185.99 ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.87/185.99 <=> ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__size__estimation,axiom, % 185.87/185.99 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__size__estimation_H,axiom, % 185.87/185.99 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__lists__conv__set,axiom, % 185.87/185.99 ! [V_A_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__pos__if__in__set,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => 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_b)),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__mem,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__conv__nth,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 <=> ? [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__eq__set,axiom, % 185.87/185.99 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__conv__nth,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_finite__lists__length__eq,axiom, % 185.87/185.99 ! [V_n_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_finite__lists__length__le,axiom, % 185.87/185.99 ! [V_n_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__iff__zip,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 185.87/185.99 & ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__zip,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),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_b,T_c)),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_b,T_c)),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_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__zip,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__zip,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__Cons__Cons,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__eq__iff__zip__eq,axiom, % 185.87/185.99 ! [T_b,V_ys_2,V_xs_2] : % 185.87/185.99 ( V_xs_2 = V_ys_2 % 185.87/185.99 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 185.87/185.99 & ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__same,axiom, % 185.87/185.99 ! [V_xs_2,V_ba_2,V_a_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 & V_a_2 = V_ba_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__zip__leftD,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 185.87/185.99 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__zip__rightD,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 185.87/185.99 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__zipE,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 185.87/185.99 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 185.87/185.99 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__zip,axiom, % 185.87/185.99 ! [V_ys,T_b,V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( 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))) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_greaterThanLessThan__upto,axiom, % 185.87/185.99 ! [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)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__setsum__nth,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 185.87/185.99 ! [V_ns_2] : % 185.87/185.99 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 185.87/185.99 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__upto,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_atLeastAtMost__upto,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_elem__le__listsum__nat,axiom, % 185.87/185.99 ! [V_ns,V_k] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__simps_I2_J,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_a) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_atLeastLessThan__upto,axiom, % 185.87/185.99 ! [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)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_greaterThanAtMost__upto,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__list__def,axiom, % 185.87/185.99 ! [V_l_2] : % 185.87/185.99 ( c_List_Onat__list(V_l_2) % 185.87/185.99 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__size__pointwise,axiom, % 185.87/185.99 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 185.87/185.99 ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__update__nat,axiom, % 185.87/185.99 ! [V_n,V_ns,V_k] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__take,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__beyond,axiom, % 185.87/185.99 ! [V_x,V_i,V_xs,T_a] : % 185.87/185.99 ( 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)) % 185.87/185.99 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__id,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__list__update__neq,axiom, % 185.87/185.99 ! [V_x,V_xs,T_a,V_j,V_i] : % 185.87/185.99 ( V_i != V_j % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__list__update,axiom, % 185.87/185.99 ! [V_x,V_xs,T_a,V_k] : % 185.87/185.99 ( ( 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)) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( 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)) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__list__update,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__update,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_update__zip,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__swap,axiom, % 185.87/185.99 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 185.87/185.99 ( V_i != V_i_H % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__overwrite,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__code_I2_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__code_I3_J,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__butlastD,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__update__subsetI,axiom, % 185.87/185.99 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__update__subset__insert,axiom, % 185.87/185.99 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__list__update__eq,axiom, % 185.87/185.99 ! [V_x,V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__same__conv,axiom, % 185.87/185.99 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 185.87/185.99 ( 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_xs_2))) % 185.87/185.99 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 185.87/185.99 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__list__update,axiom, % 185.87/185.99 ! [V_x,V_j,V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( ( V_i = V_j % 185.87/185.99 => 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 ) % 185.87/185.99 & ( V_i != V_j % 185.87/185.99 => 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) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__butlast,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__butlast,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__update__memI,axiom, % 185.87/185.99 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__conv__take,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1__iff__update,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 <=> ? [B_y,B_n] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__list__update,axiom, % 185.87/185.99 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__upto,axiom, % 185.87/185.99 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__take,axiom, % 185.87/185.99 ! [V_i,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__sublistI,axiom, % 185.87/185.99 ! [V_I_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__zipI2,axiom, % 185.87/185.99 ! [V_xs,T_b,V_ys,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__zipI1,axiom, % 185.87/185.99 ! [V_ys,T_b,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 185.87/185.99 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_card__distinct,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__card,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__eq__iff__index__eq,axiom, % 185.87/185.99 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => ( 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_xs_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) % 185.87/185.99 <=> V_i_2 = V_j_2 ) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__conv__nth,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 <=> ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => ! [B_j] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => ( B_i != B_j % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__listsum__conv__Setsum,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Ocard_H__def,axiom, % 185.87/185.99 ! [V_A_2,T_b] : % 185.87/185.99 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__take__lemma,axiom, % 185.87/185.99 ! [V_ys,V_xs,T_a,V_k] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( 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))) % 185.87/185.99 => ( ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 185.87/185.99 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__remove1__eq,axiom, % 185.87/185.99 ! [V_x_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Cons__number__of,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_v] : % 185.87/185.99 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists_ONil,axiom, % 185.87/185.99 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Nil2,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Nil1,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) % 185.87/185.99 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__butlast,axiom, % 185.87/185.99 ! [T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct_Osimps_I1_J,axiom, % 185.87/185.99 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__remove1,axiom, % 185.87/185.99 ! [V_x,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast_Osimps_I1_J,axiom, % 185.87/185.99 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_x,T_a,V_xs] : % 185.87/185.99 ( ( V_xs = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 185.87/185.99 & ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs,T_a,V_y,V_x] : % 185.87/185.99 ( ( V_x = V_y % 185.87/185.99 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 185.87/185.99 & ( V_x != V_y % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osimps_I3_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osimps_I2_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upto__empty,axiom, % 185.87/185.99 ! [V_i,V_j] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 185.87/185.99 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__0,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__eq__Nil,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Nil,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__nil,axiom, % 185.87/185.99 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1_Osimps_I1_J,axiom, % 185.87/185.99 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1__commute,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osize_I1_J,axiom, % 185.87/185.99 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrelp_ONil,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrelp_Oequations_I1_J,axiom, % 185.87/185.99 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip_Osimps_I1_J,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__Nil,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__simps_I1_J,axiom, % 185.87/185.99 ! [T_a] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_a) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osize_I3_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__0__conv,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__empty,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__empty2,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Oset_Osimps_I1_J,axiom, % 185.87/185.99 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__nonempty,axiom, % 185.87/185.99 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update_Osimps_I1_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__code_I1_J,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__remove1,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_ba_2,V_a_2] : % 185.87/185.99 ( V_a_2 != V_ba_2 % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_ba_2,V_xs_2)))) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_notin__set__remove1,axiom, % 185.87/185.99 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1__idem,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__empty,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__remove1__subset,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__greater__0__conv,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( 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_b)),V_xs_2))) % 185.87/185.99 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__1__Cons,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_not__listrel1__Nil,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_not__Nil__listrel1,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel_ONil,axiom, % 185.87/185.99 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__Nil__right,axiom, % 185.87/185.99 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nil2__notin__lex,axiom, % 185.87/185.99 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nil__notin__lex,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Cons,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upto_Osimps,axiom, % 185.87/185.99 ! [V_j,V_i] : % 185.87/185.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.87/185.99 => 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)) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 185.87/185.99 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__singleton,axiom, % 185.87/185.99 ! [V_x_2,T_b,V_A_2] : % 185.87/185.99 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 185.87/185.99 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 185.87/185.99 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__empty,axiom, % 185.87/185.99 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Cons_H,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_n] : % 185.87/185.99 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upto__rec__number__of,axiom, % 185.87/185.99 ! [V_n,V_m] : % 185.87/185.99 ( ( 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))) % 185.87/185.99 => 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))) ) % 185.87/185.99 & ( ~ 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))) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel__Nil,axiom, % 185.87/185.99 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__Cons__sing__Nil,axiom, % 185.87/185.99 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__remove1,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,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_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upto_Opsimps,axiom, % 185.87/185.99 ! [V_j_2,V_i_2] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 185.87/185.99 => 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)) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 185.87/185.99 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select,axiom, % 185.87/185.99 ! [V_s_2,T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listset_Osimps_I1_J,axiom, % 185.87/185.99 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__Cons1,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osimps_I5_J,axiom, % 185.87/185.99 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list_Osimps_I4_J,axiom, % 185.87/185.99 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ). % 185.87/185.99 % 185.87/185.99 fof(fact_listset_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__Cons,axiom, % 185.87/185.99 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sorted__list__of__set__remove,axiom, % 185.87/185.99 ! [V_x_2,V_A_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_List_Olinorder__class_Osorted__list__of__set(T_b,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))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upto_Opinduct,axiom, % 185.87/185.99 ! [V_Pa_2,V_a1_2,V_a0_2] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( ! [B_i,B_j] : % 185.87/185.99 ( 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))) % 185.87/185.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sorted__list__of__set__empty,axiom, % 185.87/185.99 ! [T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_anamorph_Osimps,axiom, % 185.87/185.99 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 185.87/185.99 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.99 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) % 185.87/185.99 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 185.87/185.99 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__Cons,axiom, % 185.87/185.99 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),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_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,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)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append1__eq__conv,axiom, % 185.87/185.99 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) % 185.87/185.99 <=> ( V_xs_2 = V_ys_2 % 185.87/185.99 & V_x_2 = V_y_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__eq__append__conv,axiom, % 185.87/185.99 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) % 185.87/185.99 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 185.87/185.99 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 185.87/185.99 | ? [B_ys_H] : % 185.87/185.99 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 185.87/185.99 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__eq__Cons__conv,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 185.87/185.99 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 185.87/185.99 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 185.87/185.99 | ? [B_ys_H] : % 185.87/185.99 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 185.87/185.99 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Cons__eq__appendI,axiom, % 185.87/185.99 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 185.87/185.99 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 185.87/185.99 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 185.87/185.99 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__Cons,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__in__lists__conv,axiom, % 185.87/185.99 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__assoc,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__eq__append__conv2,axiom, % 185.87/185.99 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2) % 185.87/185.99 <=> ? [B_us] : % 185.87/185.99 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 185.87/185.99 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 185.87/185.99 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 185.87/185.99 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_same__append__eq,axiom, % 185.87/185.99 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) % 185.87/185.99 <=> V_ys_2 = V_zs_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__same__eq,axiom, % 185.87/185.99 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) % 185.87/185.99 <=> V_ys_2 = V_zs_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__eq__appendI,axiom, % 185.87/185.99 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 185.87/185.99 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 185.87/185.99 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__append,axiom, % 185.87/185.99 ! [V_ys,V_xs,T_a] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_a) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__append,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__append,axiom, % 185.87/185.99 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 185.87/185.99 ( 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) % 185.87/185.99 => ( 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) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_eq__Nil__appendI,axiom, % 185.87/185.99 ! [T_a,V_ys,V_xs] : % 185.87/185.99 ( V_xs = V_ys % 185.87/185.99 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__self__conv2,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__self__conv,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 185.87/185.99 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__is__Nil__conv,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 185.87/185.99 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_self__append__conv2,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_ys_2] : % 185.87/185.99 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_self__append__conv,axiom, % 185.87/185.99 ! [V_ys_2,T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 185.87/185.99 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__Nil2,axiom, % 185.87/185.99 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nil__is__append__conv,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 185.87/185.99 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 185.87/185.99 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__Nil,axiom, % 185.87/185.99 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__append,axiom, % 185.87/185.99 ! [V_xs,T_a,V_ys] : % 185.87/185.99 ( ( V_ys = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 185.87/185.99 & ( V_ys != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__append__length,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__append__length__plus,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__append,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__append1,axiom, % 185.87/185.99 ! [V_x,V_ys,V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__length,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__butlast__appendI,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 185.87/185.99 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__snoc,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__listrel1I,axiom, % 185.87/185.99 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 & V_us_2 = V_vs_2 ) % 185.87/185.99 | ( V_xs_2 = V_ys_2 % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__append__leftI,axiom, % 185.87/185.99 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 185.87/185.99 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__append,axiom, % 185.87/185.99 ! [V_ys,V_xs,T_a,V_n] : % 185.87/185.99 ( ( 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))) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( ~ 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))) % 185.87/185.99 => 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))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__update__append,axiom, % 185.87/185.99 ! [V_x,V_ys,V_xs,T_a,V_n] : % 185.87/185.99 ( ( 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))) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( ~ 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))) % 185.87/185.99 => 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)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublist__append,axiom, % 185.87/185.99 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,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_b)),V_l_2)))),V_A_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1I,axiom, % 185.87/185.99 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) % 185.87/185.99 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2)) % 185.87/185.99 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__append__left__rightI,axiom, % 185.87/185.99 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_ba_2,V_a_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_ba_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Suc__conv__app__nth,axiom, % 185.87/185.99 ! [V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_snoc__listrel1__snoc__iff,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 & V_x_2 = V_y_2 ) % 185.87/185.99 | ( V_xs_2 = V_ys_2 % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listrel1E,axiom, % 185.87/185.99 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) % 185.87/185.99 => ~ ! [B_x,B_y] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 185.87/185.99 => ! [B_us,B_vs] : % 185.87/185.99 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 185.87/185.99 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__append__leftD,axiom, % 185.87/185.99 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate1__def,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_upd__conv__take__nth__drop,axiom, % 185.87/185.99 ! [V_a,V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__take__drop__id,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Suc__Cons,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__1__Cons,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__via__drop,axiom, % 185.87/185.99 ! [V_ys,V_y,V_xs,V_n,T_a] : % 185.87/185.99 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct1__rotate,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 185.87/185.99 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__drop,axiom, % 185.87/185.99 ! [V_i,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__butlast,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_butlast__drop,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__take,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__drop,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__0,axiom, % 185.87/185.99 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__drop,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__zip,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__rotate1,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__drop,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__rotate1,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__set__dropD,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__drop__subset,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate1__is__Nil__conv,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Nil,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__drop__subset__set__drop,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__eq__Nil,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__all,axiom, % 185.87/185.99 ! [V_n,V_xs,T_a] : % 185.87/185.99 ( 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)) % 185.87/185.99 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__append,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__eq__conv__conj,axiom, % 185.87/185.99 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 185.87/185.99 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) % 185.87/185.99 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Cons,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Cons_H,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_n] : % 185.87/185.99 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__drop,axiom, % 185.87/185.99 ! [V_xs,T_a,V_i,V_n] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__eq__append__conv__if,axiom, % 185.87/185.99 ! [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_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 185.87/185.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 185.87/185.99 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 185.87/185.99 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) % 185.87/185.99 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 185.87/185.99 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),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 ) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__drop_H,axiom, % 185.87/185.99 ! [V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__simps,axiom, % 185.87/185.99 ! [V_xs,V_x,T_b,T_a] : % 185.87/185.99 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 185.87/185.99 & 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Cons__number__of,axiom, % 185.87/185.99 ! [V_xs,V_x,T_a,V_v] : % 185.87/185.99 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__add,axiom, % 185.87/185.99 ! [V_xs,T_a,V_j,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate1__length01,axiom, % 185.87/185.99 ! [V_xs,T_a] : % 185.87/185.99 ( 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))) % 185.87/185.99 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__append1,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__append2,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_id__take__nth__drop,axiom, % 185.87/185.99 ! [V_xs,T_a,V_i] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__hd__drop,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n] : % 185.87/185.99 ( 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))) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__drop__conv__nth,axiom, % 185.87/185.99 ! [V_n,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => ( 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))) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd_Osimps,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__append,axiom, % 185.87/185.99 ! [V_ys,T_a,V_xs] : % 185.87/185.99 ( ( V_xs = c_List_Olist_ONil(T_a) % 185.87/185.99 => 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) ) % 185.87/185.99 & ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__append2,axiom, % 185.87/185.99 ! [V_ys,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__in__set,axiom, % 185.87/185.99 ! [T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__conv__nth,axiom, % 185.87/185.99 ! [T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate1__hd__tl,axiom, % 185.87/185.99 ! [T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__rotate__conv__nth,axiom, % 185.87/185.99 ! [V_n,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl__drop,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__tl,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl_Osimps_I2_J,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__rotate,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 185.87/185.99 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__tl,axiom, % 185.87/185.99 ! [V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__add,axiom, % 185.87/185.99 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate0,axiom, % 185.87/185.99 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__rotate,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__rotate,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__rotate,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__is__Nil__conv,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : % 185.87/185.99 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl_Osimps_I1_J,axiom, % 185.87/185.99 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate1__rotate__swap,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__def,axiom, % 185.87/185.99 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl__append2,axiom, % 185.87/185.99 ! [V_ys,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__tl,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__conv__mod,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__Suc,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__Suc,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__id,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n] : % 185.87/185.99 ( 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) % 185.87/185.99 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__length01,axiom, % 185.87/185.99 ! [V_n,V_xs,T_a] : % 185.87/185.99 ( 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))) % 185.87/185.99 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__tl,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_tl__take,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__Suc,axiom, % 185.87/185.99 ! [V_n,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__drop__take,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_fold1__set,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 185.87/185.99 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sorted__list__of__set__insert,axiom, % 185.87/185.99 ! [V_x_2,V_A_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,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)))))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__not__Nil,axiom, % 185.87/185.99 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__Nil,axiom, % 185.87/185.99 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ). % 185.87/185.99 % 185.87/185.99 fof(fact_remove1__insort,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__insort,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__insort,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_start__le__sum,axiom, % 185.87/185.99 ! [V_ns_2,V_n_2,V_m_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__assoc,axiom, % 185.87/185.99 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( class_Groups_Osemigroup__add(T_b) % 185.87/185.99 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__absorb0,axiom, % 185.87/185.99 ! [V_zs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_b) % 185.87/185.99 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__left__comm,axiom, % 185.87/185.99 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__key__left__comm,axiom, % 185.87/185.99 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_fun__left__comm__insort,axiom, % 185.87/185.99 ! [T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__Cons,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__key_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__key_Osimps_I1_J,axiom, % 185.87/185.99 ! [V_x_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__foldl,axiom, % 185.87/185.99 ! [T_b] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_b) % 185.87/185.99 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sum__eq__0__conv,axiom, % 185.87/185.99 ! [V_ns_2,V_m_2] : % 185.87/185.99 ( 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) % 185.87/185.99 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 & ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 185.87/185.99 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__insort,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) % 185.87/185.99 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 185.87/185.99 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 185.87/185.99 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Sup__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.99 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Inf__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.99 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Sup__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Lattices_Olattice(T_b) % 185.87/185.99 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Inf__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Lattices_Olattice(T_b) % 185.87/185.99 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Min__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Max__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_min__max_OInf__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_min__max_OSup__fin__set__fold,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_SUPR__set__fold,axiom, % 185.87/185.99 ! [V_f_2,V_xs_2,T_c,T_b] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_INFI__set__fold,axiom, % 185.87/185.99 ! [V_f_2,V_xs_2,T_c,T_b] : % 185.87/185.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 185.87/185.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_elem__le__sum,axiom, % 185.87/185.99 ! [V_ns_2,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__insert__insort__key,axiom, % 185.87/185.99 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 185.87/185.99 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__append__rightI,axiom, % 185.87/185.99 ! [V_r_2,V_x_2,T_b,V_y_2] : % 185.87/185.99 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__insort__insert,axiom, % 185.87/185.99 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 185.87/185.99 ( class_Orderings_Olinorder(T_c) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__insert__triv,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__insort__insert,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__insert__key__triv,axiom, % 185.87/185.99 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) % 185.87/185.99 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_insort__insert__insort,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : % 185.87/185.99 ( class_Orderings_Olinorder(T_b) % 185.87/185.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lexord__Nil__left,axiom, % 185.87/185.99 ! [V_r_2,V_y_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 185.87/185.99 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__list__update,axiom, % 185.87/185.99 ! [V_x,V_k,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => ( ( 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)) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 185.87/185.99 & ( 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)) % 185.87/185.99 => 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) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__appendL,axiom, % 185.87/185.99 ! [V_xs,T_a,V_ys] : % 185.87/185.99 ( V_ys = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__appendR,axiom, % 185.87/185.99 ! [V_xs,T_a,V_ys] : % 185.87/185.99 ( V_ys != c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__append,axiom, % 185.87/185.99 ! [V_xs,T_a,V_ys] : % 185.87/185.99 ( ( V_ys = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 185.87/185.99 & ( V_ys != c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__ConsL,axiom, % 185.87/185.99 ! [V_x,T_a,V_xs] : % 185.87/185.99 ( V_xs = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__ConsR,axiom, % 185.87/185.99 ! [V_x,T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last_Osimps,axiom, % 185.87/185.99 ! [V_x,T_a,V_xs] : % 185.87/185.99 ( ( V_xs = c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 185.87/185.99 & ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__in__set,axiom, % 185.87/185.99 ! [T_b,V_as_2] : % 185.87/185.99 ( V_as_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__snoc,axiom, % 185.87/185.99 ! [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 ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__drop,axiom, % 185.87/185.99 ! [V_xs,T_a,V_n] : % 185.87/185.99 ( 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))) % 185.87/185.99 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__butlast__last__id,axiom, % 185.87/185.99 ! [T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_snoc__eq__iff__butlast,axiom, % 185.87/185.99 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 185.87/185.99 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2 % 185.87/185.99 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 185.87/185.99 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__conv__nth,axiom, % 185.87/185.99 ! [T_a,V_xs] : % 185.87/185.99 ( V_xs != c_List_Olist_ONil(T_a) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists_Osimps,axiom, % 185.87/185.99 ! [V_A_2,V_a_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 185.87/185.99 | ? [B_a,B_l] : % 185.87/185.99 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 185.87/185.99 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select__weigth__select,axiom, % 185.87/185.99 ! [T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__mapI,axiom, % 185.87/185.99 ! [V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.87/185.99 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_last__map,axiom, % 185.87/185.99 ! [V_f_2,T_c,T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__inj__on,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 185.87/185.99 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2))) % 185.87/185.99 => V_xs_2 = V_ys_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__on__map__eq__map,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(T_b,T_c,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))) % 185.87/185.99 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 185.87/185.99 <=> V_xs_2 = V_ys_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__size__map,axiom, % 185.87/185.99 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Omap_Oidentity,axiom, % 185.87/185.99 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Omap_Oid,axiom, % 185.87/185.99 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Omap_Ocomp,axiom, % 185.87/185.99 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__comp__map,axiom, % 185.87/185.99 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_List_Omap_Ocompositionality,axiom, % 185.87/185.99 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__map,axiom, % 185.87/185.99 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_drop__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_hd__map,axiom, % 185.87/185.99 ! [V_f_2,T_c,T_b,V_xs_2] : % 185.87/185.99 ( V_xs_2 != c_List_Olist_ONil(T_b) % 185.87/185.99 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__append,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__butlast,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_take__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__ident,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__map__eq__map,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.87/185.99 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) % 185.87/185.99 <=> V_xs_2 = V_ys_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__injective,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) % 185.87/185.99 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 185.87/185.99 => V_xs_2 = V_ys_2 ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__0,axiom, % 185.87/185.99 ! [V_xs_2,T_c,T_b] : % 185.87/185.99 ( class_Groups_Omonoid__add(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__const__mult,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] : % 185.87/185.99 ( class_Rings_Osemiring__0(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__mult__const,axiom, % 185.87/185.99 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( class_Rings_Osemiring__0(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__subtractf,axiom, % 185.87/185.99 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( class_Groups_Oab__group__add(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__addf,axiom, % 185.87/185.99 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__eq__imp__length__eq,axiom, % 185.87/185.99 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__eq__conv,axiom, % 185.87/185.99 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 185.87/185.99 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__update,axiom, % 185.87/185.99 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__is__Nil__conv,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_b,T_c] : % 185.87/185.99 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map_Osimps_I1_J,axiom, % 185.87/185.99 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nil__is__map__conv,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__map2,axiom, % 185.87/185.99 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__zip__map2,axiom, % 185.87/185.99 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,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_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__zip__map,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__map1,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__map__map,axiom, % 185.87/185.99 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,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_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),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_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__same__conv__map,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_rotate__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__tl,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_foldl__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nth__map,axiom, % 185.87/185.99 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__fun__upd,axiom, % 185.87/185.99 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 185.87/185.99 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 185.87/185.99 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__abs,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_uminus__listsum__map,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( class_Groups_Oab__group__add(T_b) % 185.87/185.99 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__on__mapI,axiom, % 185.87/185.99 ! [V_A_2,V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) % 185.87/185.99 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__mapD,axiom, % 185.87/185.99 ! [V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 185.87/185.99 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_inj__map,axiom, % 185.87/185.99 ! [V_f_2,T_c,T_b] : % 185.87/185.99 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) % 185.87/185.99 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 185.87/185.99 ! [V_f_2,V_xs_2,T_b,T_c] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__triv,axiom, % 185.87/185.99 ! [V_xs_2,V_r_2,T_c,T_b] : % 185.87/185.99 ( class_Rings_Osemiring__1(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__map__remove1,axiom, % 185.87/185.99 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Nitpick_Osetsum_H__def,axiom, % 185.87/185.99 ! [V_f_2,V_A_2,T_b,T_c] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_c) % 185.87/185.99 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) % 185.87/185.99 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 185.87/185.99 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_pick__same,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_l_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),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_b),V_xs_2),V_l_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_one__code__numeral__def,axiom, % 185.87/185.99 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_less__code__numeral__code,axiom, % 185.87/185.99 ! [V_m_2,V_n_2] : % 185.87/185.99 ( 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))) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 185.87/185.99 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 185.87/185.99 % 185.87/185.99 fof(fact_times__code__numeral__code,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 185.87/185.99 ! [V_m_2,V_n_2] : % 185.87/185.99 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 185.87/185.99 <=> V_n_2 = V_m_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zero__code__numeral__def,axiom, % 185.87/185.99 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_code__numeral_Oof__nat__inject,axiom, % 185.87/185.99 ! [V_y_2,V_x_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.87/185.99 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 185.87/185.99 <=> V_x_2 = V_y_2 ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__fst__zip,axiom, % 185.87/185.99 ! [V_ys_2,T_c,V_xs_2,T_b] : % 185.87/185.99 ( 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) % 185.87/185.99 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_map__snd__zip,axiom, % 185.87/185.99 ! [V_ys_2,T_c,V_xs_2,T_b] : % 185.87/185.99 ( 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) % 185.87/185.99 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_number__of__code__numeral__def,axiom, % 185.87/185.99 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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__map__fst__snd,axiom, % 185.87/185.99 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ). % 185.87/185.99 % 185.87/185.99 fof(fact_plus__code__numeral__code,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_less__eq__code__numeral__code,axiom, % 185.87/185.99 ! [V_m_2,V_n_2] : % 185.87/185.99 ( 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))) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_pick__member,axiom, % 185.87/185.99 ! [V_xs_2,T_b,V_i_2] : % 185.87/185.99 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_zip__eq__conv,axiom, % 185.87/185.99 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 185.87/185.99 ( 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) % 185.87/185.99 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 185.87/185.99 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 % 185.87/185.99 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__size__conv__listsum,axiom, % 185.87/185.99 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,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_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_code__numeral__not__eq__zero,axiom, % 185.87/185.99 ! [V_i_2] : % 185.87/185.99 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.99 <=> 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)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 185.87/185.99 ! [V_l_2,V_k_2,V_f_2,T_b] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.99 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 185.87/185.99 ! [V_j_2,V_i_2,V_f_2,T_b] : % 185.87/185.99 ( class_Groups_Ocomm__monoid__add(T_b) % 185.87/185.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select__weight__member,axiom, % 185.87/185.99 ! [V_s_2,V_xs_2,T_b] : % 185.87/185.99 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select__weight__def,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,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_b,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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_select__def,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,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_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_subtract__code__numeral__code,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_times__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of__inverse,axiom, % 185.87/185.99 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 185.87/185.99 % 185.87/185.99 fof(fact_of__nat__nat__of,axiom, % 185.87/185.99 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of__of__nat,axiom, % 185.87/185.99 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 185.87/185.99 % 185.87/185.99 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 185.87/185.99 ! [V_l_2,V_k_2] : % 185.87/185.99 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 185.87/185.99 <=> V_k_2 = V_l_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_code__numeral_Onat__of__inject,axiom, % 185.87/185.99 ! [V_y_2,V_x_2] : % 185.87/185.99 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 185.87/185.99 <=> V_x_2 = V_y_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_type__definition__code__numeral,axiom, % 185.87/185.99 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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_less__code__numeral__def,axiom, % 185.87/185.99 ! [V_m_2,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 185.87/185.99 <=> 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of,axiom, % 185.87/185.99 ! [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)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of__number,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_int__of__def,axiom, % 185.87/185.99 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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_less__eq__code__numeral__def,axiom, % 185.87/185.99 ! [V_m_2,V_n_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 185.87/185.99 <=> 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of__code,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_nat__of__aux__def,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_Suc__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_minus__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_of__nat__inverse,axiom, % 185.87/185.99 ! [V_y_2] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 185.87/185.99 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_plus__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_div__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_subtract__code__numeral__def,axiom, % 185.87/185.99 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 185.87/185.99 % 185.87/185.99 fof(fact_minus__code__numeral__code,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_mod__code__numeral__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_code__numeral__decr,axiom, % 185.87/185.99 ! [V_k] : % 185.87/185.99 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 185.87/185.99 => 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))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsum__mono,axiom, % 185.87/185.99 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 185.87/185.99 ( ( class_Groups_Omonoid__add(T_c) % 185.87/185.99 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_partition__set,axiom, % 185.87/185.99 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 185.87/185.99 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 185.87/185.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__Int__eq,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp_ONil,axiom, % 185.87/185.99 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_append__in__listsp__conv,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 185.87/185.99 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp_Oequations_I2_J,axiom, % 185.87/185.99 ! [V_a2_2,V_a1_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) % 185.87/185.99 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 185.87/185.99 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp__inf__eq,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,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(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp__infI,axiom, % 185.87/185.99 ! [V_B_2,V_l_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) % 185.87/185.99 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp__conj__eq,axiom, % 185.87/185.99 ! [V_x_2,V_B_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(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),V_A_2)),V_B_2)),V_x_2)) % 185.87/185.99 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) % 185.87/185.99 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_in__listsp__conv__set,axiom, % 185.87/185.99 ! [V_xs_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 185.87/185.99 <=> ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp_Oequations_I1_J,axiom, % 185.87/185.99 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp__mono,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_partition__P,axiom, % 185.87/185.99 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 185.87/185.99 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) % 185.87/185.99 => ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 185.87/185.99 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 185.87/185.99 & ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 185.87/185.99 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_partition_Osimps_I1_J,axiom, % 185.87/185.99 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_listsp__lists__eq,axiom, % 185.87/185.99 ! [V_x_2,V_A_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) % 185.87/185.99 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_partition_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_lists__IntI,axiom, % 185.87/185.99 ! [V_B_2,V_A_2,V_l_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) % 185.87/185.99 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_product_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__def,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 <=> ( 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) % 185.87/185.99 & ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__map1,axiom, % 185.87/185.99 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2) % 185.87/185.99 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__map2,axiom, % 185.87/185.99 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2)) % 185.87/185.99 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__Nil,axiom, % 185.87/185.99 ! [V_ys_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) % 185.87/185.99 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__Nil2,axiom, % 185.87/185.99 ! [V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) % 185.87/185.99 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__lengthD,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => 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) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__eq,axiom, % 185.87/185.99 ! [T_b,V_ys_2,V_xs_2] : % 185.87/185.99 ( V_xs_2 = V_ys_2 % 185.87/185.99 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__takeI,axiom, % 185.87/185.99 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__Cons,axiom, % 185.87/185.99 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) % 185.87/185.99 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.87/185.99 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__append,axiom, % 185.87/185.99 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 185.87/185.99 ( 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) % 185.87/185.99 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2)) % 185.87/185.99 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__appendI,axiom, % 185.87/185.99 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) % 185.87/185.99 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_ba_2),V_d_2)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__dropI,axiom, % 185.87/185.99 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_product_Osimps_I1_J,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__conv__all__nth,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 <=> ( 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) % 185.87/185.99 & ! [B_i] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__nthD,axiom, % 185.87/185.99 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => ( 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_xs_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__nthD2,axiom, % 185.87/185.99 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 185.87/185.99 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__update__cong,axiom, % 185.87/185.99 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] : % 185.87/185.99 ( 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_xs_2))) % 185.87/185.99 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2__update__cong2,axiom, % 185.87/185.99 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 185.87/185.99 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 185.87/185.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__product,axiom, % 185.87/185.99 ! [V_ys,T_b,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_product__list__set,axiom, % 185.87/185.99 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublists__powset,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__sublists,axiom, % 185.87/185.99 ! [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)) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublists_Osimps_I1_J,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_sublists_Osimps_I2_J,axiom, % 185.87/185.99 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__set__sublists,axiom, % 185.87/185.99 ! [V_xs_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_set__n__lists,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_enum__the__def,axiom, % 185.87/185.99 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ). % 185.87/185.99 % 185.87/185.99 fof(fact_distinct__n__lists,axiom, % 185.87/185.99 ! [V_n,V_xs,T_a] : % 185.87/185.99 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/185.99 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_n__lists__Nil,axiom, % 185.87/185.99 ! [T_a,V_n] : % 185.87/185.99 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => 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))) ) % 185.87/185.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 185.87/185.99 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_n__lists_Osimps_I1_J,axiom, % 185.87/185.99 ! [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))) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__n__lists,axiom, % 185.87/185.99 ! [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) ). % 185.87/185.99 % 185.87/185.99 fof(fact_length__n__lists__elem,axiom, % 185.87/185.99 ! [V_xs_2,V_n_2,V_ys_2,T_b] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) % 185.87/185.99 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ). % 185.87/185.99 % 185.87/185.99 fof(fact_list__all2I,axiom, % 185.87/185.99 ! [V_Pa_2,V_ba_2,V_a_2,T_c,T_b] : % 185.87/185.99 ( ! [B_x] : % 185.87/185.99 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_ba_2)))) % 185.87/185.99 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) % 185.87/185.99 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ba_2) % 185.87/185.99 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) ) ) ). % 185.87/185.99 % 185.87/186.00 fof(fact_all__nth__imp__all__set,axiom, % 185.87/186.00 ! [V_x_2,V_Pa_2,V_xs_2,T_b] : % 185.87/186.00 ( ! [B_i] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 185.87/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 185.87/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 185.87/186.00 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 185.87/186.00 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 185.87/186.00 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_map__removeAll__inj__on,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 185.87/186.00 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__remdups,axiom, % 185.87/186.00 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__remdups__leq,axiom, % 185.87/186.00 ! [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))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__remdups__id,axiom, % 185.87/186.00 ! [V_xs,T_a] : % 185.87/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/186.00 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__removeAll,axiom, % 185.87/186.00 ! [V_x,V_xs,T_a] : % 185.87/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/186.00 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups__id__iff__distinct,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : % 185.87/186.00 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2 % 185.87/186.00 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__remdups__eq,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : % 185.87/186.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 185.87/186.00 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_set__remdups,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups__remdups,axiom, % 185.87/186.00 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 185.87/186.00 % 185.87/186.00 fof(fact_removeAll__append,axiom, % 185.87/186.00 ! [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)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_removeAll_Osimps_I2_J,axiom, % 185.87/186.00 ! [V_xs,T_a,V_y,V_x] : % 185.87/186.00 ( ( V_x = V_y % 185.87/186.00 => 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) ) % 185.87/186.00 & ( V_x != V_y % 185.87/186.00 => 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)) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups__eq__nil__iff,axiom, % 185.87/186.00 ! [V_x_2,T_b] : % 185.87/186.00 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) % 185.87/186.00 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_removeAll_Osimps_I1_J,axiom, % 185.87/186.00 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups__eq__nil__right__iff,axiom, % 185.87/186.00 ! [V_x_2,T_b] : % 185.87/186.00 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) % 185.87/186.00 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups_Osimps_I1_J,axiom, % 185.87/186.00 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups__map__remdups,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remove1__remdups,axiom, % 185.87/186.00 ! [V_x,V_xs,T_a] : % 185.87/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/186.00 => 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)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_removeAll__id,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,T_b] : % 185.87/186.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__remove1__removeAll,axiom, % 185.87/186.00 ! [V_x,V_xs,T_a] : % 185.87/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 185.87/186.00 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_remdups_Osimps_I2_J,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,T_b] : % 185.87/186.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) % 185.87/186.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__remdups__card__conv,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_map__removeAll__inj,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 185.87/186.00 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 185.87/186.00 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_set__removeAll,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__remdups__concat,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : % 185.87/186.00 ( class_Orderings_Olinorder(T_b) % 185.87/186.00 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__conv__foldl,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_foldl__conv__concat,axiom, % 185.87/186.00 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat_Osimps_I1_J,axiom, % 185.87/186.00 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 185.87/186.00 % 185.87/186.00 fof(fact_sort__key__simps_I1_J,axiom, % 185.87/186.00 ! [V_f_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_set__sort,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__sort,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__sort,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) % 185.87/186.00 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat_Osimps_I2_J,axiom, % 185.87/186.00 ! [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)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__eq__Nil__conv,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : % 185.87/186.00 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 185.87/186.00 <=> ! [B_x] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 185.87/186.00 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_Nil__eq__concat__conv,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : % 185.87/186.00 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 185.87/186.00 <=> ! [B_x] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 185.87/186.00 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_map__concat,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__concat,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_set__concat,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_sort__key__simps_I2_J,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__append,axiom, % 185.87/186.00 ! [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)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_sort__foldl__insort,axiom, % 185.87/186.00 ! [V_xs_2,T_b] : % 185.87/186.00 ( class_Orderings_Olinorder(T_b) % 185.87/186.00 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__injective,axiom, % 185.87/186.00 ! [V_ys_2,V_xs_2,T_b] : % 185.87/186.00 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 185.87/186.00 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 185.87/186.00 => ( ! [B_x] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 185.87/186.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 185.87/186.00 => V_xs_2 = V_ys_2 ) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__eq__concat__iff,axiom, % 185.87/186.00 ! [V_ys_2,V_xs_2,T_b] : % 185.87/186.00 ( ! [B_x] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) % 185.87/186.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) ) % 185.87/186.00 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) % 185.87/186.00 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 185.87/186.00 <=> V_xs_2 = V_ys_2 ) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_concat__map__singleton,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_n__lists_Osimps_I2_J,axiom, % 185.87/186.00 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_transpose_Osimps_I3_J,axiom, % 185.87/186.00 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_transpose__aux__filter__head,axiom, % 185.87/186.00 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),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)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_filter__concat,axiom, % 185.87/186.00 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ). % 185.87/186.00 % 185.87/186.00 fof(fact_filter__sort,axiom, % 185.87/186.00 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] : % 185.87/186.00 ( class_Orderings_Olinorder(T_c) % 185.87/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_partition__filter2,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_distinct__filter,axiom, % 185.87/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 185.87/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 185.87/186.00 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_sum__length__filter__compl,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_length__filter__le,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_filter__id__conv,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 185.87/186.00 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 185.87/186.00 <=> ! [B_x] : % 185.87/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 185.87/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 185.87/186.00 % 185.87/186.00 fof(fact_filter__is__subset,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 185.87/186.00 % 185.87/186.00 fof(fact_partition__filter1,axiom, % 185.87/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ). % 185.87/186.00 % 185.87/186.00 fof(fact_filter__remove1,axiom, % 185.87/186.00 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_remove1__filter__not,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_Q_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(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),V_Q_2)),V_Pa_2)),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__insort__triv,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 186.01/186.00 ( class_Orderings_Olinorder(T_c) % 186.01/186.00 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__append,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose_Osimps_I1_J,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__empty__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_remdups__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_removeAll__filter__not,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_removeAll__filter__not__eq,axiom, % 186.01/186.00 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose_Osimps_I2_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__transpose,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_i_2] : % 186.01/186.00 ( 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_b))),c_List_Otranspose(T_b,V_xs_2)))) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__map__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__filter__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__filter__less,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_partition__filter__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__minus__filter__out,axiom, % 186.01/186.00 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__in__sublist,axiom, % 186.01/186.00 ! [V_s_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__empty,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__filter__conv__card,axiom, % 186.01/186.00 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__aux__filter__tail,axiom, % 186.01/186.00 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose_Opsimps_I3_J,axiom, % 186.01/186.00 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) % 186.01/186.00 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose_Opsimps_I2_J,axiom, % 186.01/186.00 ! [V_xss_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) % 186.01/186.00 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sublist__shift__lemma__Suc,axiom, % 186.01/186.00 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pick__drop__zero,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_select__weigth__drop__zero,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose_Opsimps_I1_J,axiom, % 186.01/186.00 ! [T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) % 186.01/186.00 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__max__length,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : 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))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),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_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__aux__max,axiom, % 186.01/186.00 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr__append,axiom, % 186.01/186.00 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr__conv__foldl,axiom, % 186.01/186.00 ! [V_a_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Groups_Oab__semigroup__add(T_b) % 186.01/186.00 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr__map,axiom, % 186.01/186.00 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldl__foldr1,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( class_Groups_Omonoid__add(T_b) % 186.01/186.00 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldl__foldr1__lemma,axiom, % 186.01/186.00 ! [V_xs_2,V_a_2,T_b] : % 186.01/186.00 ( class_Groups_Omonoid__add(T_b) % 186.01/186.00 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__transpose,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,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_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sublist__def,axiom, % 186.01/186.00 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sublist__shift__lemma,axiom, % 186.01/186.00 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__upt,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_atLeastLessThan__upt,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__0,axiom, % 186.01/186.00 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__conv__Nil,axiom, % 186.01/186.00 ! [V_i,V_j] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 186.01/186.00 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__eq__Nil__conv,axiom, % 186.01/186.00 ! [V_j_2,V_i_2] : % 186.01/186.00 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 186.01/186.00 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__conv__Cons,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__rec,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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)) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__add__eq__append,axiom, % 186.01/186.00 ! [V_k,V_j,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__Suc,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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))) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__Suc__append,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_drop__upt,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_hd__upt,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__list__of__set__range,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_take__upt,axiom, % 186.01/186.00 ! [V_n,V_m,V_i] : % 186.01/186.00 ( 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)) % 186.01/186.00 => 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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__upt,axiom, % 186.01/186.00 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__upt,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__rec__number__of,axiom, % 186.01/186.00 ! [V_n,V_m] : % 186.01/186.00 ( ( 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))) % 186.01/186.00 => 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))) ) % 186.01/186.00 & ( ~ 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))) % 186.01/186.00 => 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) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_upt__eq__Cons__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 186.01/186.00 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 186.01/186.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 186.01/186.00 & V_i_2 = V_x_2 % 186.01/186.00 & 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 ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_last__upt,axiom, % 186.01/186.00 ! [V_j,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => 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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__Suc__upt,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_atLeastAtMost__upt,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_atLeast__upt,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__upt,axiom, % 186.01/186.00 ! [V_j,V_k,V_i] : % 186.01/186.00 ( 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)) % 186.01/186.00 => 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) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_greaterThanAtMost__upt,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_greaterThanLessThan__upt,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_atMost__upto,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__nth,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 186.01/186.00 ! [V_n_2,V_m_2,V_f_2,T_b] : % 186.01/186.00 ( class_Groups_Ocomm__monoid__add(T_b) % 186.01/186.00 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 186.01/186.00 ! [V_n_2,V_m_2,V_f_2,T_b] : % 186.01/186.00 ( class_Groups_Ocomm__monoid__add(T_b) % 186.01/186.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__map__upt,axiom, % 186.01/186.00 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 186.01/186.00 ( 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))) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__rectangle,axiom, % 186.01/186.00 ! [V_n_2,T_b,V_xs_2] : % 186.01/186.00 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.01/186.00 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 186.01/186.00 => ( ! [B_i] : % 186.01/186.00 ( 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_b))),V_xs_2))) % 186.01/186.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 ) % 186.01/186.00 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),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_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_insort__key__remove1,axiom, % 186.01/186.00 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 186.01/186.00 ( class_Orderings_Olinorder(T_c) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 186.01/186.00 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 186.01/186.00 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted_ONil,axiom, % 186.01/186.00 ! [T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__single,axiom, % 186.01/186.00 ! [V_x,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__upt,axiom, % 186.01/186.00 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__sort,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__insort__insert,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__tl,axiom, % 186.01/186.00 ! [V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__remove1,axiom, % 186.01/186.00 ! [V_a,V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__take,axiom, % 186.01/186.00 ! [V_n,V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__upto,axiom, % 186.01/186.00 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__drop,axiom, % 186.01/186.00 ! [V_n,V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__insort,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) % 186.01/186.00 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__many__eq,axiom, % 186.01/186.00 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) % 186.01/186.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__many,axiom, % 186.01/186.00 ! [V_zs,V_y,V_x,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 186.01/186.00 => 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))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted_Oequations_I1_J,axiom, % 186.01/186.00 ! [T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__butlast,axiom, % 186.01/186.00 ! [V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( V_xs != c_List_Olist_ONil(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__remdups,axiom, % 186.01/186.00 ! [V_l,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__distinct__set__unique,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 186.01/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 186.01/186.00 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 186.01/186.00 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__sort__key,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__insort__insert__key,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__map__remove1,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__insort__key,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) % 186.01/186.00 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__filter,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__map__same,axiom, % 186.01/186.00 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__same,axiom, % 186.01/186.00 ! [V_xs_2,V_g_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__Cons,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 186.01/186.00 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 & ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__append,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 186.01/186.00 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 186.01/186.00 & ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ! [B_xa] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__insort,axiom, % 186.01/186.00 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 186.01/186.00 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted_Oequations_I2_J,axiom, % 186.01/186.00 ! [V_a1_2,V_a2_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 186.01/186.00 <=> ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__list__of__set,axiom, % 186.01/186.00 ! [V_A_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.01/186.00 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 186.01/186.00 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_insort__remove1,axiom, % 186.01/186.00 ! [V_xs_2,V_a_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__nth__mono,axiom, % 186.01/186.00 ! [V_j,V_i,V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => ( 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))) % 186.01/186.00 => 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))) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__equals__nth__mono,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 <=> ! [B_j] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ! [B_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__sorted__distinct__set__unique,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 186.01/186.00 ( class_Orderings_Olinorder(T_c) % 186.01/186.00 => ( c_Fun_Oinj__on(T_b,T_c,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))) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 186.01/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 186.01/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 186.01/186.00 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 186.01/186.00 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__column,axiom, % 186.01/186.00 ! [V_i_2,V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 186.01/186.00 => ( 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_b))),V_xs_2))) % 186.01/186.00 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__nth__transpose__sorted,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 186.01/186.00 => ( 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_b))),c_List_Otranspose(T_b,V_xs_2)))) % 186.01/186.00 => ( 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_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)))) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_inj__on__rev,axiom, % 186.01/186.00 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__rev,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 186.01/186.00 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__append,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_singleton__rev__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2) % 186.01/186.00 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__singleton__conv,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) % 186.01/186.00 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__is__Nil__conv,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 186.01/186.00 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Nil__is__rev__conv,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 186.01/186.00 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev_Osimps_I1_J,axiom, % 186.01/186.00 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__concat,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_zip__rev,axiom, % 186.01/186.00 ! [V_ys,T_b,V_xs,T_a] : % 186.01/186.00 ( 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) % 186.01/186.00 => 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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__rev,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all2__rev,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 186.01/186.00 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2)) % 186.01/186.00 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all2__rev1,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 186.01/186.00 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) % 186.01/186.00 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__rev__ident,axiom, % 186.01/186.00 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__swap,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 186.01/186.00 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__is__rev__conv,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 186.01/186.00 <=> V_xs_2 = V_ys_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_listsum__rev,axiom, % 186.01/186.00 ! [V_xs,T_a] : % 186.01/186.00 ( class_Groups_Ocomm__monoid__add(T_a) % 186.01/186.00 => 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) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__rev,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr__foldl,axiom, % 186.01/186.00 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldl__foldr,axiom, % 186.01/186.00 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__eq__Cons__iff,axiom, % 186.01/186.00 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 186.01/186.00 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev_Osimps_I2_J,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_hd__rev,axiom, % 186.01/186.00 ! [T_a,V_xs] : % 186.01/186.00 ( V_xs != c_List_Olist_ONil(T_a) % 186.01/186.00 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_last__rev,axiom, % 186.01/186.00 ! [T_a,V_xs] : % 186.01/186.00 ( V_xs != c_List_Olist_ONil(T_a) % 186.01/186.00 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__transpose,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__foldl__cons,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__take,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__drop,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rotate__rev,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__nth,axiom, % 186.01/186.00 ! [V_xs,T_a,V_n] : % 186.01/186.00 ( 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))) % 186.01/186.00 => 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))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__update,axiom, % 186.01/186.00 ! [V_y,V_xs,T_a,V_k] : % 186.01/186.00 ( 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))) % 186.01/186.00 => 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) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__rev__nth__mono,axiom, % 186.01/186.00 ! [V_j,V_i,V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 186.01/186.00 => ( 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))) % 186.01/186.00 => 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))) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldr__max__sorted,axiom, % 186.01/186.00 ! [V_y_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 186.01/186.00 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 186.01/186.00 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 186.01/186.00 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.01/186.00 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__transpose__sorted,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 186.01/186.00 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.01/186.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 186.01/186.00 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 186.01/186.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__column__length,axiom, % 186.01/186.00 ! [V_i_2,V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 186.01/186.00 => ( 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_b))),V_xs_2))) % 186.01/186.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpose__transpose,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) % 186.01/186.00 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(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_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 186.01/186.00 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__takeWhile,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__takeWhile__le,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__takeWhileD,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__eq__all__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_zip__takeWhile__fst,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_zip__takeWhile__snd,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__tail,axiom, % 186.01/186.00 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__eq__take,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__takeWhile,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_return__list__def,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__append1,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__nth,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__length__takeWhile,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__not__last,axiom, % 186.01/186.00 ! [T_b,V_xs_2] : % 186.01/186.00 ( V_xs_2 != c_List_Olist_ONil(T_b) % 186.01/186.00 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 186.01/186.00 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 186.01/186.00 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transfer__nat__int__list__return__embed,axiom, % 186.01/186.00 ! [V_l] : % 186.01/186.00 ( c_List_Onat__list(V_l) % 186.01/186.00 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_embed__list__def,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__neq__rev,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__neq__rev,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__dropWhile__id,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__dropWhile,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__dropWhile__le,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_hd__dropWhile,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__eq__Nil__conv,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__dropWhile,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 186.01/186.00 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__map,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__append1,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__eq__Cons__conv,axiom, % 186.01/186.00 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 186.01/186.00 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 186.01/186.00 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__eq__drop,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__nth,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),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_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_listsum__map__filter,axiom, % 186.01/186.00 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] : % 186.01/186.00 ( class_Groups_Omonoid__add(T_c) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 186.01/186.00 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) % 186.01/186.00 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted__nth__monoI,axiom, % 186.01/186.00 ! [V_xs,T_a] : % 186.01/186.00 ( class_Orderings_Olinorder(T_a) % 186.01/186.00 => ( ! [B_i,B_j] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 186.01/186.00 => ( 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))) % 186.01/186.00 => 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))) ) ) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__eq__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__eq__take__P__nth,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 186.01/186.00 ( ! [B_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) % 186.01/186.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__takeWhile__less__P__nth,axiom, % 186.01/186.00 ! [V_xs_2,T_b,V_Pa_2,V_j_2] : % 186.01/186.00 ( ! [B_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 186.01/186.00 => ( 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_b)),V_xs_2))) % 186.01/186.00 => 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_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted_Osimps,axiom, % 186.01/186.00 ! [V_a_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2) % 186.01/186.00 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 186.01/186.00 | ? [B_xs,B_x] : % 186.01/186.00 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 186.01/186.00 & ! [B_xa] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_List_Oinsert__def,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_not__in__set__insert,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_insert__remdups,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__insert,axiom, % 186.01/186.00 ! [V_x,V_xs,T_a] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 186.01/186.00 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__insert,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_List_Oset__insert,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_insert__Nil,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_maps__def,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_concat__map__maps,axiom, % 186.01/186.00 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_maps__simps_I2_J,axiom, % 186.01/186.00 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_maps__simps_I1_J,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_distinct__concat,axiom, % 186.01/186.00 ! [V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) % 186.01/186.00 => ( ! [B_ys] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) ) % 186.01/186.00 => ( ! [B_ys] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ! [B_zs] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ( B_ys != B_zs % 186.01/186.00 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 186.01/186.00 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measures__lesseq,axiom, % 186.01/186.00 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 186.01/186.00 ( 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))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_wf__measures,axiom, % 186.01/186.00 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__measures_I1_J,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measures__def,axiom, % 186.01/186.00 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measures__less,axiom, % 186.01/186.00 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 186.01/186.00 ( 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))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__measures_I2_J,axiom, % 186.01/186.00 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 186.01/186.00 <=> ( 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))) % 186.01/186.00 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 186.01/186.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_foldl__apply,axiom, % 186.01/186.00 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) ) % 186.01/186.00 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_order__fun_I2_J,axiom, % 186.01/186.00 ! [V_g_2,V_f_2,T_b,T_c] : % 186.01/186.00 ( ( class_Orderings_Oorder(T_c) % 186.01/186.00 & class_Enum_Oenum(T_b) ) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 186.01/186.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 186.01/186.00 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_enum__ex__prod__def,axiom, % 186.01/186.00 ! [V_Pa_2,T_b,T_c] : % 186.01/186.00 ( ( class_Enum_Oenum(T_c) % 186.01/186.00 & class_Enum_Oenum(T_b) ) % 186.01/186.00 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) % 186.01/186.00 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_enum__ex,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ( class_Enum_Oenum(T_b) % 186.01/186.00 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) % 186.01/186.00 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_exists__code,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ( class_Enum_Oenum(T_b) % 186.01/186.00 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 186.01/186.00 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_zip__obtain__same__length,axiom, % 186.01/186.00 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 186.01/186.00 ( ( 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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)))) ) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__not__random__dseq__def,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dropWhile__append2,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all2__all__nthI,axiom, % 186.01/186.00 ! [V_Pa_2,V_ba_2,T_c,V_a_2,T_b] : % 186.01/186.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ba_2) % 186.01/186.00 => ( ! [B_n] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_ba_2),B_n))) ) % 186.01/186.00 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_ba_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_finite__sorted__distinct__unique,axiom, % 186.01/186.00 ! [V_A_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.01/186.00 => ? [B_x] : % 186.01/186.00 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2 % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,B_x) % 186.01/186.00 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) % 186.01/186.00 & ! [B_y] : % 186.01/186.00 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2 % 186.01/186.00 & c_List_Olinorder__class_Osorted(T_b,B_y) % 186.01/186.00 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) ) % 186.01/186.00 => B_y = B_x ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_takeWhile__append2,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_insort__is__Cons,axiom, % 186.01/186.00 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] : % 186.01/186.00 ( class_Orderings_Olinorder(T_c) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 186.01/186.00 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Cons__eq__filter__iff,axiom, % 186.01/186.00 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) % 186.01/186.00 <=> ? [B_us,B_vs] : % 186.01/186.00 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 186.01/186.00 & ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__eq__Cons__iff,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] : % 186.01/186.00 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 186.01/186.00 <=> ? [B_us,B_vs] : % 186.01/186.00 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 186.01/186.00 & ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 186.01/186.00 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_order__fun_I1_J,axiom, % 186.01/186.00 ! [V_g_2,V_f_2,T_b,T_c] : % 186.01/186.00 ( ( class_Orderings_Oorder(T_c) % 186.01/186.00 & class_Enum_Oenum(T_b) ) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 186.01/186.00 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_all__code,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ( class_Enum_Oenum(T_b) % 186.01/186.00 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 186.01/186.00 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_enum__all,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ( class_Enum_Oenum(T_b) % 186.01/186.00 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) % 186.01/186.00 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_enum__all__prod__def,axiom, % 186.01/186.00 ! [V_Pa_2,T_b,T_c] : % 186.01/186.00 ( ( class_Enum_Oenum(T_c) % 186.01/186.00 & class_Enum_Oenum(T_b) ) % 186.01/186.00 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) % 186.01/186.00 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ball__nth,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b,V_n_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sorted_OCons,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( class_Orderings_Olinorder(T_b) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) % 186.01/186.00 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 186.01/186.00 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__length,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ? [B_n] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__conv__decomp,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__simps_I2_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__append,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 186.01/186.00 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__iff,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__rev,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 186.01/186.00 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__simps_I1_J,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 186.01/186.00 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__conv__decomp__first,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 <=> ? [B_ys] : % 186.01/186.00 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 186.01/186.00 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__conv__decomp__last,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 <=> ? [B_ys,B_zs] : % 186.01/186.00 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 186.01/186.00 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__length,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ! [B_n] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_finite__induct,axiom, % 186.01/186.00 ! [V_Pa_2,V_F_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 186.01/186.00 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 186.01/186.00 => ( ! [B_x,B_F] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 186.01/186.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) % 186.01/186.00 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) ) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__simps_I2_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__append,axiom, % 186.01/186.00 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 186.01/186.00 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__iff,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__rev,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 186.01/186.00 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__simps_I1_J,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 186.01/186.00 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Ball__set__list__all,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__iff__raw,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex1__simps_I2_J,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 186.01/186.00 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_Olist__all(T_b,hAPP(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_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measure__function__int,axiom, % 186.01/186.00 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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measure__fst,axiom, % 186.01/186.00 ! [T_c,V_f_2,T_b] : % 186.01/186.00 ( c_FunDef_Ois__measure(T_b,V_f_2) % 186.01/186.00 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measure__snd,axiom, % 186.01/186.00 ! [T_c,V_f_2,T_b] : % 186.01/186.00 ( c_FunDef_Ois__measure(T_b,V_f_2) % 186.01/186.00 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_is__measure_Ointros,axiom, % 186.01/186.00 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_is__measure_Oequations,axiom, % 186.01/186.00 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_is__measure_Osimps,axiom, % 186.01/186.00 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_measure__size,axiom, % 186.01/186.00 ! [T_b] : % 186.01/186.00 ( class_Nat_Osize(T_b) % 186.01/186.00 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex1__simps_I1_J,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex1__iff,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) % 186.01/186.00 & ! [B_y] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 186.01/186.00 => B_y = B_x ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transfer__morphism__int__nat,axiom, % 186.01/186.00 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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 186.01/186.00 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 186.01/186.00 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.01/186.00 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) % 186.01/186.00 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.01/186.00 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bool_Osize_I4_J,axiom, % 186.01/186.00 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bool_Osize_I3_J,axiom, % 186.01/186.00 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 186.01/186.00 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_neg__bind__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 186.01/186.00 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 186.01/186.00 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.01/186.00 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) % 186.01/186.00 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 186.01/186.00 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__empty__def,axiom, % 186.01/186.00 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__empty__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__bind__def,axiom, % 186.01/186.00 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__bind__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_neg__map__def,axiom, % 186.01/186.00 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_neg__single__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__map__def,axiom, % 186.01/186.00 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Oneg__single__def,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__single__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__single__def,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__splice,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_splice__Nil2,axiom, % 186.01/186.00 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 186.01/186.00 % 186.01/186.00 fof(fact_splice_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 186.01/186.00 % 186.01/186.00 fof(fact_splice_Osimps_I3_J,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_splice_Osimps_I2_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_,axiom, % 186.01/186.00 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_acyclicP__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) % 186.01/186.00 <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_converse__pred__comp,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_converse__join,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep__noteq,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 186.01/186.00 <=> V_x_2 != V_y_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep__eq,axiom, % 186.01/186.00 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep__conversep,axiom, % 186.01/186.00 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep__iff,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_r_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_ba_2)) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_a_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep_Oequations,axiom, % 186.01/186.00 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep_Ointros,axiom, % 186.01/186.00 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_ba_2),V_a_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversepD,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_r_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_ba_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_r_2,V_ba_2),V_a_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_converse__meet,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_conversep__converse__eq,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,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_r_2)),V_x_2),V_y_2)) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy__list_Osimps,axiom, % 186.01/186.00 ! [V_d_2,T_b] : % 186.01/186.00 ( class_Lazy__Sequence_Osmall__lazy(T_b) % 186.01/186.00 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),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_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,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_b),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_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_tl__replicate,axiom, % 186.01/186.00 ! [V_x,T_a,V_n] : % 186.01/186.00 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => 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) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy__prod__def,axiom, % 186.01/186.00 ! [V_d,T_b,T_a] : % 186.01/186.00 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 186.01/186.00 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 186.01/186.00 => 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)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__replicate__const,axiom, % 186.01/186.00 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_length__replicate,axiom, % 186.01/186.00 ! [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 ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__length__filter,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__replicate,axiom, % 186.01/186.00 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__empty,axiom, % 186.01/186.00 ! [V_x_2,V_n_2,T_b] : % 186.01/186.00 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b) % 186.01/186.00 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_empty__replicate,axiom, % 186.01/186.00 ! [V_x_2,V_n_2,T_b] : % 186.01/186.00 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2) % 186.01/186.00 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__0,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_concat__replicate__trivial,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_filter__replicate,axiom, % 186.01/186.00 ! [V_n_2,T_b,V_x_2,V_Pa_2] : % 186.01/186.00 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 186.01/186.00 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_append__replicate__commute,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__add,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nth__replicate,axiom, % 186.01/186.00 ! [V_x,T_a,V_n,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 186.01/186.00 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__eq__replicate,axiom, % 186.01/186.00 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] : % 186.01/186.00 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2) % 186.01/186.00 <=> ( V_m_2 = V_n_2 % 186.01/186.00 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => V_x_2 = V_y_2 ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Ball__set__replicate,axiom, % 186.01/186.00 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 186.01/186.00 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Bex__set__replicate,axiom, % 186.01/186.00 ! [V_Pa_2,V_a_2,V_n_2,T_b] : % 186.01/186.00 ( ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 186.01/186.00 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_zip__replicate,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_last__replicate,axiom, % 186.01/186.00 ! [V_x,T_a,V_n] : % 186.01/186.00 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_drop__replicate,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_hd__replicate,axiom, % 186.01/186.00 ! [V_x,T_a,V_n] : % 186.01/186.00 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_take__replicate,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rev__replicate,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__Suc,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__app__Cons__same,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__replicate,axiom, % 186.01/186.00 ! [V_y_2,V_n_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2)))) % 186.01/186.00 <=> ( V_x_2 = V_y_2 % 186.01/186.00 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_replicate__append__same,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_map__replicate__trivial,axiom, % 186.01/186.00 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__replicate,axiom, % 186.01/186.00 ! [V_x_2,T_b,V_n_2] : % 186.01/186.00 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__replicate__conv__if,axiom, % 186.01/186.00 ! [V_x_2,T_b,V_n_2] : % 186.01/186.00 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 186.01/186.00 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 186.01/186.00 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_set__replicate__Suc,axiom, % 186.01/186.00 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__union__def,axiom, % 186.01/186.00 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_eq__comp__r,axiom, % 186.01/186.00 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_pos__union__def,axiom, % 186.01/186.00 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy_H_Osimps,axiom, % 186.01/186.00 ! [V_i,V_d] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 186.01/186.00 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 186.01/186.00 => 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)))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy__int__def,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy_H_Opsimps,axiom, % 186.01/186.00 ! [V_i_2,V_d_2] : % 186.01/186.00 ( 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))) % 186.01/186.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 186.01/186.00 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 186.01/186.00 => 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)))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_field__le__epsilon,axiom, % 186.01/186.00 ! [V_y,V_x,T_a] : % 186.01/186.00 ( class_Fields_Olinordered__field(T_a) % 186.01/186.00 => ( ! [B_e] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 186.01/186.00 => 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))) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_small__lazy_H_Opinduct,axiom, % 186.01/186.00 ! [V_Pa_2,V_a1_2,V_a0_2] : % 186.01/186.00 ( 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))) % 186.01/186.00 => ( ! [B_d,B_i] : % 186.01/186.00 ( 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))) % 186.01/186.00 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 186.01/186.00 ! [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))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Oinject,axiom, % 186.01/186.00 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] : % 186.01/186.00 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2) % 186.01/186.00 <=> ( V_a_2 = V_a_H_2 % 186.01/186.00 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact__01,axiom, % 186.01/186.00 ! [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)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 186.01/186.00 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,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_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_size__code,axiom, % 186.01/186.00 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence__size__code,axiom, % 186.01/186.00 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_seq__case,axiom, % 186.01/186.00 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_yieldn__def,axiom, % 186.01/186.00 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 186.01/186.00 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_refl__on__INTER,axiom, % 186.01/186.00 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 186.01/186.00 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 186.01/186.00 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__set__member,axiom, % 186.01/186.00 ! [V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_member__rec_I1_J,axiom, % 186.01/186.00 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2)) % 186.01/186.00 <=> ( V_x_2 = V_y_2 % 186.01/186.00 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_member__set,axiom, % 186.01/186.00 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_member__rec_I2_J,axiom, % 186.01/186.00 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_List_Omember__def,axiom, % 186.01/186.00 ! [V_x_2,V_xs_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pair__box_Osize_I1_J,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_ba_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_ba_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex1__iff__raw,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) % 186.01/186.00 & ! [B_y] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 186.01/186.00 => B_y = B_x ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pair__box_Oinject,axiom, % 186.01/186.00 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 186.01/186.00 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_ba_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) % 186.01/186.00 <=> ( V_a_2 = V_a_H_2 % 186.01/186.00 & V_ba_2 = V_b_H_2 ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pair__box_Osize_I2_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pair__box_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_pair__box_Orecs,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_THE__default__def,axiom, % 186.01/186.00 ! [V_d_2,T_b,V_Pa_2] : % 186.01/186.00 ( ( ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 186.01/186.00 & ! [B_y] : % 186.01/186.00 ( hBOOL(hAPP(V_Pa_2,B_y)) % 186.01/186.00 => B_y = B_x ) ) % 186.01/186.00 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) % 186.01/186.00 & ( ~ ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 186.01/186.00 & ! [B_y] : % 186.01/186.00 ( hBOOL(hAPP(V_Pa_2,B_y)) % 186.01/186.00 => B_y = B_x ) ) % 186.01/186.00 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_setsum__UNION__zero,axiom, % 186.01/186.00 ! [V_f_2,V_S_2,T_b,T_c] : % 186.01/186.00 ( class_Groups_Ocomm__monoid__add(T_c) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2)) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) % 186.01/186.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 186.01/186.00 => ( ! [B_T1] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) % 186.01/186.00 => ! [B_T2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) % 186.01/186.00 => ( B_T1 != B_T2 % 186.01/186.00 => ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2)) % 186.01/186.00 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) % 186.01/186.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_INF2__I,axiom, % 186.01/186.00 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_ba_2),V_ca_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_finite__maxlen,axiom, % 186.01/186.00 ! [V_M_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) % 186.01/186.00 => ? [B_n] : % 186.01/186.00 ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 186.01/186.00 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact__02,axiom, % 186.01/186.00 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 186.01/186.00 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__iff__all__interval__int,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 186.01/186.00 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 186.01/186.00 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_all__interval__int__def,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_code__numeral_Orecs_I2_J,axiom, % 186.01/186.00 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,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_b,V_f1_2,V_f2_2,V_code__numeral_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Random_Osimps,axiom, % 186.01/186.00 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 186.01/186.00 ( ( 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))) % 186.01/186.00 => c_Random__Sequence_ORandom(T_b,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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) % 186.01/186.00 & ( ~ 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))) % 186.01/186.00 => c_Random__Sequence_ORandom(T_b,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_b,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_b)))),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_b)))),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_b)))),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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,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_b)))),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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,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_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,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_b)))),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_b)))),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_b))))),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_b)))),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_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_code__numeral_Orecs_I1_J,axiom, % 186.01/186.00 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_Random__Sequence_Oempty__def,axiom, % 186.01/186.00 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Random__Sequence_Osingle__def,axiom, % 186.01/186.00 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Random__Sequence_Omap__def,axiom, % 186.01/186.00 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,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_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_exE__realizer,axiom, % 186.01/186.00 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) % 186.01/186.00 => ( ! [B_x,B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 186.01/186.00 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 186.01/186.00 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Image__Collect__split,axiom, % 186.01/186.00 ! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lexord__trans,axiom, % 186.01/186.00 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) % 186.01/186.00 => ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__less__than,axiom, % 186.01/186.00 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__lex__prod,axiom, % 186.01/186.00 ! [V_R2_2,T_c,V_R1_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_R1_2) % 186.01/186.00 => ( c_Relation_Otrans(T_c,V_R2_2) % 186.01/186.00 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transD,axiom, % 186.01/186.00 ! [V_ca_2,V_ba_2,V_a_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__def,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 <=> ! [B_x,B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 186.01/186.00 => ! [B_z] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Union__eq,axiom, % 186.01/186.00 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bex__UNIV,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ( ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_finite__Collect__bex,axiom, % 186.01/186.00 ! [V_Q_2,T_c,V_A_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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)))),V_Q_2))))) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 186.01/186.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_listrel__trans,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bex__empty,axiom, % 186.01/186.00 ! [V_Pa_2,T_b] : % 186.01/186.00 ~ ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 186.01/186.00 <=> c_Relation_Otrans(T_b,V_r_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lexord__transI,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__finite__psubset,axiom, % 186.01/186.00 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__trancl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trancl__id,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__Id,axiom, % 186.01/186.00 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__Id__on,axiom, % 186.01/186.00 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__rtrancl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__Int,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Otrans(T_b,V_s_2) % 186.01/186.00 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__O__subset,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_SUPR__bool__eq,axiom, % 186.01/186.00 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__reflclI,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__inv__image,axiom, % 186.01/186.00 ! [V_f_2,T_c,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_UN__eq,axiom, % 186.01/186.00 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Bex__set__list__ex,axiom, % 186.01/186.00 ! [V_Pa_2,V_xs_2,T_b] : % 186.01/186.00 ( ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__iff__raw,axiom, % 186.01/186.00 ! [V_xs_2,V_Pa_2,T_b] : % 186.01/186.00 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 186.01/186.00 <=> ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_INT__eq,axiom, % 186.01/186.00 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Sup__fun__def,axiom, % 186.01/186.00 ! [V_x_2,V_A_2,T_c,T_b] : % 186.01/186.00 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.01/186.00 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,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)))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Sup__apply,axiom, % 186.01/186.00 ! [V_x_2,V_A_2,T_c,T_b] : % 186.01/186.00 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.01/186.00 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,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)))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Inf__fun__def,axiom, % 186.01/186.00 ! [V_x_2,V_A_2,T_c,T_b] : % 186.01/186.00 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.01/186.00 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,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)))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Inf__apply,axiom, % 186.01/186.00 ! [V_x_2,V_A_2,T_c,T_b] : % 186.01/186.00 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 186.01/186.00 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,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)))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_max__extp_Ointros,axiom, % 186.01/186.00 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 186.01/186.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 186.01/186.00 => ? [B_xa] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 186.01/186.00 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 186.01/186.00 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transp__def,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Predicate_Otransp(T_b,V_r_2) % 186.01/186.00 <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_transpE,axiom, % 186.01/186.00 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 186.01/186.00 ( c_Predicate_Otransp(T_b,V_r_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivpE,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 => ~ ( c_Predicate_Oreflp(T_b,V_R_2) % 186.01/186.00 => ( c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivpI,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Predicate_Oreflp(T_b,V_R_2) % 186.01/186.00 => ( c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 => ( c_Predicate_Otransp(T_b,V_R_2) % 186.01/186.00 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sympE,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,V_r_2,T_b] : % 186.01/186.00 ( c_Predicate_Osymp(T_b,V_r_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivp__reflp__symp__transp,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 <=> ( c_Predicate_Oreflp(T_b,V_R_2) % 186.01/186.00 & c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_max__extp_Osimps,axiom, % 186.01/186.00 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 186.01/186.00 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 186.01/186.00 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 186.01/186.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 186.01/186.00 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 186.01/186.00 & ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 186.01/186.00 => ? [B_xa] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 186.01/186.00 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_trans__diff__Id,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Oantisym(T_b,V_r_2) % 186.01/186.00 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__subset,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 186.01/186.00 => ( c_Relation_Oantisym(T_b,V_s_2) % 186.01/186.00 => c_Relation_Oantisym(T_b,V_r_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__Id,axiom, % 186.01/186.00 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__Id__on,axiom, % 186.01/186.00 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 186.01/186.00 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__empty,axiom, % 186.01/186.00 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisymD,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Oantisym(T_b,V_r_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),V_r_2)) % 186.01/186.00 => V_a_2 = V_ba_2 ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__def,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Oantisym(T_b,V_r_2) % 186.01/186.00 <=> ! [B_x,B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) % 186.01/186.00 => B_x = B_y ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_antisym__reflcl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) % 186.01/186.00 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 186.01/186.00 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_fun__lub__def,axiom, % 186.01/186.00 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__trans__comp__subset,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_symD,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ba_2)),V_r_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),V_r_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__def,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 <=> ! [B_x,B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_listrel__sym,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__conv__converse__eq,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 186.01/186.00 <=> c_Relation_Osym(T_b,V_r_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__trancl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Un,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Osym(T_b,V_s_2) % 186.01/186.00 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Id,axiom, % 186.01/186.00 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Id__on,axiom, % 186.01/186.00 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__rtrancl,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Int,axiom, % 186.01/186.00 ! [V_s_2,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Osym(T_b,V_s_2) % 186.01/186.00 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Un__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__Int__converse,axiom, % 186.01/186.00 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_sym__inv__image,axiom, % 186.01/186.00 ! [V_f_2,T_c,V_r_2,T_b] : % 186.01/186.00 ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equiv__def,axiom, % 186.01/186.00 ! [V_r_2,V_A_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 186.01/186.00 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 186.01/186.00 & c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 & c_Relation_Otrans(T_b,V_r_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivI,axiom, % 186.01/186.00 ! [V_r_2,V_A_2,T_b] : % 186.01/186.00 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 186.01/186.00 => ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ( c_Relation_Otrans(T_b,V_r_2) % 186.01/186.00 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivE,axiom, % 186.01/186.00 ! [V_r_2,V_A_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 186.01/186.00 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 186.01/186.00 => ( c_Relation_Osym(T_b,V_r_2) % 186.01/186.00 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_symp__def,axiom, % 186.01/186.00 ! [V_r_2,T_b] : % 186.01/186.00 ( c_Predicate_Osymp(T_b,V_r_2) % 186.01/186.00 <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivpI,axiom, % 186.01/186.00 ! [T_b,V_R_2] : % 186.01/186.00 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 186.01/186.00 => ( c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 => ( c_Predicate_Otransp(T_b,V_R_2) % 186.01/186.00 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivp__refl__symp__transp,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 186.01/186.00 & c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivp__transp,axiom, % 186.01/186.00 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivp__symp,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivp__def,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 186.01/186.00 & ! [B_x,B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 186.01/186.00 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 186.01/186.00 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) % 186.01/186.00 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_equivp__implies__part__equivp,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivpE,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 186.01/186.00 => ( c_Predicate_Osymp(T_b,V_R_2) % 186.01/186.00 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_part__equivp__typedef,axiom, % 186.01/186.00 ! [V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 186.01/186.00 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,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_b,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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_fold__image__UN__disjoint,axiom, % 186.01/186.00 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] : % 186.01/186.00 ( class_Groups_Ocomm__monoid__mult(T_d) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2)) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 186.01/186.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 186.01/186.00 => ! [B_xa] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) % 186.01/186.00 => ( B_x != B_xa % 186.01/186.00 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 186.01/186.00 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nat__of__induct,axiom, % 186.01/186.00 ! [V_Pa_2,V_y_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 186.01/186.00 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_nat__of__cases,axiom, % 186.01/186.00 ! [V_y_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 186.01/186.00 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_of__nat__induct,axiom, % 186.01/186.00 ! [V_x_2,V_Pa_2] : % 186.01/186.00 ( ! [B_y] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) ) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_of__nat__cases,axiom, % 186.01/186.00 ! [V_x_2] : % 186.01/186.00 ~ ! [B_y] : % 186.01/186.00 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) % 186.01/186.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Orecs_I1_J,axiom, % 186.01/186.00 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_lazy__sequence_Orecs_I2_J,axiom, % 186.01/186.00 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_beyond__def,axiom, % 186.01/186.00 ! [V_l,V_k] : % 186.01/186.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 186.01/186.00 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 186.01/186.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 186.01/186.00 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curry__def,axiom, % 186.01/186.00 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curryI,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,T_c,T_b,V_f_2] : % 186.01/186.00 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curryD,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 186.01/186.00 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curryE,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 186.01/186.00 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curry__conv,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_curry__split,axiom, % 186.01/186.00 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_split__curry,axiom, % 186.01/186.00 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ). % 186.01/186.00 % 186.01/186.00 fof(fact_beyond__zero,axiom, % 186.01/186.00 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.00 % 186.01/186.00 fof(fact_refl__on__UNION,axiom, % 186.01/186.00 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 186.01/186.00 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 186.01/186.00 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bex__reg__eqv,axiom, % 186.01/186.00 ! [V_Pa_2,V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 => ( ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Respects__def,axiom, % 186.01/186.00 ! [V_x_2,V_R_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_in__respects,axiom, % 186.01/186.00 ! [V_R_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) % 186.01/186.00 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_bex__reg__right,axiom, % 186.01/186.00 ! [V_Pa_2,V_Q_2,V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(V_Q_2,B_x)) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 186.01/186.00 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1)) % 186.01/186.00 => ? [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 186.01/186.00 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_babs__reg__eqv,axiom, % 186.01/186.00 ! [V_Pa_2,T_c,V_R_2,T_b] : % 186.01/186.00 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 186.01/186.00 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_Babs__def,axiom, % 186.01/186.00 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) % 186.01/186.00 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_wf__weak__decr__stable,axiom, % 186.01/186.00 ! [V_r_2,V_f_2,T_b] : % 186.01/186.00 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 186.01/186.00 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) % 186.01/186.00 => ? [B_i] : % 186.01/186.00 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_INT__greatest,axiom, % 186.01/186.00 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : % 186.01/186.00 ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_INT__anti__mono,axiom, % 186.01/186.00 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_hoare__derivs_OLocal,axiom, % 186.01/186.00 ! [V_a_2,V_s_H_2,V_X_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 186.01/186.00 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,V_Pa_2,V_ca_2,hAPP(hAPP(c_COMBC(T_b,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_b),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_b),tc_HOL_Obool)))) % 186.01/186.00 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),c_Hoare__Mirabelle_Otriple_Otriple(T_b,hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),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_b,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_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_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_b),tc_HOL_Obool)))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I2_J,axiom, % 186.01/186.00 ! [V_loc_H_2,V_loc_2] : % 186.01/186.00 ( c_Com_Ovname_OLoc(V_loc_2) = c_Com_Ovname_OLoc(V_loc_H_2) % 186.01/186.00 <=> V_loc_2 = V_loc_H_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osize_I4_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osize_I2_J,axiom, % 186.01/186.00 ! [V_loc] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(V_loc)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Orecs_I2_J,axiom, % 186.01/186.00 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osize_I3_J,axiom, % 186.01/186.00 ! [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) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osize_I1_J,axiom, % 186.01/186.00 ! [V_glb] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(V_glb)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I1_J,axiom, % 186.01/186.00 ! [V_glb_H_2,V_glb_2] : % 186.01/186.00 ( c_Com_Ovname_OGlb(V_glb_2) = c_Com_Ovname_OGlb(V_glb_H_2) % 186.01/186.00 <=> V_glb_2 = V_glb_H_2 ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I4_J,axiom, % 186.01/186.00 ! [V_glb,V_loc_H] : c_Com_Ovname_OLoc(V_loc_H) != c_Com_Ovname_OGlb(V_glb) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I3_J,axiom, % 186.01/186.00 ! [V_loc_H,V_glb] : c_Com_Ovname_OGlb(V_glb) != c_Com_Ovname_OLoc(V_loc_H) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Orecs_I1_J,axiom, % 186.01/186.00 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__rec(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I5_J,axiom, % 186.01/186.00 ! [V_glb_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OGlb(V_glb_2)) = hAPP(V_f1_2,V_glb_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_vname_Osimps_I6_J,axiom, % 186.01/186.00 ! [V_loc_2,V_f2_2,V_f1_2,T_b] : c_Com_Ovname_Ovname__case(T_b,V_f1_2,V_f2_2,c_Com_Ovname_OLoc(V_loc_2)) = hAPP(V_f2_2,V_loc_2) ). % 186.01/186.00 % 186.01/186.00 fof(fact_converse__rtranclE2,axiom, % 186.01/186.00 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 186.01/186.00 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2) % 186.01/186.00 => ~ ! [B_a,B_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2)) % 186.01/186.00 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_converse__rtrancl__induct2,axiom, % 186.01/186.00 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) % 186.01/186.00 => ( ! [B_a,B_b,B_aa,B_ba] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_rtrancl__induct2,axiom, % 186.01/186.00 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) % 186.01/186.00 => ( ! [B_a,B_b] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 186.01/186.00 => ! [B_aa,B_ba] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) ) % 186.01/186.00 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact__03,axiom, % 186.01/186.00 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ). % 186.01/186.00 % 186.01/186.00 fof(fact__04,axiom, % 186.01/186.00 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 186.01/186.00 % 186.01/186.00 fof(fact__05,axiom, % 186.01/186.00 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__all__iff__all__interval__nat,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 186.01/186.00 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact__06,axiom, % 186.01/186.00 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact__07,axiom, % 186.01/186.00 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ). % 186.01/186.00 % 186.01/186.00 fof(fact_all__interval__nat__def,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) % 186.01/186.00 <=> ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) % 186.01/186.00 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_list__ex__iff__not__all__inverval__nat,axiom, % 186.01/186.00 ! [V_j_2,V_i_2,V_Pa_2] : % 186.01/186.00 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 186.01/186.00 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_New__DSequence_Opos__map__def,axiom, % 186.01/186.00 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_folding__image_Ocong,axiom, % 186.01/186.00 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 186.01/186.00 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 186.01/186.00 => ( ! [B_x] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 186.01/186.00 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 186.01/186.00 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_power__dvd__imp__le,axiom, % 186.01/186.00 ! [V_n,V_m,V_i] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_finite__nonempty__imp__fold1Set,axiom, % 186.01/186.00 ! [V_f_2,V_A_2,T_b] : % 186.01/186.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 186.01/186.00 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 186.01/186.00 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_Oorder__refl,axiom, % 186.01/186.00 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd__0__right,axiom, % 186.01/186.00 ! [V_a,T_a] : % 186.01/186.00 ( class_Rings_Ocomm__semiring__1(T_a) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd__1__left,axiom, % 186.01/186.00 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ). % 186.01/186.00 % 186.01/186.00 fof(fact_setprod__dvd__setprod__subset,axiom, % 186.01/186.00 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 186.01/186.00 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 186.01/186.00 & class_Rings_Odvd(T_c) ) % 186.01/186.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 186.01/186.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 186.01/186.00 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2] : % 186.01/186.00 ( V_a_2 = V_ba_2 % 186.01/186.00 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 186.01/186.00 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 186.01/186.00 ! [V_ca_2,V_ba_2,V_a_2] : % 186.01/186.00 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) % 186.01/186.00 <=> ( V_a_2 = V_ba_2 % 186.01/186.00 & V_ba_2 = V_ca_2 ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 186.01/186.00 ! [V_k_2,V_l_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 186.01/186.00 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 186.01/186.00 ! [V_a_2,V_ba_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 186.01/186.00 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 186.01/186.00 ! [V_k_2,V_l_2] : % 186.01/186.00 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 186.01/186.00 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 186.01/186.00 ! [V_l_2,V_k_2] : % 186.01/186.00 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 186.01/186.00 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 186.01/186.00 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2] : % 186.01/186.00 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 186.01/186.00 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 186.01/186.00 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 186.01/186.00 ! [V_l_2,V_k_2] : % 186.01/186.00 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) % 186.01/186.00 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 186.01/186.00 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 186.01/186.00 % 186.01/186.00 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 186.01/186.00 ! [V_ba_2,V_a_2] : % 186.01/186.00 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_ba_2) % 186.01/186.00 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 186.01/186.01 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd_OatLeastatMost__empty,axiom, % 186.01/186.01 ! [V_a_2,V_ba_2] : % 186.01/186.01 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 186.01/186.01 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) % 186.01/186.01 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 186.01/186.01 ! [V_ba_2,V_a_2] : % 186.01/186.01 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 186.01/186.01 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 186.01/186.01 ! [V_ba_2,V_a_2] : % 186.01/186.01 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) % 186.01/186.01 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_div__power,axiom, % 186.01/186.01 ! [V_n,V_x,V_y,T_a] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_a) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 186.01/186.01 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(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_y),V_n)) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd__mod__imp__dvd,axiom, % 186.01/186.01 ! [V_n,V_m,V_k,T_a] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_a) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 186.01/186.01 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd__mod,axiom, % 186.01/186.01 ! [V_n,V_m,V_k,T_a] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_a) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 186.01/186.01 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_mod__mod__cancel,axiom, % 186.01/186.01 ! [V_a,V_b,V_c,T_a] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_a) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 186.01/186.01 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd__mod__iff,axiom, % 186.01/186.01 ! [V_m_2,V_n_2,V_k_2,T_b] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_b) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) % 186.01/186.01 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_nat__dvd__1__iff__1,axiom, % 186.01/186.01 ! [V_m_2] : % 186.01/186.01 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 186.01/186.01 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_dvd__0__left,axiom, % 186.01/186.01 ! [V_a,T_a] : % 186.01/186.01 ( class_Rings_Ocomm__semiring__1(T_a) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 186.01/186.01 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_one__dvd,axiom, % 186.01/186.01 ! [V_a,T_a] : % 186.01/186.01 ( class_Rings_Ocomm__semiring__1(T_a) % 186.01/186.01 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 186.01/186.01 % 186.01/186.01 fof(fact_div__dvd__div,axiom, % 186.01/186.01 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 186.01/186.01 ( class_Divides_Osemiring__div(T_b) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2)) % 186.01/186.01 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ca_2),V_a_2))) % 186.01/186.01 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ba_2),V_ca_2)) ) ) ) ) ). % 186.01/186.01 % 186.01/186.01 %----Arity declarations (222) % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 186.01/186.01 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Obounded__lattice(T_1) % 186.01/186.01 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 186.01/186.01 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Obounded__lattice(T_1) % 186.01/186.01 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Obounded__lattice(T_1) % 186.01/186.01 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Olattice(T_1) % 186.01/186.01 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Olattice(T_1) % 186.01/186.01 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Odistrib__lattice(T_1) % 186.01/186.01 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Oboolean__algebra(T_1) % 186.01/186.01 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Orderings_Opreorder,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Orderings_Opreorder(T_1) % 186.01/186.01 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Finite__Set_Ofinite,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Finite__Set_Ofinite(T_2) % 186.01/186.01 & class_Finite__Set_Ofinite(T_1) ) % 186.01/186.01 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Lattices_Olattice,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Lattices_Olattice(T_1) % 186.01/186.01 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Orderings_Oorder,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Orderings_Oorder(T_1) % 186.01/186.01 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Orderings_Otop,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Orderings_Otop(T_1) % 186.01/186.01 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Orderings_Oord,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Orderings_Oord(T_1) % 186.01/186.01 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Orderings_Obot,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Orderings_Obot(T_1) % 186.01/186.01 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Groups_Ouminus,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Groups_Ouminus(T_1) % 186.01/186.01 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Groups_Ominus,axiom, % 186.01/186.01 ! [T_2,T_1] : % 186.01/186.01 ( class_Groups_Ominus(T_1) % 186.01/186.01 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_fun__Enum_Oenum,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Enum_Oenum(T_2) % 186.01/186.01 & class_Enum_Oenum(T_1) ) % 186.01/186.01 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Com__Ocom__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Com_Ocom) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 186.01/186.01 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 186.01/186.01 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 186.01/186.01 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 186.01/186.01 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 186.01/186.01 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 186.01/186.01 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 186.01/186.01 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 186.01/186.01 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 186.01/186.01 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 186.01/186.01 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 186.01/186.01 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 186.01/186.01 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 186.01/186.01 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 186.01/186.01 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 186.01/186.01 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 186.01/186.01 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 186.01/186.01 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 186.01/186.01 class_Divides_Osemiring__div(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 186.01/186.01 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 186.01/186.01 class_Groups_Oab__group__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 186.01/186.01 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 186.01/186.01 class_Rings_Oordered__ring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 186.01/186.01 class_Orderings_Opreorder(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 186.01/186.01 class_Orderings_Olinorder(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 186.01/186.01 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 186.01/186.01 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 186.01/186.01 class_Groups_Omonoid__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 186.01/186.01 class_Rings_Osemiring__1(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 186.01/186.01 class_Rings_Osemiring__0(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 186.01/186.01 class_Lattices_Olattice(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 186.01/186.01 class_Groups_Ogroup__add(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 186.01/186.01 class_Divides_Oring__div(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 186.01/186.01 class_Rings_Omult__zero(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 186.01/186.01 class_Orderings_Oorder(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 186.01/186.01 class_Int_Oring__char__0(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 186.01/186.01 class_Int_Onumber__ring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 186.01/186.01 class_Rings_Osemiring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Orderings_Oord,axiom, % 186.01/186.01 class_Orderings_Oord(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 186.01/186.01 class_Groups_Ouminus(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 186.01/186.01 class_Groups_Osgn__if(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 186.01/186.01 class_Groups_Oabs__if(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 186.01/186.01 class_Rings_Oring__1(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ominus,axiom, % 186.01/186.01 class_Groups_Ominus(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Power_Opower,axiom, % 186.01/186.01 class_Power_Opower(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Ozero,axiom, % 186.01/186.01 class_Groups_Ozero(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oring,axiom, % 186.01/186.01 class_Rings_Oring(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Oidom,axiom, % 186.01/186.01 class_Rings_Oidom(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Int_Onumber,axiom, % 186.01/186.01 class_Int_Onumber(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Groups_Oone,axiom, % 186.01/186.01 class_Groups_Oone(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Int__Oint__Rings_Odvd,axiom, % 186.01/186.01 class_Rings_Odvd(tc_Int_Oint) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 186.01/186.01 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 186.01/186.01 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 186.01/186.01 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 186.01/186.01 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 186.01/186.01 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 186.01/186.01 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 186.01/186.01 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 186.01/186.01 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 186.01/186.01 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 186.01/186.01 class_Orderings_Owellorder(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 186.01/186.01 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 186.01/186.01 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 186.01/186.01 class_Orderings_Opreorder(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 186.01/186.01 class_Orderings_Olinorder(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 186.01/186.01 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 186.01/186.01 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 186.01/186.01 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 186.01/186.01 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 186.01/186.01 class_Lattices_Olattice(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 186.01/186.01 class_Rings_Omult__zero(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 186.01/186.01 class_Orderings_Oorder(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 186.01/186.01 class_Rings_Osemiring(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 186.01/186.01 class_Orderings_Oord(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 186.01/186.01 class_Orderings_Obot(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 186.01/186.01 class_Groups_Ominus(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Power_Opower,axiom, % 186.01/186.01 class_Power_Opower(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 186.01/186.01 class_Groups_Ozero(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Int_Onumber,axiom, % 186.01/186.01 class_Int_Onumber(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Groups_Oone,axiom, % 186.01/186.01 class_Groups_Oone(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 186.01/186.01 class_Rings_Odvd(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nat__Onat__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Nat_Onat) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 186.01/186.01 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 186.01/186.01 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 186.01/186.01 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 186.01/186.01 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 186.01/186.01 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 186.01/186.01 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 186.01/186.01 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 186.01/186.01 class_Orderings_Opreorder(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 186.01/186.01 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 186.01/186.01 class_Lattices_Olattice(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 186.01/186.01 class_Orderings_Oorder(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 186.01/186.01 class_Orderings_Otop(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 186.01/186.01 class_Orderings_Oord(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 186.01/186.01 class_Orderings_Obot(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 186.01/186.01 class_Groups_Ouminus(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 186.01/186.01 class_Groups_Ominus(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 186.01/186.01 class_Enum_Oenum(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_HOL__Obool__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_HOL_Obool) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Com__Ostate__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Com_Ostate) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Com__Ovname__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Com_Ovname) ). % 186.01/186.01 % 186.01/186.01 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 186.01/186.01 ! [T_1] : % 186.01/186.01 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 186.01/186.01 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_List__Olist__Nat_Osize,axiom, % 186.01/186.01 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_sum__Finite__Set_Ofinite,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Finite__Set_Ofinite(T_2) % 186.01/186.01 & class_Finite__Set_Ofinite(T_1) ) % 186.01/186.01 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_sum__Enum_Oenum,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Enum_Oenum(T_2) % 186.01/186.01 & class_Enum_Oenum(T_1) ) % 186.01/186.01 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_sum__Nat_Osize,axiom, % 186.01/186.01 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 186.01/186.01 ! [T_1] : % 186.01/186.01 ( class_Finite__Set_Ofinite(T_1) % 186.01/186.01 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 186.01/186.01 ! [T_1] : % 186.01/186.01 ( class_Enum_Oenum(T_1) % 186.01/186.01 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Option__Ooption__Nat_Osize,axiom, % 186.01/186.01 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 186.01/186.01 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 186.01/186.01 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 186.01/186.01 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_prod__Finite__Set_Ofinite,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Finite__Set_Ofinite(T_2) % 186.01/186.01 & class_Finite__Set_Ofinite(T_1) ) % 186.01/186.01 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_prod__Enum_Oenum,axiom, % 186.01/186.01 ! [T_1,T_2] : % 186.01/186.01 ( ( class_Enum_Oenum(T_2) % 186.01/186.01 & class_Enum_Oenum(T_1) ) % 186.01/186.01 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 186.01/186.01 % 186.01/186.01 fof(arity_prod__Nat_Osize,axiom, % 186.01/186.01 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 186.01/186.01 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 186.01/186.01 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 186.01/186.01 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Product__Type_Ounit) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 186.01/186.01 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 186.01/186.01 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 186.01/186.01 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 186.01/186.01 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 186.01/186.01 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 186.01/186.01 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 186.01/186.01 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 186.01/186.01 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 186.01/186.01 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 186.01/186.01 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 186.01/186.01 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 186.01/186.01 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 186.01/186.01 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 186.01/186.01 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 186.01/186.01 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 186.01/186.01 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 186.01/186.01 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 186.01/186.01 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 186.01/186.01 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 186.01/186.01 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 186.01/186.01 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 186.01/186.01 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 186.01/186.01 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 186.01/186.01 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 186.01/186.01 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 186.01/186.01 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 186.01/186.01 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 186.01/186.01 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 186.01/186.01 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 186.01/186.01 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 186.01/186.01 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 186.01/186.01 % 186.01/186.01 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 186.01/186.01 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 186.01/186.01 % 186.01/186.01 %----Helper facts (20) % 186.01/186.01 fof(help_c__COMBI__1,axiom, % 186.01/186.01 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 186.01/186.01 % 186.01/186.01 fof(help_c__COMBK__1,axiom, % 186.01/186.01 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 186.01/186.01 % 186.01/186.01 fof(help_c__COMBB__1,axiom, % 186.01/186.01 ! [V_R_2,V_Q_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__COMBC__1,axiom, % 186.01/186.01 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__COMBS__1,axiom, % 186.01/186.01 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fequal__1,axiom, % 186.01/186.01 ! [V_y_2,V_x_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 186.01/186.01 | V_x_2 = V_y_2 ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fequal__2,axiom, % 186.01/186.01 ! [V_y_2,V_x_2] : % 186.01/186.01 ( V_x_2 != V_y_2 % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fFalse__1,axiom, % 186.01/186.01 ~ hBOOL(c_fFalse) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fTrue__1,axiom, % 186.01/186.01 hBOOL(c_fTrue) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fNot__1,axiom, % 186.01/186.01 ! [V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 186.01/186.01 | ~ hBOOL(V_Pa_2) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fNot__2,axiom, % 186.01/186.01 ! [V_Pa_2] : % 186.01/186.01 ( ~ ~ hBOOL(V_Pa_2) % 186.01/186.01 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fconj__1,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(V_Pa_2) % 186.01/186.01 | ~ hBOOL(V_Q_2) % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fconj__2,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 186.01/186.01 | hBOOL(V_Pa_2) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fconj__3,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 186.01/186.01 | hBOOL(V_Q_2) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fdisj__1,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(V_Pa_2) % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fdisj__2,axiom, % 186.01/186.01 ! [V_Pa_2,V_Q_2] : % 186.01/186.01 ( ~ hBOOL(V_Q_2) % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fdisj__3,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) % 186.01/186.01 | hBOOL(V_Pa_2) % 186.01/186.01 | hBOOL(V_Q_2) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fimplies__1,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( hBOOL(V_Pa_2) % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fimplies__2,axiom, % 186.01/186.01 ! [V_Pa_2,V_Q_2] : % 186.01/186.01 ( ~ hBOOL(V_Q_2) % 186.01/186.01 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 186.01/186.01 % 186.01/186.01 fof(help_c__fimplies__3,axiom, % 186.01/186.01 ! [V_Q_2,V_Pa_2] : % 186.01/186.01 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) % 186.01/186.01 | ~ hBOOL(V_Pa_2) % 186.01/186.01 | hBOOL(V_Q_2) ) ). % 186.01/186.01 % 186.01/186.01 %----Conjectures (1) % 186.01/186.01 fof(conj_0,conjecture, % 186.01/186.01 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,c_Hoare__Mirabelle_Opeek__and(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))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)),v_b),v_c,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))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),v_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ). % 186.01/186.01 % 186.01/186.01 %------------------------------------------------------------------------------ % 186.01/186.01 %------------------------------------------- % 186.01/186.01 % Proof found % 186.01/186.01 % SZS status Theorem for theBenchmark % 186.01/186.01 % SZS output start Proof % 186.01/186.01 %ClaNum:10485(EqnAxiom:3143) % 186.01/186.01 %VarNum:70786(SingletonVarNum:20511) % 186.01/186.01 %MaxLitNum:8 % 186.01/186.01 %MaxfuncDepth:13 % 186.01/186.01 %SharedTerms:1039 % 186.01/186.01 %goalClause: 4807 % 186.01/186.01 %singleGoalClaCount:1 % 186.01/186.01 [3147]P1(a194) % 186.01/186.01 [3148]P2(a922) % 186.01/186.01 [3149]P2(a927) % 186.01/186.01 [3150]P3(a922) % 186.01/186.01 [3151]P3(a927) % 186.01/186.01 [3152]P3(a1) % 186.01/186.01 [3153]P3(a106) % 186.01/186.01 [3154]P107(a922) % 186.01/186.01 [3155]P107(a927) % 186.01/186.01 [3156]P107(a1) % 186.01/186.01 [3157]P107(a106) % 186.01/186.01 [3158]P111(a922) % 186.01/186.01 [3159]P108(a922) % 186.01/186.01 [3160]P108(a927) % 186.01/186.01 [3161]P108(a1) % 186.01/186.01 [3162]P108(a106) % 186.01/186.01 [3163]P109(a927) % 186.01/186.01 [3164]P109(a1) % 186.01/186.01 [3165]P109(a106) % 186.01/186.01 [3166]P110(a922) % 186.01/186.01 [3167]P110(a927) % 186.01/186.01 [3168]P110(a1) % 186.01/186.01 [3169]P110(a106) % 186.01/186.01 [3170]P79(a1) % 186.01/186.01 [3171]P83(a922) % 186.01/186.01 [3172]P84(a922) % 186.01/186.01 [3173]P84(a1) % 186.01/186.01 [3174]P4(a1) % 186.01/186.01 [3175]P5(a1) % 186.01/186.01 [3176]P6(a922) % 186.01/186.01 [3177]P70(a927) % 186.01/186.01 [3178]P70(a1) % 186.01/186.01 [3179]P70(a106) % 186.01/186.01 [3180]P112(a1) % 186.01/186.01 [3181]P97(a922) % 186.01/186.01 [3182]P97(a927) % 186.01/186.01 [3183]P97(a1) % 186.01/186.01 [3184]P98(a922) % 186.01/186.01 [3185]P98(a927) % 186.01/186.01 [3186]P98(a1) % 186.01/186.01 [3187]P99(a922) % 186.01/186.01 [3188]P101(a922) % 186.01/186.01 [3189]P113(a1) % 186.01/186.01 [3190]P114(a1) % 186.01/186.01 [3191]P103(a922) % 186.01/186.01 [3192]P103(a927) % 186.01/186.01 [3193]P103(a1) % 186.01/186.01 [3194]P102(a922) % 186.01/186.01 [3195]P102(a927) % 186.01/186.01 [3196]P102(a1) % 186.01/186.01 [3197]P62(a922) % 186.01/186.01 [3198]P62(a930) % 186.01/186.01 [3199]P80(a927) % 186.01/186.01 [3200]P80(a1) % 186.01/186.01 [3201]P80(a106) % 186.01/186.01 [3202]P81(a927) % 186.01/186.01 [3203]P81(a1) % 186.01/186.01 [3204]P81(a106) % 186.01/186.01 [3205]P72(a927) % 186.01/186.01 [3206]P72(a1) % 186.01/186.01 [3207]P72(a106) % 186.01/186.01 [3208]P125(a927) % 186.01/186.01 [3209]P125(a1) % 186.01/186.01 [3210]P125(a106) % 186.01/186.01 [3211]P139(a1) % 186.01/186.01 [3212]P115(a927) % 186.01/186.01 [3213]P116(a1) % 186.01/186.01 [3214]P118(a927) % 186.01/186.01 [3215]P118(a1) % 186.01/186.01 [3216]P118(a106) % 186.01/186.01 [3217]P71(a927) % 186.01/186.01 [3218]P71(a1) % 186.01/186.01 [3219]P71(a106) % 186.01/186.01 [3220]P73(a927) % 186.01/186.01 [3221]P73(a1) % 186.01/186.01 [3222]P73(a106) % 186.01/186.01 [3223]P74(a927) % 186.01/186.01 [3224]P74(a1) % 186.01/186.01 [3225]P74(a106) % 186.01/186.01 [3226]P85(a927) % 186.01/186.01 [3227]P85(a1) % 186.01/186.01 [3228]P85(a106) % 186.01/186.01 [3229]P86(a927) % 186.01/186.01 [3230]P86(a1) % 186.01/186.01 [3231]P86(a106) % 186.01/186.01 [3232]P88(a927) % 186.01/186.01 [3233]P88(a1) % 186.01/186.01 [3234]P88(a106) % 186.01/186.01 [3235]P141(a927) % 186.01/186.01 [3236]P141(a1) % 186.01/186.01 [3237]P141(a106) % 186.01/186.01 [3238]P119(a927) % 186.01/186.01 [3239]P119(a1) % 186.01/186.01 [3240]P119(a106) % 186.01/186.01 [3241]P143(a927) % 186.01/186.01 [3242]P143(a1) % 186.01/186.01 [3243]P128(a1) % 186.01/186.01 [3244]P77(a927) % 186.01/186.01 [3245]P77(a1) % 186.01/186.01 [3246]P77(a106) % 186.01/186.01 [3247]P78(a1) % 186.01/186.01 [3248]P92(a927) % 186.01/186.01 [3249]P92(a1) % 186.01/186.01 [3250]P92(a106) % 186.01/186.01 [3251]P82(a927) % 186.01/186.01 [3252]P82(a1) % 186.01/186.01 [3253]P82(a106) % 186.01/186.01 [3254]P76(a927) % 186.01/186.01 [3255]P76(a1) % 186.01/186.01 [3256]P76(a106) % 186.01/186.01 [3257]P129(a927) % 186.01/186.01 [3258]P129(a1) % 186.01/186.01 [3259]P129(a106) % 186.01/186.01 [3260]P142(a1) % 186.01/186.01 [3261]P130(a927) % 186.01/186.01 [3262]P130(a1) % 186.01/186.01 [3263]P130(a106) % 186.01/186.01 [3264]P144(a927) % 186.01/186.01 [3265]P144(a1) % 186.01/186.01 [3266]P144(a106) % 186.01/186.01 [3267]P89(a927) % 186.01/186.01 [3268]P89(a1) % 186.01/186.01 [3269]P89(a106) % 186.01/186.01 [3270]P126(a1) % 186.01/186.01 [3271]P127(a1) % 186.01/186.01 [3272]P135(a927) % 186.01/186.01 [3273]P135(a1) % 186.01/186.01 [3274]P135(a106) % 186.01/186.01 [3275]P137(a927) % 186.01/186.01 [3276]P137(a1) % 186.01/186.01 [3277]P137(a106) % 186.01/186.01 [3278]P136(a927) % 186.01/186.01 [3279]P136(a1) % 186.01/186.01 [3280]P136(a106) % 186.01/186.01 [3281]P123(a927) % 186.01/186.01 [3282]P123(a1) % 186.01/186.01 [3283]P123(a106) % 186.01/186.01 [3284]P131(a927) % 186.01/186.01 [3285]P131(a1) % 186.01/186.01 [3286]P131(a106) % 186.01/186.01 [3287]P132(a927) % 186.01/186.01 [3288]P132(a1) % 186.01/186.01 [3289]P132(a106) % 186.01/186.01 [3290]P133(a1) % 186.01/186.01 [3291]P134(a1) % 186.01/186.01 [3292]P145(a927) % 186.01/186.01 [3293]P145(a1) % 186.01/186.01 [3294]P145(a106) % 186.01/186.01 [3295]P104(a927) % 186.01/186.01 [3296]P104(a1) % 186.01/186.01 [3297]P104(a106) % 186.01/186.01 [3298]P146(a927) % 186.01/186.01 [3299]P146(a1) % 186.01/186.01 [3300]P146(a106) % 186.01/186.01 [3301]P140(a1) % 186.01/186.01 [3302]P93(a1) % 186.01/186.01 [3303]P117(a927) % 186.01/186.01 [3304]P117(a1) % 186.01/186.01 [3305]P117(a106) % 186.01/186.01 [3306]P63(a927) % 186.01/186.01 [3307]P63(a1) % 186.01/186.01 [3308]P63(a106) % 186.01/186.01 [3309]P64(a1) % 186.01/186.01 [3310]P94(a1) % 186.01/186.01 [3311]P95(a927) % 186.01/186.01 [3312]P95(a1) % 186.01/186.01 [3313]P95(a106) % 186.01/186.01 [3314]P90(a1) % 186.01/186.01 [3315]P87(a1) % 186.01/186.01 [3316]P138(a1) % 186.01/186.01 [3317]P75(a1) % 186.01/186.01 [3318]P91(a927) % 186.01/186.01 [3319]P91(a1) % 186.01/186.01 [3320]P91(a106) % 186.01/186.01 [3321]P65(a922) % 186.01/186.01 [3322]P65(a930) % 186.01/186.01 [3323]P106(a922) % 186.01/186.01 [3324]P106(a923) % 186.01/186.01 [3325]P106(a927) % 186.01/186.01 [3326]P106(a925) % 186.01/186.01 [3327]P106(a930) % 186.01/186.01 [3328]P106(a924) % 186.01/186.01 [3329]P106(a106) % 186.01/186.01 [3330]P106(a331) % 186.01/186.01 [3331]P105(a930) % 186.01/186.01 [3332]P105(a1) % 186.01/186.01 [3333]P120(a927) % 186.01/186.01 [3334]P120(a1) % 186.01/186.01 [3335]P120(a106) % 186.01/186.01 [3336]P100(a922) % 186.01/186.01 [3352]P38(a927,a248) % 186.01/186.01 [3353]P38(a927,a325) % 186.01/186.01 [3354]P39(a927,a248) % 186.01/186.01 [4706]~E(a104,a89) % 186.01/186.01 [4707]~P1(a247) % 186.01/186.01 [3144]E(f2(a1),a89) % 186.01/186.01 [3145]E(f107(a106),a3) % 186.01/186.01 [3146]E(f23(a106),a24) % 186.01/186.01 [3337]E(f195(a927),f2(a927)) % 186.01/186.01 [3338]E(f108(a927),f241(a927)) % 186.01/186.01 [3339]E(f117(a927),f242(a927)) % 186.01/186.01 [3340]E(f109(a1),f25(a1)) % 186.01/186.01 [3341]E(f30(a26),f2(a927)) % 186.01/186.01 [3342]E(f90(a247),f2(a927)) % 186.01/186.01 [3343]E(f90(a194),f2(a927)) % 186.01/186.01 [3344]P7(f84(a1)) % 186.01/186.01 [3345]P7(f2(a1)) % 186.01/186.01 [3406]P38(f933(a927,a927),a38) % 186.01/186.01 [3752]E(f328(a927,a927,a248,a248),a38) % 186.01/186.01 [4708]~E(f84(a1),f2(a1)) % 186.01/186.01 [3346]E(f118(f2(a927)),f2(a927)) % 186.01/186.01 [3347]E(f4(f2(a106)),f2(a927)) % 186.01/186.01 [3358]E(f335(f85(a1),a89),a89) % 186.01/186.01 [3361]E(f335(a119,f2(a927)),f84(a927)) % 186.01/186.01 [3362]E(f335(a111,f84(a1)),f84(a927)) % 186.01/186.01 [3363]E(f335(a3,f84(a927)),f84(a106)) % 186.01/186.01 [3365]E(f335(a3,f2(a927)),f2(a106)) % 186.01/186.01 [3367]E(f335(f110(a1),a89),f2(a1)) % 186.01/186.01 [3368]E(f335(f110(a106),a89),f2(a106)) % 186.01/186.01 [3369]E(f335(a111,f2(a1)),f2(a927)) % 186.01/186.01 [3370]E(f335(f196(a922),a247),f2(a927)) % 186.01/186.01 [3371]E(f335(f196(a922),a194),f2(a927)) % 186.01/186.01 [3372]E(f335(f196(a924),a26),f2(a927)) % 186.01/186.01 [3373]E(f335(f110(a927),a89),f2(a927)) % 186.01/186.01 [3379]E(f335(f85(a1),f84(a1)),a104) % 186.01/186.01 [3386]E(f335(f85(a1),f2(a1)),f2(a1)) % 186.01/186.01 [3388]E(f335(f196(a106),f2(a106)),f2(a927)) % 186.01/186.01 [3389]E(f335(f107(a1),f84(a927)),f84(a1)) % 186.01/186.01 [3390]E(f335(f107(a1),f2(a927)),f2(a1)) % 186.01/186.01 [3402]E(f335(a111,f84(a1)),f335(a119,f2(a927))) % 186.01/186.01 [3404]E(f326(f933(a927,a927),a38),a39) % 186.01/186.01 [3405]E(f327(f933(a927,a927),a38),a40) % 186.01/186.01 [3432]E(f335(f290(a927),f2(a927)),f195(f934(a927,a922))) % 186.01/186.01 [3433]E(f335(f291(a927),f2(a927)),f250(f934(a927,a922))) % 186.01/186.01 [3442]P41(f195(f934(a1,a922))) % 186.01/186.01 [3476]E(f335(f335(f23(a106),f2(a106)),f84(a106)),f2(a106)) % 186.01/186.01 [3551]P1(f335(f335(f244(a1),a104),f2(a1))) % 186.01/186.01 [3575]P1(f335(f335(f243(a1),f2(a1)),f84(a1))) % 186.01/186.01 [3577]P1(f335(f335(f244(a1),f2(a1)),f84(a1))) % 186.01/186.01 [3783]E(f335(f335(f297(a927,a927,a927),a325),f315(a927,a325)),a248) % 186.01/186.01 [3825]P42(a1,a927,a111,f335(f243(a1),f2(a1))) % 186.01/186.01 [3829]E(f335(f335(f45(a927,f934(a927,a922)),f250(f934(a927,a922))),f290(a927)),f250(f934(a927,a922))) % 186.01/186.01 [3830]E(f335(f335(f45(a927,f934(a927,a922)),f250(f934(a927,a922))),f291(a927)),f250(f934(a927,a922))) % 186.01/186.01 [3831]E(f335(f335(f45(a927,f934(a927,a922)),f250(f934(a927,a922))),f309(a927)),f250(f934(a927,a922))) % 186.01/186.01 [3832]E(f335(f335(f46(a927,f934(a927,a922)),f250(f934(a927,a922))),f312(a927)),f195(f934(a927,a922))) % 186.01/186.01 [3847]P26(a927,a1,f107(a1),f250(f934(a927,a922))) % 186.01/186.01 [3861]P42(a927,a1,f107(a1),f335(f16(a922,a927),a194)) % 186.01/186.01 [3998]E(f335(f78(a927,a106,a1,a3),a111),f110(a106)) % 186.01/186.01 [4223]P58(a106,a927,a20,a3,f250(f934(a927,a922))) % 186.01/186.01 [4228]P58(a1,f934(f933(a927,a927),a922),a113,a95,a105) % 186.01/186.01 [4484]E(f266(a1,a1,a1,a1,f25(a1),f85(a1)),a57) % 186.01/186.01 [4731]~E(f335(f110(a1),a104),f335(f110(a1),a89)) % 186.01/186.01 [4732]~P1(f335(a200,f84(a1))) % 186.01/186.01 [4733]~P1(f335(a200,f2(a1))) % 186.01/186.01 [4774]~P1(f335(f335(f244(a1),a89),f2(a1))) % 186.01/186.01 [3424]E(f335(f335(f23(a1),a104),a104),a89) % 186.01/186.01 [3440]E(f335(f107(a1),f335(a119,f2(a927))),f84(a1)) % 186.01/186.01 [3505]E(f335(f41(a930),f250(f934(a930,a922))),f84(a927)) % 186.01/186.01 [3525]P1(f335(a200,f335(f110(a1),a104))) % 186.01/186.01 [3527]P1(f335(f335(f243(a1),a104),a89)) % 186.01/186.01 [3529]P1(f335(f335(f244(a1),a104),a89)) % 186.01/186.01 [3586]E(f335(f335(f317(a927),f2(a927)),f195(f934(a927,a922))),f335(f309(a927),f2(a927))) % 186.01/186.01 [3641]P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),a89))) % 186.01/186.01 [3653]E(f335(f318(a927,a927,a119),f250(f934(a927,a922))),f335(f312(a927),f2(a927))) % 186.01/186.01 [3690]P9(f933(a927,a927),f250(f934(f933(a927,a927),a922)),a115) % 186.01/186.01 [4005]E(f335(f78(a927,a1,a106,f107(a1)),a20),a22) % 186.01/186.01 [4066]P38(a927,f335(f270(f933(a927,a927)),f335(f265(a927,a927,a922),f244(a927)))) % 186.01/186.01 [4765]~P1(f335(a200,f335(f110(a1),a89))) % 186.01/186.01 [4766]~P1(f335(f335(f243(a1),a89),a104)) % 186.01/186.01 [4767]~P1(f335(f335(f244(a1),a89),a89)) % 186.01/186.01 [4768]~P1(f335(f335(f244(a1),a89),a104)) % 186.01/186.01 [4769]~P1(f335(f335(f244(a1),a104),a104)) % 186.01/186.01 [4780]~P1(f335(f67(a927),f250(f934(a927,a922)))) % 186.01/186.01 [4781]~P1(f335(f67(a1),f250(f934(a1,a922)))) % 186.01/186.01 [4650]E(f335(f265(a1,a1,a922),f335(f335(f8(f934(a1,a922),f934(a1,a922),a1),f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f244(a1),f2(a1))))),f335(f335(f7(a1,a1,f934(a1,a922)),f335(f335(f8(f934(a1,f934(a1,a922)),f934(a1,f934(a1,a922)),a1),f7(a1,a1,a922)),f335(f335(f8(f934(a1,a1),f934(a1,f934(a1,a922)),a1),f335(f8(a1,f934(a1,a922),a1),a332)),a226))),f84(a1)))),a222) % 186.01/186.01 [4807]~P25(a921,a936,f335(f335(f317(f926(a921)),f98(a921,f99(a921,f335(f335(f7(a921,f934(a923,a922),f934(a923,a922)),f335(f335(f8(f934(a923,f934(a922,a922)),f934(f934(a923,a922),f934(a923,a922)),a921),f18(a923,a922,a922)),f335(f335(f8(f934(a923,a922),f934(a923,f934(a922,a922)),a921),f335(f8(a922,f934(a922,a922),a923),a333)),a937))),f335(f335(f8(a922,a922,a923),a330),a938)),a938),a939,f335(f335(f7(a921,f934(a923,a922),f934(a923,a922)),f335(f335(f8(f934(a923,f934(a922,a922)),f934(f934(a923,a922),f934(a923,a922)),a921),f18(a923,a922,a922)),f335(f335(f8(f934(a923,a922),f934(a923,f934(a922,a922)),a921),f335(f8(a922,f934(a922,a922),a923),a333)),a937))),f335(f335(f8(a922,a922,a923),a330),a938)))),f195(f934(f926(a921),a922)))) % 186.01/186.01 [3727]E(f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104),f335(f85(a1),a104)) % 186.01/186.01 [3765]E(f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104),f335(f335(f23(a1),a89),a104)) % 186.01/186.01 [3931]E(f335(f335(f66(f933(a927,a927)),f250(f934(f933(a927,a927),a922))),a115),a105) % 186.01/186.01 [3960]E(f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f84(a1)) % 186.01/186.01 [3961]E(f335(f110(a106),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f84(a106)) % 186.01/186.01 [3962]E(f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f84(a927)) % 186.01/186.01 [3966]E(f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(a119,f2(a927))) % 186.01/186.01 [4350]E(f335(f335(f117(f934(f933(f933(a927,a927),f933(a927,a927)),a922)),a38),f315(f933(a927,a927),f195(f934(f933(f933(a927,a927),f933(a927,a927)),a922)))),a76) % 186.01/186.01 [4418]E(f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),f84(a927)),f2(a927))),f195(f934(f933(a927,a927),a922))))),f84(a1)) % 186.01/186.01 [4419]E(f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),f2(a927)),f2(a927))),f195(f934(f933(a927,a927),a922))))),f2(a1)) % 186.01/186.01 [4432]E(f335(f270(f933(a927,a927)),f335(f265(a927,a927,a922),f335(f335(f8(a927,f934(a927,a922),a927),f335(f7(a927,a927,a922),a332)),a119))),a325) % 186.01/186.01 [4404]E(f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),f335(a119,f335(a119,f2(a927)))) % 186.01/186.01 [4407]E(f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),f335(f335(f86(a927),f84(a927)),f84(a927))) % 186.01/186.01 [4408]E(f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),f335(f41(a922),f250(f934(a922,a922)))) % 186.01/186.01 [4471]P7(f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))) % 186.01/186.01 [4540]P28(f934(f933(a927,a927),a922),f335(f335(f260(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922),f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)),a39),a77)) % 186.01/186.01 [4541]P28(f934(f933(a927,a927),a922),f335(f335(f260(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922),f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)),a40),a75)) % 186.01/186.01 [4581]E(f335(f335(f117(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)),f327(f933(a927,a927),a76)),f335(f335(f317(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f195(f934(f933(a927,a927),a922))),f195(f934(f933(a927,a927),a922)))),f195(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)))),a75) % 186.01/186.01 [4582]E(f335(f335(f117(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)),f326(f933(a927,a927),a76)),f335(f335(f317(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f195(f934(f933(a927,a927),a922))),f195(f934(f933(a927,a927),a922)))),f195(f934(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a922)))),a77) % 186.01/186.01 [4473]E(f335(a111,f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(a119,f335(a119,f2(a927)))) % 186.01/186.01 [4518]E(f335(f107(a1),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))) % 186.01/186.01 [4551]P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.01 [4552]E(f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104)),f335(a119,f335(a119,f335(a119,f2(a927))))) % 186.01/186.01 [4596]P7(f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))) % 186.01/186.01 [4622]E(f335(f107(a1),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))) % 186.01/186.01 [4635]P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104)))) % 186.01/186.01 [3355]P8(x33551,a332) % 186.01/186.01 [3753]P26(a927,a927,a119,x37531) % 186.01/186.01 [3348]P106(f926(x33481)) % 186.01/186.01 [3349]P106(f931(x33491)) % 186.01/186.01 [3350]P106(f928(x33501)) % 186.01/186.01 [3351]P106(f929(x33511)) % 186.01/186.01 [3374]P38(a1,f112(x33741)) % 186.01/186.01 [3375]P38(a1,f114(x33751)) % 186.01/186.01 [3428]P38(f934(x34281,a922),f322(x34281)) % 186.01/186.01 [3429]P39(f934(x34291,a922),f322(x34291)) % 186.01/186.01 [3454]E(f251(x34541,x34541,a332),a332) % 186.01/186.01 [3469]E(f51(a1,x34691,x34691),f2(a1)) % 186.01/186.01 [3522]P15(x35221,f934(x35221,a922),f317(x35221)) % 186.01/186.01 [4712]~E(f335(a119,x47121),x47121) % 186.01/186.01 [4724]~E(f335(a119,x47241),f2(a927)) % 186.01/186.01 [3356]E(f35(f33(x33561)),f2(a927)) % 186.01/186.01 [3357]E(f35(f34(x33571)),f2(a927)) % 186.01/186.01 [3359]E(f335(f196(a927),x33591),x33591) % 186.01/186.01 [3360]E(f335(f110(a1),x33601),x33601) % 186.01/186.01 [3376]E(f335(a95,f336(x33761)),x33761) % 186.01/186.01 [3377]E(f335(a3,f573(x33771)),x33771) % 186.01/186.01 [3378]E(f249(x33781,f2(a106)),f2(a106)) % 186.01/186.01 [3391]E(f121(x33911,f120(x33911)),f120(x33911)) % 186.01/186.01 [3392]E(f159(x33921,f120(x33921)),f120(x33921)) % 186.01/186.01 [3394]E(f335(f196(a925),f33(x33941)),f2(a927)) % 186.01/186.01 [3395]E(f335(f196(a925),f34(x33951)),f2(a927)) % 186.01/186.01 [3399]E(f335(f174(x33991),f120(x33991)),f120(x33991)) % 186.01/186.01 [3400]E(f335(f178(x34001),f120(x34001)),f120(x34001)) % 186.01/186.01 [3401]E(f335(f175(x34011),f120(x34011)),f120(x34011)) % 186.01/186.01 [3407]E(f335(f110(a1),x34071),f335(f109(a1),x34071)) % 186.01/186.01 [3408]E(f335(a95,f335(a113,x34081)),x34081) % 186.01/186.01 [3410]E(f335(a3,f335(a20,x34101)),x34101) % 186.01/186.01 [3411]E(f335(a20,f335(a3,x34111)),x34111) % 186.01/186.01 [3413]P7(f335(f107(a1),x34131)) % 186.01/186.01 [3422]E(f335(f196(f928(x34221)),f120(x34221)),f2(a927)) % 186.01/186.01 [3423]E(f335(f196(f929(x34231)),f126(x34231)),f2(a927)) % 186.01/186.01 [3445]E(f335(f335(f23(a927),x34451),f2(a927)),x34451) % 186.01/186.01 [3446]E(f335(f335(f87(a927),x34461),f84(a927)),x34461) % 186.01/186.01 [3447]E(f335(f335(f87(a1),x34471),f84(a1)),x34471) % 186.01/186.01 [3448]E(f335(f335(f86(a927),x34481),f2(a927)),x34481) % 186.01/186.01 [3449]E(f335(f335(f86(a1),x34491),f2(a1)),x34491) % 186.01/186.01 [3450]E(f335(f335(f242(a927),x34501),f2(a927)),x34501) % 186.01/186.01 [3451]E(f335(f335(f87(a927),x34511),f2(a927)),f2(a927)) % 186.01/186.01 [3452]E(f335(f335(f241(a927),x34521),f2(a927)),f2(a927)) % 186.01/186.01 [3453]E(f335(f335(f42(a1),x34531),f2(a1)),f2(a1)) % 186.01/186.01 [3460]E(f335(f179(x34601),f120(x34601)),f195(f934(x34601,a922))) % 186.01/186.01 [3464]P1(f335(f144(x34641),f120(x34641))) % 186.01/186.01 [3470]E(f335(f161(x34701,x34701),f5(x34701)),f25(f928(x34701))) % 186.01/186.01 [3471]E(f335(f161(x34711,x34711),f25(x34711)),f25(f928(x34711))) % 186.01/186.01 [3472]E(f51(a1,x34721,f2(a1)),x34721) % 186.01/186.01 [3473]E(f335(f243(a927),f335(a119,x34731)),f335(f244(a927),x34731)) % 186.01/186.01 [3474]E(f335(f290(a927),f335(a119,x34741)),f335(f309(a927),x34741)) % 186.01/186.01 [3475]E(f335(f291(a927),f335(a119,x34751)),f335(f312(a927),x34751)) % 186.01/186.01 [3477]E(f51(a1,f2(a1),x34771),f2(a1)) % 186.01/186.01 [3490]E(f335(f335(f86(a927),x34901),f84(a927)),f335(a119,x34901)) % 186.01/186.01 [3499]E(f335(f310(a927,x34991),f2(a927)),f195(f934(a927,a922))) % 186.01/186.01 [3511]E(f311(a927,f2(a927),x35111),f335(f309(a927),x35111)) % 186.01/186.01 [3554]E(f335(f335(f23(a927),f335(a119,x35541)),f84(a927)),x35541) % 186.01/186.01 [3566]E(f53(f2(a1),x35661),f335(f335(f260(a1,a1),f2(a1)),f2(a1))) % 186.01/186.01 [3616]P1(f335(f335(f244(a927),x36161),f335(a119,x36161))) % 186.01/186.01 [3628]P1(f335(f335(f244(a927),f2(a927)),f335(a119,x36281))) % 186.01/186.01 [3860]E(f97(x38601,x38601,f250(f934(x38601,a922)),f25(x38601)),f25(x38601)) % 186.01/186.01 [3918]E(f335(f335(f23(a106),f335(a3,f335(a119,f335(a20,x39181)))),f84(a106)),x39181) % 186.01/186.01 [3989]P1(f335(f335(f243(a1),f335(f85(a1),f335(f107(a1),x39891))),f2(a1))) % 186.01/186.01 [4138]P1(f335(f335(f244(a1),f335(f85(a1),f335(f107(a1),f335(a119,x41381)))),f2(a1))) % 186.01/186.01 [4738]~E(f250(f934(x47381,a922)),f195(f934(x47381,a922))) % 186.01/186.01 [4777]~P1(f335(f335(f244(a927),x47771),f2(a927))) % 186.01/186.01 [4790]~P1(f335(f335(f244(a1),f335(f107(a1),x47901)),f2(a1))) % 186.01/186.01 [3412]E(f127(x34121,f126(f929(x34121))),f126(x34121)) % 186.01/186.01 [3427]E(f186(x34271,f120(f928(x34271))),f120(f928(x34271))) % 186.01/186.01 [3430]E(f335(f335(f87(a1),a89),x34301),a89) % 186.01/186.01 [3431]E(f335(f335(f86(a1),a89),x34311),x34311) % 186.01/186.01 [3434]E(f335(a111,f335(f107(a1),x34341)),x34341) % 186.01/186.01 [3435]E(f335(f335(f23(a1),x34351),a89),x34351) % 186.01/186.01 [3436]E(f335(f335(f86(a1),x34361),a89),x34361) % 186.01/186.01 [3439]E(f335(f335(f23(a927),x34391),x34391),f2(a927)) % 186.01/186.01 [3443]E(f335(f85(a1),f335(f85(a1),x34431)),x34431) % 186.01/186.01 [3444]E(f335(f41(a927),f335(f290(a927),x34441)),x34441) % 186.01/186.01 [3455]E(f335(f335(f87(a927),f84(a927)),x34551),x34551) % 186.01/186.01 [3456]E(f335(f335(f87(a1),f84(a1)),x34561),x34561) % 186.01/186.01 [3457]E(f335(f335(f86(a927),f2(a927)),x34571),x34571) % 186.01/186.01 [3458]E(f335(f335(f86(a1),f2(a1)),x34581),x34581) % 186.01/186.01 [3459]E(f335(f335(f242(a927),f2(a927)),x34591),x34591) % 186.01/186.01 [3465]E(f335(f335(f23(a927),f2(a927)),x34651),f2(a927)) % 186.01/186.01 [3466]E(f335(f335(f87(a927),f2(a927)),x34661),f2(a927)) % 186.01/186.01 [3467]E(f335(f335(f241(a927),f2(a927)),x34671),f2(a927)) % 186.01/186.01 [3468]E(f335(f335(f42(a1),f2(a1)),x34681),f2(a1)) % 186.01/186.01 [3478]E(f135(x34781,f335(f85(a1),x34781)),f139(a1,x34781)) % 186.01/186.01 [3483]E(f335(f310(a927,f2(a927)),x34831),f335(f290(a927),x34831)) % 186.01/186.01 [3484]E(f335(f335(f87(a1),a104),x34841),f335(f85(a1),x34841)) % 186.01/186.01 [3492]E(f335(a111,f335(f110(a1),x34921)),f335(f110(a927),x34921)) % 186.01/186.01 [3493]E(f335(a20,f335(f110(a106),x34931)),f335(f110(a927),x34931)) % 186.01/186.01 [3494]E(f335(f41(a927),f335(f309(a927),x34941)),f335(a119,x34941)) % 186.01/186.01 [3503]E(f335(f335(f86(a927),f84(a927)),x35031),f335(a119,x35031)) % 186.01/186.01 [3507]E(f335(f109(a1),f335(f107(a1),x35071)),f335(f107(a1),x35071)) % 186.01/186.01 [3508]E(f335(f81(a1),f335(f107(a1),x35081)),f335(f107(a1),x35081)) % 186.01/186.01 [3512]E(f335(f41(x35121),f195(f934(x35121,a922))),f2(a927)) % 186.01/186.01 [3514]E(f335(f335(f42(a927),x35141),f335(a119,f2(a927))),x35141) % 186.01/186.01 [3523]E(f51(a927,x35231,f335(a119,f2(a927))),f2(a927)) % 186.01/186.01 [3524]E(f51(a1,x35241,f335(f110(a1),a104)),f2(a1)) % 186.01/186.01 [3538]E(f335(f335(f42(a1),x35381),f335(f110(a1),a104)),f335(f85(a1),x35381)) % 186.01/186.01 [3542]E(f146(a927,f335(f310(a927,x35421),f2(a927))),f120(a927)) % 186.01/186.01 [3543]E(f335(f335(f86(a1),x35431),f84(a1)),f335(f335(f23(a1),x35431),a104)) % 186.01/186.01 [3544]E(f335(f335(f23(a1),x35441),f84(a1)),f335(f335(f86(a1),x35441),a104)) % 186.01/186.01 [3548]P1(f335(f335(f243(a927),x35481),x35481)) % 186.01/186.01 [3549]P1(f335(f335(f243(a1),x35491),x35491)) % 186.01/186.01 [3550]P1(f335(f335(f295(a927),x35501),x35501)) % 186.01/186.01 [3555]E(f335(f85(a1),f335(f110(a1),x35551)),f335(f110(a1),f335(f85(a1),x35551))) % 186.01/186.01 [3556]P1(f335(f67(a927),f335(f290(a927),x35561))) % 186.01/186.01 [3557]P1(f335(f67(a927),f335(f309(a927),x35571))) % 186.01/186.01 [3564]E(f168(x35641,f250(f934(x35641,a922))),f250(f934(f928(x35641),a922))) % 186.01/186.01 [3569]P1(f335(f335(f243(a927),f2(a927)),x35691)) % 186.01/186.01 [3579]E(f335(f335(f86(a927),f118(x35791)),f335(a119,f2(a927))),f118(f335(a119,x35791))) % 186.01/186.01 [3580]E(f335(f270(x35801),f335(f16(a922,x35801),a247)),f195(f934(x35801,a922))) % 186.01/186.01 [3581]E(f335(f270(x35811),f335(f16(a922,x35811),a194)),f250(f934(x35811,a922))) % 186.01/186.01 [3585]E(f335(f335(f317(a927),x35851),f335(f290(a927),x35851)),f335(f290(a927),f335(a119,x35851))) % 186.01/186.01 [3597]E(f335(f335(f86(a1),f84(a1)),f335(f107(a1),x35971)),f335(f107(a1),f335(a119,x35971))) % 186.01/186.01 [3599]E(f335(f335(f158(f928(x35991)),f120(x35991)),f120(f928(x35991))),f60(x35991,f120(x35991))) % 186.01/186.01 [3619]E(f195(f934(f933(x36191,x36191),a922)),f271(x36191,f195(f934(x36191,a922)))) % 186.01/186.01 [3620]E(f335(f316(x36201),f250(f934(x36201,a922))),f250(f934(f934(x36201,a922),a922))) % 186.01/186.01 [3621]E(f335(f85(f934(x36211,a922)),f195(f934(x36211,a922))),f250(f934(x36211,a922))) % 186.01/186.01 [3622]E(f335(f85(f934(x36221,a922)),f250(f934(x36221,a922))),f195(f934(x36221,a922))) % 186.01/186.01 [3624]P1(f335(f67(x36241),f195(f934(x36241,a922)))) % 186.01/186.01 [3626]E(f335(f310(a927,x36261),f335(a119,x36261)),f335(f335(f317(a927),x36261),f195(f934(a927,a922)))) % 186.01/186.01 [3627]E(f91(f933(a927,a927),f54(x36271,f2(a927))),f335(f335(f260(a927,a927),f2(a927)),x36271)) % 186.01/186.01 [3640]E(f335(f335(f317(a927),f335(a119,x36401)),f335(f309(a927),x36401)),f335(f309(a927),f335(a119,x36401))) % 186.01/186.01 [3644]P38(x36441,f195(f934(f933(x36441,x36441),a922))) % 186.01/186.01 [3645]P40(x36451,f195(f934(f933(x36451,x36451),a922))) % 186.01/186.01 [3648]P1(f335(f335(f243(a1),f2(a1)),f335(f107(a1),x36481))) % 186.01/186.01 [3655]E(f335(f335(f86(a927),f335(f196(a927),x36551)),f335(a119,f2(a927))),f335(f196(a927),f335(a119,x36551))) % 186.01/186.01 [3760]P41(f335(f318(a927,a1,f107(a1)),x37601)) % 186.01/186.01 [3798]P54(x37981,f195(f934(x37981,a922)),f195(f934(f933(x37981,x37981),a922))) % 186.01/186.01 [3821]E(f335(f335(f260(a1,a1),f335(f110(a1),a104)),f335(f335(f23(a1),x38211),f84(a1))),f56(f335(f110(a1),a104),x38211)) % 186.01/186.01 [3873]P61(x38731,f335(f16(f934(x38731,a922),x38731),f335(f16(a922,x38731),a247))) % 186.01/186.01 [3885]E(f298(a927,f295(a927),x38851,x38851),f335(f335(f317(a927),x38851),f195(f934(a927,a922)))) % 186.01/186.01 [4078]P1(f335(f335(f337(f934(f933(a927,a927),a922)),f336(x40781)),a105)) % 186.01/186.01 [4104]P1(f335(f335(f337(f934(f933(a927,a927),a922)),f335(a113,x41041)),a105)) % 186.01/186.01 [4237]P26(x42371,f934(x42371,a922),f335(f335(f7(x42371,f934(x42371,a922),f934(x42371,a922)),f317(x42371)),f195(f934(x42371,a922))),f250(f934(x42371,a922))) % 186.01/186.01 [4735]~E(f335(f335(f86(a1),x47351),x47351),a104) % 186.01/186.01 [4764]~E(f335(a3,f335(a119,f335(a20,x47641))),f2(a106)) % 186.01/186.01 [4770]~P1(f335(a200,f335(f107(a1),x47701))) % 186.01/186.01 [4773]~P1(f335(f335(f244(a927),x47731),x47731)) % 186.01/186.01 [4783]~P1(f335(f335(f243(a927),f335(a119,x47831)),x47831)) % 186.01/186.01 [3571]E(f335(a111,f335(f85(a1),f335(f107(a1),x35711))),f2(a927)) % 186.01/186.01 [3574]E(f335(f335(f86(a1),f335(f85(a1),x35741)),x35741),f2(a1)) % 186.01/186.01 [3578]E(f335(f41(a1),f335(f310(a1,f2(a1)),x35781)),f335(a111,x35781)) % 186.01/186.01 [3590]E(f335(f335(f252(a927),f335(a119,f2(a927))),x35901),f335(a119,f2(a927))) % 186.01/186.01 [3687]E(f335(f289(x36871),f195(f934(f933(x36871,x36871),a922))),f195(f934(x36871,a922))) % 186.01/186.01 [3695]E(f44(f934(x36951,a922),f195(f934(f934(x36951,a922),a922))),f250(f934(x36951,a922))) % 186.01/186.01 [3696]E(f44(f934(x36961,a922),f250(f934(f934(x36961,a922),a922))),f195(f934(x36961,a922))) % 186.01/186.01 [3697]E(f43(f934(x36971,a922),f195(f934(f934(x36971,a922),a922))),f195(f934(x36971,a922))) % 186.01/186.01 [3698]E(f43(f934(x36981,a922),f250(f934(f934(x36981,a922),a922))),f250(f934(x36981,a922))) % 186.01/186.01 [3702]P1(f335(f335(f295(a927),f335(a119,f2(a927))),x37021)) % 186.01/186.01 [3743]E(f335(f335(f317(f928(x37431)),f120(x37431)),f195(f934(f928(x37431),a922))),f168(x37431,f195(f934(x37431,a922)))) % 186.01/186.01 [3744]E(f335(f335(f317(f928(x37441)),f120(x37441)),f195(f934(f928(x37441),a922))),f169(x37441,f120(f934(x37441,a922)))) % 186.01/186.01 [3782]E(f335(f335(f86(a927),f4(x37821)),f335(a119,f2(a927))),f4(f335(a3,f335(a119,f335(a20,x37821))))) % 186.01/186.01 [3812]E(f335(f41(a1),f335(f318(a927,a1,f107(a1)),x38121)),f335(f41(a927),x38121)) % 186.01/186.01 [3813]P1(f335(f335(f243(a927),x38131),f335(f335(f87(a927),x38131),x38131))) % 186.01/186.01 [3851]E(f335(f318(a1,a927,a111),f311(a1,f2(a1),f335(f107(a1),x38511))),f335(f309(a927),x38511)) % 186.01/186.01 [3868]E(f335(f335(f42(a927),f335(a119,f2(a927))),f335(f110(a927),x38681)),f335(a111,f335(f335(f42(a1),f84(a1)),f335(f110(a1),x38681)))) % 186.01/186.01 [3870]E(f335(f179(a927),f146(a927,f335(f310(a927,f2(a927)),f335(a119,x38701)))),f335(f309(a927),x38701)) % 186.01/186.01 [3871]E(f335(f335(f86(a927),f335(f196(a106),x38711)),f335(a119,f2(a927))),f335(f196(a106),f335(a3,f335(a119,f335(a20,x38711))))) % 186.01/186.01 [3891]P40(x38911,f315(x38911,f195(f934(f933(x38911,x38911),a922)))) % 186.01/186.01 [3892]P53(x38921,f315(x38921,f195(f934(f933(x38921,x38921),a922)))) % 186.01/186.01 [3893]E(f335(f318(a1,a927,a111),f335(f318(a927,a1,f107(a1)),x38931)),x38931) % 186.01/186.01 [3924]E(f335(f335(f317(a927),f2(a927)),f335(f318(a927,a927,a119),f335(f290(a927),x39241))),f335(f290(a927),f335(a119,x39241))) % 186.01/186.01 [3930]P56(x39301,x39301,f315(x39301,f195(f934(f933(x39301,x39301),a922)))) % 186.01/186.01 [3936]P1(f335(a200,f335(f85(a1),f335(f107(a1),f335(a119,x39361))))) % 186.01/186.01 [3946]E(f335(f335(f23(f934(a927,a922)),f335(f291(a927),x39461)),f335(f335(f317(a927),x39461),f195(f934(a927,a922)))),f335(f291(a927),f335(a119,x39461))) % 186.01/186.01 [3963]E(f335(f335(f86(a1),f335(f335(f23(a1),a89),x39631)),f335(f335(f23(a1),a89),x39631)),f335(f335(f23(a1),a89),f335(f335(f86(a1),x39631),x39631))) % 186.01/186.01 [3978]E(f335(f335(f317(f934(x39781,a922)),f195(f934(x39781,a922))),f195(f934(f934(x39781,a922),a922))),f335(f316(x39781),f195(f934(x39781,a922)))) % 186.01/186.01 [4006]E(f335(f335(f23(f934(a927,a922)),f335(f312(a927),x40061)),f335(f335(f317(a927),f335(a119,x40061)),f195(f934(a927,a922)))),f335(f312(a927),f335(a119,x40061))) % 186.01/186.01 [4116]E(f335(f110(a927),f335(f335(f86(a1),x41161),x41161)),f335(f335(f92(a927,a927),f335(f110(a927),x41161)),f335(f335(f18(a927,a927,a927),f86(a927)),f5(a927)))) % 186.01/186.01 [4493]P15(x44931,f934(x44931,a922),f335(f335(f8(f934(x44931,a922),f934(f934(x44931,a922),f934(x44931,a922)),x44931),f335(f7(f934(x44931,a922),f934(x44931,a922),f934(x44931,a922)),f23(f934(x44931,a922)))),f335(f335(f7(x44931,f934(x44931,a922),f934(x44931,a922)),f317(x44931)),f195(f934(x44931,a922))))) % 186.01/186.01 [4580]E(f335(f270(f933(a1,a1)),f335(f265(a1,a1,a922),f335(f335(f8(f934(a1,a922),f934(a1,a922),a1),f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),x45801)))),f244(a1)))),f114(x45801)) % 186.01/186.01 [4613]E(f335(f270(f933(a1,a1)),f335(f265(a1,a1,a922),f335(f335(f18(a1,f934(a1,a922),f934(a1,a922)),f335(f335(f8(f934(a922,a922),f934(f934(a1,a922),f934(a1,a922)),a1),f8(a922,a922,a1)),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),x46131)))),f244(a1)))),f112(x46131)) % 186.01/186.01 [4666]E(f335(f270(f933(f934(x46661,a922),f934(x46661,a922))),f335(f265(f934(x46661,a922),f934(x46661,a922),a922),f335(f335(f7(f934(x46661,a922),f934(f934(x46661,a922),a922),f934(f934(x46661,a922),a922)),f335(f335(f8(f934(f934(x46661,a922),f934(a922,a922)),f934(f934(f934(x46661,a922),a922),f934(f934(x46661,a922),a922)),f934(x46661,a922)),f18(f934(x46661,a922),a922,a922)),f335(f335(f8(f934(f934(x46661,a922),a922),f934(f934(x46661,a922),f934(a922,a922)),f934(x46661,a922)),f335(f8(a922,f934(a922,a922),f934(x46661,a922)),a333)),f244(f934(x46661,a922))))),f67(x46661)))),f322(x46661)) % 186.01/186.01 [4787]~P1(f335(f67(f928(x47871)),f250(f934(f928(x47871),a922)))) % 186.01/186.01 [4799]~P1(f335(f335(f243(a1),f2(a1)),f335(f85(a1),f335(f107(a1),f335(a119,x47991))))) % 186.01/186.01 [3722]E(f335(f335(f23(a1),f335(f335(f86(a1),x37221),a104)),a104),x37221) % 186.01/186.01 [3736]E(f335(f179(a927),f146(a927,f335(f310(a927,f2(a927)),x37361))),f335(f290(a927),x37361)) % 186.01/186.01 [3985]E(f335(f335(f86(a1),f335(f335(f86(a1),f84(a1)),x39851)),x39851),f335(f335(f23(a1),f335(f335(f86(a1),x39851),x39851)),a104)) % 186.01/186.01 [4034]E(f335(f294(x40341,x40341),f315(x40341,f195(f934(f933(x40341,x40341),a922)))),f315(x40341,f195(f934(f933(x40341,x40341),a922)))) % 186.01/186.01 [4081]P1(f335(f335(f243(a927),x40811),f335(f335(f87(a927),x40811),f335(f335(f87(a927),x40811),x40811)))) % 186.01/186.01 [4354]P1(f335(f67(a927),f335(f270(a927),f335(f335(f7(a927,a927,a922),f243(a927)),x43541)))) % 186.01/186.01 [4355]P1(f335(f67(a927),f335(f270(a927),f335(f335(f7(a927,a927,a922),f244(a927)),x43551)))) % 186.01/186.01 [4629]E(f335(f270(f933(x46291,x46291)),f335(f335(f8(f934(x46291,a922),a922,f933(x46291,x46291)),f93(x46291)),f335(f335(f7(f933(x46291,x46291),f934(x46291,f933(x46291,x46291)),f934(x46291,a922)),f335(f335(f8(f934(f933(x46291,x46291),a922),f934(f934(x46291,f933(x46291,x46291)),f934(x46291,a922)),f933(x46291,x46291)),f8(f933(x46291,x46291),a922,x46291)),a332)),f335(f335(f18(x46291,x46291,f933(x46291,x46291)),f260(x46291,x46291)),f5(x46291))))),f315(x46291,f195(f934(f933(x46291,x46291),a922)))) % 186.01/186.01 [4789]~E(f335(f335(f23(a1),f335(f335(f86(a1),x47891),x47891)),a104),a89) % 186.01/186.01 [4791]~E(f335(f335(f86(a1),f335(f335(f86(a1),f84(a1)),x47911)),x47911),f2(a1)) % 186.01/186.01 [4127]E(f335(f335(f86(a1),f335(f335(f23(a1),a104),x41271)),f335(f335(f23(a1),a104),x41271)),f335(f335(f23(a1),a104),f335(f335(f23(a1),f335(f335(f86(a1),x41271),x41271)),a104))) % 186.01/186.01 [4245]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),a104),x42451)),f335(f335(f23(a1),a104),x42451))),a104),f335(f335(f23(a1),a104),f335(f335(f86(a1),x42451),x42451))) % 186.01/186.01 [4277]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f86(a1),x42771),a104)),f335(f335(f86(a1),x42771),a104))),a104),f335(f335(f86(a1),f335(f335(f86(a1),x42771),x42771)),a104)) % 186.01/186.01 [4315]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),a104),x43151)),f335(f335(f23(a1),a104),x43151))),a104),f335(f335(f23(a1),a89),f335(f335(f23(a1),f335(f335(f86(a1),x43151),x43151)),a104))) % 186.01/186.01 [4414]E(f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x44141),f2(a927))),f195(f934(f933(a927,a927),a922))))),f335(f107(a1),x44141)) % 186.01/186.01 [4424]E(f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),f399(x44241)),f435(x44241))),f195(f934(f933(a927,a927),a922))))),x44241) % 186.01/186.01 [4457]E(f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x44571)),f335(f318(a927,a1,f107(a1)),f335(f270(a927),f335(f335(f8(a1,a922,a927),x44571),f107(a1))))) % 186.01/186.01 [4501]P41(f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x45011))) % 186.01/186.01 [4521]P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x45211),f195(f934(f933(a927,a927),a922)))),a77)) % 186.01/186.01 [4526]E(f335(f318(a1,a927,a111),f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),f335(f335(f8(a927,a922,a1),x45261),a111)))),f335(f270(a927),x45261)) % 186.01/186.01 [4683]E(f320(a927,f335(f335(f45(f933(a927,a927),f934(a927,a922)),f335(a113,x46831)),f335(f265(a927,a927,f934(a927,a922)),f335(f335(f7(a927,f934(a927,a922),f934(a927,f934(a927,a922))),f335(f335(f8(f934(a927,f934(f934(a927,a922),f934(a927,a922))),f934(f934(a927,a922),f934(a927,f934(a927,a922))),a927),f7(a927,f934(a927,a922),f934(a927,a922))),f335(f335(f8(f934(a927,a927),f934(a927,f934(f934(a927,a922),f934(a927,a922))),a927),f335(f8(a927,f934(f934(a927,a922),f934(a927,a922)),a927),f317(a927))),f23(a927)))),f195(f934(a927,a922)))))),f335(a111,x46831)) % 186.01/186.01 [4174]E(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),x41741),x41741)),a104)),a104),f335(f335(f86(a1),x41741),x41741)) % 186.01/186.01 [4224]E(f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f86(a1),x42241),x42241)),a104)),a104),f335(f335(f86(a1),f335(f335(f23(a1),x42241),a104)),f335(f335(f23(a1),x42241),a104))) % 186.01/186.01 [4430]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f86(a1),f335(f85(a1),x44301)),a104)),f335(f335(f86(a1),f335(f85(a1),x44301)),a104))),a104),f335(f85(a1),f335(f335(f23(a1),f335(f335(f86(a1),x44301),x44301)),a104))) % 186.01/186.01 [4474]E(f335(f335(f86(a927),x44741),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(a119,f335(a119,x44741))) % 186.01/186.01 [4475]E(f335(f335(f87(a927),x44751),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f86(a927),x44751),x44751)) % 186.01/186.01 [4476]E(f335(f335(f42(a927),f335(f335(f86(a927),x44761),x44761)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x44761) % 186.01/186.01 [4554]E(f51(a927,f335(a119,f335(a119,x45541)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a927,x45541,f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.01 [4697]E(f335(a95,f335(f335(f45(f933(a927,a927),f934(f933(a927,a927),a922)),f335(a113,x46971)),f335(f265(a927,a927,f934(f933(a927,a927),a922)),f335(f335(f8(f934(a927,f934(f933(a927,a927),a922)),f934(a927,f934(f933(a927,a927),a922)),a927),f335(f8(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922),a927),f293(f933(a927,a927),f933(a927,a927),a115))),f335(f335(f7(a927,f934(f933(a927,a927),a922),f934(a927,f934(f933(a927,a927),a922))),f335(f335(f8(f934(a927,f934(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f934(f934(f933(a927,a927),a922),f934(a927,f934(f933(a927,a927),a922))),a927),f7(a927,f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f8(f934(a927,f933(a927,a927)),f934(a927,f934(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),a927),f335(f8(f933(a927,a927),f934(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),a927),f317(f933(a927,a927)))),f335(f7(a927,a927,f933(a927,a927)),f260(a927,a927))))),f195(f934(f933(a927,a927),a922))))))),f335(f85(a1),x46971)) % 186.01/186.01 [4549]E(f335(f335(f86(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x45491),f335(a119,f335(a119,x45491))) % 186.01/186.01 [4550]E(f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x45501),f335(f335(f86(a927),x45501),x45501)) % 186.01/186.01 [4586]E(f335(f335(f42(a927),f335(a119,f335(a119,x45861))),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(a119,f335(f335(f42(a927),x45861),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.01 [4636]E(f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46361),f335(a119,f335(a119,f335(a119,x46361)))) % 186.01/186.01 [4704]E(f335(f265(a1,a1,f933(a1,a1)),f335(f335(f18(a1,f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f934(f933(a1,a1),f933(a1,a1))),f934(f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),a1),f18(a1,f933(a1,a1),f933(a1,a1))),f335(f335(f8(f934(a1,f933(a1,a1)),f934(a1,f934(f933(a1,a1),f933(a1,a1))),a1),f335(f18(a1,f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),f335(f335(f8(a922,f934(f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),a1),f103(f933(a1,a1))),f335(f335(f8(a1,a922,a1),f335(f243(a1),f2(a1))),f335(f335(f7(a1,a1,a1),f23(a1)),x47041))))),f335(f335(f7(a1,f934(a1,a1),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f933(a1,a1)),f934(f934(a1,a1),f934(a1,f933(a1,a1))),a1),f8(a1,f933(a1,a1),a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f934(a1,a1),a1),f86(a1)),f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f84(a1))))),f335(f335(f7(a1,a1,a1),f23(a1)),x47041))))),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))),f49(x47041)) % 186.01/186.01 [3396]P106(f933(x33961,x33962)) % 186.01/186.01 [3397]P106(f935(x33971,x33972)) % 186.01/186.01 [3398]P106(f932(x33981,x33982)) % 186.01/186.01 [3416]P14(a1,f185(x34161,x34162)) % 186.01/186.01 [3417]P38(x34171,f160(x34171,x34172)) % 186.01/186.01 [3418]P39(x34181,f271(x34181,x34182)) % 186.01/186.01 [3419]P39(x34191,f315(x34191,x34192)) % 186.01/186.01 [3420]P40(x34201,f271(x34201,x34202)) % 186.01/186.01 [3421]P53(x34211,f271(x34211,x34212)) % 186.01/186.01 [3485]P32(x34851,x34852,f120(x34851)) % 186.01/186.01 [3518]P54(x35181,x35182,f271(x35181,x35182)) % 186.01/186.01 [3519]P56(x35191,x35191,f271(x35191,x35192)) % 186.01/186.01 [3785]P26(x37851,x37851,f5(x37851),x37852) % 186.01/186.01 [3786]P26(x37861,x37861,f25(x37861),x37862) % 186.01/186.01 [3794]P33(x37941,x37942,f120(x37941),f120(x37941)) % 186.01/186.01 [3802]P26(f928(x38021),f928(x38021),f175(x38021),x38022) % 186.01/186.01 [4214]P27(x42141,x42141,f25(x42141),x42142,x42142) % 186.01/186.01 [4710]~E(f34(x47101),f33(x47102)) % 186.01/186.01 [4716]~E(f32(x47161,x47162),a26) % 186.01/186.01 [4717]~E(f31(x47171,x47172),a26) % 186.01/186.01 [4718]~E(f27(x47181,x47182),a26) % 186.01/186.01 [4747]~P34(x47471,x47472,f120(x47471)) % 186.01/186.01 [4748]~P36(x47481,x47482,f120(x47481)) % 186.01/186.01 [3380]E(f335(f270(x33801),x33802),x33802) % 186.01/186.01 [3381]E(f335(f5(x33811),x33812),x33812) % 186.01/186.01 [3383]E(f335(f25(x33831),x33832),x33832) % 186.01/186.01 [3393]E(f335(f198(x33931),x33932),f122(x33931)) % 186.01/186.01 [3403]E(f30(f27(x34031,x34032)),f2(a927)) % 186.01/186.01 [3414]E(f91(x34141,f335(a332,x34142)),x34142) % 186.01/186.01 [3415]E(f96(x34151,f335(a332,x34152)),x34152) % 186.01/186.01 [3437]E(f335(f196(a924),f27(x34371,x34372)),f2(a927)) % 186.01/186.01 [3438]E(f335(f132(x34381,x34382),f126(x34381)),f2(a927)) % 186.01/186.01 [3441]E(f335(f143(x34411,x34412),f120(x34411)),f120(x34411)) % 186.01/186.01 [3461]E(f315(x34611,f315(x34611,x34612)),f315(x34611,x34612)) % 186.01/186.01 [3462]E(f159(x34621,f159(x34621,x34622)),f159(x34621,x34622)) % 186.01/186.01 [3480]E(f335(f335(f141(x34801),x34802),f120(x34801)),x34802) % 186.01/186.01 [3486]E(f180(x34861,x34862,f120(x34861)),x34862) % 186.01/186.01 [3487]E(f180(x34871,f120(x34871),x34872),x34872) % 186.01/186.01 [3488]E(f123(x34881,f126(x34881),x34882),x34882) % 186.01/186.01 [3489]E(f176(x34891,f2(a927),x34892),f120(x34891)) % 186.01/186.01 [3495]E(f335(f335(f182(x34951),x34952),f120(x34951)),f120(x34951)) % 186.01/186.01 [3496]E(f335(f335(f145(x34961),x34962),f120(x34961)),f120(x34961)) % 186.01/186.01 [3498]E(f162(x34981,x34982,f120(x34981)),f2(a927)) % 186.01/186.01 [3500]E(f177(x35001,x35002,f120(x35001)),f120(x35001)) % 186.01/186.01 [3501]E(f184(x35011,x35012,f120(x35011)),f120(x35011)) % 186.01/186.01 [3502]E(f183(x35021,f120(x35021),x35022),f120(x35021)) % 186.01/186.01 [3506]E(f335(f179(x35061),f159(x35061,x35062)),f335(f179(x35061),x35062)) % 186.01/186.01 [3509]E(f335(f292(x35091,x35091),f271(x35091,x35092)),x35092) % 186.01/186.01 [3510]E(f335(f272(x35101,x35101),f271(x35101,x35102)),x35102) % 186.01/186.01 [3517]E(f335(f294(x35171,x35171),f271(x35171,x35172)),f271(x35171,x35172)) % 186.01/186.01 [3530]E(f315(f928(x35301),f164(x35301,x35302)),f165(x35301,f315(x35301,x35302))) % 186.01/186.01 [3532]P1(f335(f144(a1),f185(x35321,x35322))) % 186.01/186.01 [3540]E(f335(f292(x35401,x35401),f315(x35401,x35402)),f250(f934(x35401,a922))) % 186.01/186.01 [3541]E(f335(f272(x35411,x35411),f315(x35411,x35412)),f250(f934(x35411,a922))) % 186.01/186.01 [3545]P1(f335(f144(x35451),f159(x35451,x35452))) % 186.01/186.01 [3547]P1(f335(f167(x35471,x35472),f120(x35471))) % 186.01/186.01 [3553]E(f335(f179(a1),f185(x35531,x35532)),f311(a1,x35531,x35532)) % 186.01/186.01 [3567]P57(x35671,f195(f934(x35671,a922)),x35672) % 186.01/186.01 [3572]E(f335(f264(a1,a1),f52(x35721,x35722)),f51(a1,x35721,x35722)) % 186.01/186.01 [3573]E(f335(f310(a927,x35731),f335(a119,x35732)),f311(a927,x35731,x35732)) % 186.01/186.01 [3589]E(f335(f335(f158(x35891),x35892),f120(x35891)),f147(x35891,x35892,f120(x35891))) % 186.01/186.01 [3601]E(f311(a927,f335(a119,x36011),x36012),f313(a927,x36011,x36012)) % 186.01/186.01 [3604]P54(x36041,f250(f934(x36041,a922)),f315(x36041,x36042)) % 186.01/186.01 [3667]E(f335(f335(f23(a927),x36671),f335(a119,x36672)),f335(f41(a927),f314(a927,x36672,x36671))) % 186.01/186.01 [3723]E(f173(x37231,x37232,f120(x37231)),f335(f335(f260(f928(x37231),f928(x37231)),f120(x37231)),f120(x37231))) % 186.01/186.01 [3741]E(f335(f265(x37411,x37412,f933(x37411,x37412)),f260(x37411,x37412)),f25(f933(x37411,x37412))) % 186.01/186.01 [3745]P1(f335(f335(f337(f928(x37451)),f120(x37451)),f168(x37451,x37452))) % 186.01/186.01 [3746]E(f335(f196(f928(x37461)),f121(x37461,x37462)),f335(f335(f23(a927),f335(f196(f928(x37461)),x37462)),f84(a927))) % 186.01/186.01 [3754]P1(f335(f67(a927),f314(a927,x37541,x37542))) % 186.01/186.01 [3755]P1(f335(f67(a927),f313(a927,x37551,x37552))) % 186.01/186.01 [3756]P1(f335(f67(a927),f311(a927,x37561,x37562))) % 186.01/186.01 [3757]P1(f335(f67(a1),f314(a1,x37571,x37572))) % 186.01/186.01 [3758]P1(f335(f67(a1),f313(a1,x37581,x37582))) % 186.01/186.01 [3759]P1(f335(f67(a1),f311(a1,x37591,x37592))) % 186.01/186.01 [3867]E(f335(f318(a927,a927,a119),f311(a927,x38671,x38672)),f311(a927,f335(a119,x38671),f335(a119,x38672))) % 186.01/186.01 [3887]E(f335(f335(f297(x38871,x38871,x38871),f315(x38871,x38872)),f315(x38871,x38872)),f315(x38871,x38872)) % 186.01/186.01 [3922]E(f335(f335(f260(a1,a1),f335(f335(f42(a1),x39221),x39222)),f51(a1,x39221,x39222)),f52(x39221,x39222)) % 186.01/186.01 [3923]E(f335(f335(f260(a106,a106),f335(f335(f42(a106),x39231),x39232)),f51(a106,x39231,x39232)),f21(x39231,x39232)) % 186.01/186.01 [3950]E(f335(f335(f260(a927,a927),f335(f335(f42(a927),x39501),x39502)),f51(a927,x39501,x39502)),f91(f933(a927,a927),f54(x39501,x39502))) % 186.01/186.01 [4002]P1(f335(f335(f244(a927),f335(f335(f23(a927),x40021),x40022)),f335(a119,x40021))) % 186.01/186.01 [4052]P39(x40521,f335(f335(f297(x40521,x40521,x40521),x40522),f315(x40521,x40522))) % 186.01/186.01 [4103]E(f335(f335(f86(a1),f335(f335(f87(a1),x41031),f335(f335(f42(a1),x41032),x41031))),f51(a1,x41032,x41031)),x41032) % 186.01/186.01 [4107]E(f335(f335(f45(a927,f934(f933(f928(x41071),f928(x41071)),a922)),f250(f934(a927,a922))),f150(x41071,x41072)),f152(x41071,x41072)) % 186.01/186.01 [4331]P1(f335(f335(f337(f933(f928(x43311),f928(x43311))),f335(f335(f260(f928(x43311),f928(x43311)),f120(x43311)),f120(x43311))),f165(x43311,x43312))) % 186.01/186.01 [4442]E(f261(x44421,x44421,x44421,a332,f261(x44421,x44421,x44421,x44422,a332)),x44422) % 186.01/186.01 [4486]E(f266(x44861,x44861,x44862,x44862,f5(x44861),f5(x44862)),f25(f933(x44861,x44862))) % 186.01/186.01 [4488]E(f266(x44881,x44881,x44882,x44882,f25(x44881),f25(x44882)),f25(f933(x44881,x44882))) % 186.01/186.01 [3479]E(f335(f175(x34791),f335(f175(x34791),x34792)),x34792) % 186.01/186.01 [3481]E(f335(f335(f145(x34811),f2(a927)),x34812),x34812) % 186.01/186.01 [3497]E(f335(f335(f182(x34971),f2(a927)),x34972),f120(x34971)) % 186.01/186.01 [3504]E(f335(f335(f141(x35041),f120(x35041)),x35042),x35042) % 186.01/186.01 [3513]E(f43(f934(x35131,a922),f335(f316(x35131),x35132)),x35132) % 186.01/186.01 [3515]E(f335(f179(x35151),f335(f174(x35151),x35152)),f335(f179(x35151),x35152)) % 186.01/186.01 [3516]E(f335(f179(x35161),f335(f175(x35161),x35162)),f335(f179(x35161),x35162)) % 186.01/186.01 [3521]E(f335(f335(f23(a106),x35211),x35212),f335(f335(a24,x35211),x35212)) % 186.01/186.01 [3534]E(f335(f335(f87(a927),x35341),x35342),f335(f335(f87(a927),x35342),x35341)) % 186.01/186.01 [3535]E(f335(f335(f87(a1),x35351),x35352),f335(f335(f87(a1),x35352),x35351)) % 186.01/186.01 [3536]E(f335(f335(f86(a927),x35361),x35362),f335(f335(f86(a927),x35362),x35361)) % 186.01/186.01 [3537]E(f335(f335(f86(a1),x35371),x35372),f335(f335(f86(a1),x35372),x35371)) % 186.01/186.01 [3559]E(f335(f335(f190(x35591,x35591),f2(a927)),x35592),f25(x35591)) % 186.01/186.01 [3560]E(f335(f196(f928(x35601)),f335(f174(x35601),x35602)),f335(f196(f928(x35601)),x35602)) % 186.01/186.01 [3561]E(f335(f196(f928(x35611)),f335(f175(x35611),x35612)),f335(f196(f928(x35611)),x35612)) % 186.01/186.01 [3562]E(f183(x35621,x35622,f195(f934(a927,a922))),f120(x35621)) % 186.01/186.01 [3563]E(f335(f335(f161(x35631,x35631),f5(x35631)),x35632),x35632) % 186.01/186.01 [3565]E(f335(f259(a1,a1),f52(x35651,x35652)),f335(f335(f42(a1),x35651),x35652)) % 186.01/186.01 [3582]E(f335(f196(f928(x35821)),f159(x35821,x35822)),f335(f41(x35821),f335(f179(x35821),x35822))) % 186.01/186.01 [3583]E(f30(f31(x35831,x35832)),f335(f335(f86(a927),f30(x35832)),f335(a119,f2(a927)))) % 186.01/186.01 [3584]E(f335(f289(x35841),f335(f294(x35841,x35841),x35842)),f335(f289(x35841),x35842)) % 186.01/186.01 [3588]P1(f335(f67(x35881),f335(f179(x35881),x35882))) % 186.01/186.01 [3596]E(f335(f335(f86(a1),x35961),f335(f85(a1),x35962)),f335(f335(f23(a1),x35961),x35962)) % 186.01/186.01 [3603]P25(x36031,x36032,f195(f934(f926(x36031),a922))) % 186.01/186.01 [3605]E(f335(f318(x36051,x36051,f5(x36051)),x36052),x36052) % 186.01/186.01 [3606]E(f335(f318(x36061,x36061,f25(x36061)),x36062),x36062) % 186.01/186.01 [3607]E(f335(f319(x36071,x36071,f5(x36071)),x36072),x36072) % 186.01/186.01 [3608]E(f335(f319(x36081,x36081,f25(x36081)),x36082),x36082) % 186.01/186.01 [3609]P1(f335(f250(f934(x36091,a922)),x36092)) % 186.01/186.01 [3611]E(f335(f41(a927),f335(f310(a927,x36111),x36112)),f335(f335(f23(a927),x36112),x36111)) % 186.01/186.01 [3612]E(f335(f310(a927,f335(a119,x36121)),x36122),f314(a927,x36121,x36122)) % 186.01/186.01 [3625]E(f335(f335(f317(x36251),x36252),f195(f934(x36251,a922))),f335(f270(x36251),f335(a332,x36252))) % 186.01/186.01 [3630]E(f315(x36301,f335(f294(x36301,x36301),x36302)),f335(f294(x36301,x36301),f315(x36301,x36302))) % 186.01/186.01 [3635]E(f335(f335(f86(a927),f335(a119,x36351)),x36352),f335(f335(f86(a927),x36351),f335(a119,x36352))) % 186.01/186.01 [3636]E(f335(f335(f23(a927),f335(a119,x36361)),f335(a119,x36362)),f335(f335(f23(a927),x36361),x36362)) % 186.01/186.01 [3642]E(f61(x36421,f2(a927),x36422),f335(f335(f158(f928(x36421)),f120(x36421)),f120(f928(x36421)))) % 186.01/186.01 [3643]E(f335(f41(a927),f313(a927,x36431,x36432)),f335(f335(f23(a927),x36432),x36431)) % 186.01/186.01 [3652]P38(x36521,f335(f335(f296(a927,x36521),a248),x36522)) % 186.01/186.01 [3654]P14(a927,f146(a927,f335(f310(a927,x36541),x36542))) % 186.01/186.01 [3656]P1(f335(f67(a927),f335(f310(a927,x36561),x36562))) % 186.01/186.01 [3657]P1(f335(f67(a1),f335(f310(a1,x36571),x36572))) % 186.01/186.01 [3660]E(f335(f294(f928(x36601),f928(x36601)),f164(x36601,x36602)),f164(x36601,f335(f294(x36601,x36601),x36602))) % 186.01/186.01 [3661]E(f335(f196(a924),f31(x36611,x36612)),f335(f335(f86(a927),f335(f196(a924),x36612)),f335(a119,f2(a927)))) % 186.01/186.01 [3663]E(f335(f310(a1,x36631),f335(f335(f86(a1),x36632),f84(a1))),f311(a1,x36631,x36632)) % 186.01/186.01 [3666]E(f335(f335(f42(a1),f335(f85(a1),x36661)),f335(f85(a1),x36662)),f335(f335(f42(a1),x36661),x36662)) % 186.01/186.01 [3674]E(f335(f335(f190(f933(x36741,x36741),a922),f84(a927)),x36742),x36742) % 186.01/186.01 [3676]E(f335(f335(f23(f934(x36761,a922)),x36762),f195(f934(x36761,a922))),x36762) % 186.01/186.01 [3677]E(f335(f335(f108(f934(x36771,a922)),x36772),f250(f934(x36771,a922))),x36772) % 186.01/186.01 [3678]E(f335(f335(f117(f934(x36781,a922)),x36782),f195(f934(x36781,a922))),x36782) % 186.01/186.01 [3679]E(f335(f259(a927,a927),f91(f933(a927,a927),f54(x36791,x36792))),f335(f335(f42(a927),x36791),x36792)) % 186.01/186.01 [3686]E(f311(a1,f335(f335(f86(a1),x36861),f84(a1)),x36862),f313(a1,x36861,x36862)) % 186.01/186.01 [3691]E(f335(f264(a927,a927),f91(f933(a927,a927),f54(x36911,x36912))),f51(a927,x36911,x36912)) % 186.01/186.01 [3701]P1(f335(f335(f337(x37011),x37012),f250(f934(x37011,a922)))) % 186.01/186.01 [3706]E(f335(f335(f23(a927),f335(a119,x37061)),x37062),f335(f41(a927),f311(a927,x37062,x37061))) % 186.01/186.01 [3732]E(f335(f335(f23(f934(x37321,a922)),x37322),f250(f934(x37321,a922))),f195(f934(x37321,a922))) % 186.01/186.01 [3733]E(f335(f335(f108(f934(x37331,a922)),x37332),f195(f934(x37331,a922))),f195(f934(x37331,a922))) % 186.01/186.01 [3734]E(f335(f335(f117(f934(x37341,a922)),x37342),f250(f934(x37341,a922))),f250(f934(x37341,a922))) % 186.01/186.01 [3749]E(f51(a1,f335(f85(a1),x37491),f335(f85(a1),x37492)),f335(f85(a1),f51(a1,x37491,x37492))) % 186.01/186.01 [3750]E(f51(a1,f335(f107(a1),x37501),f335(f107(a1),x37502)),f335(f107(a1),f51(a927,x37501,x37502))) % 186.01/186.01 [3761]E(f335(f196(f928(x37611)),f335(f178(x37611),x37612)),f335(f335(f23(a927),f335(f196(f928(x37611)),x37612)),f84(a927))) % 186.01/186.01 [3787]E(f335(f335(f42(a1),f51(a1,x37871,x37872)),x37872),f2(a1)) % 186.01/186.01 [3796]E(f335(a3,f51(a927,f335(a20,x37961),f335(a20,x37962))),f51(a106,x37961,x37962)) % 186.01/186.01 [3834]E(f335(a3,f335(f335(f23(a927),f335(a20,x38341)),f335(a20,x38342))),f335(f335(f23(a106),x38341),x38342)) % 186.01/186.01 [3835]E(f335(a3,f335(f335(f87(a927),f335(a20,x38351)),f335(a20,x38352))),f335(f335(f87(a106),x38351),x38352)) % 186.01/186.01 [3836]E(f335(a3,f335(f335(f86(a927),f335(a20,x38361)),f335(a20,x38362))),f335(f335(f86(a106),x38361),x38362)) % 186.01/186.01 [3837]E(f335(a3,f335(f335(f42(a927),f335(a20,x38371)),f335(a20,x38372))),f335(f335(f42(a106),x38371),x38372)) % 186.01/186.01 [3845]E(f335(f318(a927,a927,a119),f335(f310(a927,x38451),x38452)),f335(f310(a927,f335(a119,x38451)),f335(a119,x38452))) % 186.01/186.01 [3872]P1(f335(f54(x38721,x38722),f91(f933(a927,a927),f54(x38721,x38722)))) % 186.01/186.01 [3896]E(f335(f335(f86(a927),f335(f335(f86(a927),f30(x38961)),f30(x38962))),f335(a119,f2(a927))),f30(f32(x38961,x38962))) % 186.01/186.01 [3897]E(f51(a927,f335(a119,f51(a927,x38971,x38972)),x38972),f51(a927,f335(a119,x38971),x38972)) % 186.01/186.01 [3909]E(f335(f335(f46(f934(x39091,a922),f934(x39091,a922)),x39092),f5(f934(x39091,a922))),f44(f934(x39091,a922),x39092)) % 186.01/186.01 [3910]E(f335(f335(f45(f934(x39101,a922),f934(x39101,a922)),x39102),f5(f934(x39101,a922))),f43(f934(x39101,a922),x39102)) % 186.01/186.01 [3911]E(f335(f318(f928(x39111),f934(x39111,a922),f179(x39111)),f335(f179(f928(x39111)),f60(x39111,x39112))),f335(f316(x39111),f335(f179(x39111),x39112))) % 186.01/186.01 [3915]P1(f335(f335(f337(f934(x39151,a922)),x39152),f335(f316(x39151),x39152))) % 186.01/186.01 [3921]E(f51(a1,f335(f85(a1),f51(a1,x39211,x39212)),x39212),f51(a1,f335(f85(a1),x39211),x39212)) % 186.01/186.01 [3932]P1(f335(f335(f243(f934(x39321,a922)),x39322),f250(f934(x39321,a922)))) % 186.01/186.01 [3934]E(f335(f335(f297(x39341,x39341,x39341),f315(x39341,x39342)),f315(x39341,f315(x39341,x39342))),f315(x39341,x39342)) % 186.01/186.01 [3935]E(f335(f335(f117(f934(x39351,a922)),f335(f272(x39351,x39351),x39352)),f335(f292(x39351,x39351),x39352)),f335(f289(x39351),x39352)) % 186.01/186.01 [3956]E(f321(x39561,x39562,f250(f934(x39561,a922)),f250(f934(x39562,a922))),f250(f934(f935(x39561,x39562),a922))) % 186.01/186.01 [4007]P1(f335(f335(f243(a927),f51(a927,x40071,x40072)),x40071)) % 186.01/186.01 [4032]P1(f335(f335(f243(a1),f335(f85(a1),f335(f107(a1),x40321))),f335(f107(a1),x40322))) % 186.01/186.01 [4057]P1(f335(f335(f337(f934(x40571,a922)),f195(f934(x40571,a922))),f335(f316(x40571),x40572))) % 186.01/186.01 [4062]E(f315(x40621,f335(f335(f297(x40621,x40621,x40621),x40622),f315(x40621,x40622))),f315(x40621,x40622)) % 186.01/186.01 [4065]E(f335(f335(f297(x40651,x40651,x40651),f315(x40651,x40652)),x40652),f335(f335(f297(x40651,x40651,x40651),x40652),f315(x40651,x40652))) % 186.01/186.01 [4067]E(f335(a111,f335(f335(f86(a1),f335(f335(f23(a1),x40671),x40672)),f84(a1))),f335(f41(a1),f311(a1,x40672,x40671))) % 186.01/186.01 [4082]E(f335(f292(x40821,x40821),f335(f335(f297(x40821,x40821,x40821),x40822),f315(x40821,x40822))),f335(f292(x40821,x40821),x40822)) % 186.01/186.01 [4083]E(f335(f272(x40831,x40831),f335(f335(f297(x40831,x40831,x40831),x40832),f315(x40831,x40832))),f335(f272(x40831,x40831),x40832)) % 186.01/186.01 [4099]E(f335(f335(f86(a927),f335(f335(f86(a927),f335(f196(a924),x40991)),f335(f196(a924),x40992))),f335(a119,f2(a927))),f335(f196(a924),f32(x40991,x40992))) % 186.01/186.01 [4102]E(f335(f149(f928(x41021),f928(x41021),f141(x41021),f120(x41021)),f176(f928(x41021),x41022,f120(x41021))),f120(x41021)) % 186.01/186.01 [4111]P26(a927,a927,f335(f335(f7(a927,a927,a927),f86(a927)),x41111),x41112) % 186.01/186.01 [4113]P14(a927,f335(f175(a927),f335(f335(f161(f928(x41131),a927),f196(f928(x41131))),f186(x41131,x41132)))) % 186.01/186.01 [4146]P53(x41461,f335(f335(f108(f934(f933(x41461,x41461),a922)),x41462),f335(f294(x41461,x41461),x41462))) % 186.01/186.01 [4147]P53(x41471,f335(f335(f117(f934(f933(x41471,x41471),a922)),x41472),f335(f294(x41471,x41471),x41472))) % 186.01/186.01 [4158]P1(f335(f335(f244(a1),f335(f85(a1),f335(f107(a1),f335(a119,x41581)))),f335(f107(a1),x41582))) % 186.01/186.01 [4203]E(f335(f149(f928(x42031),x42031,f335(f7(x42031,f928(x42031),f928(x42031)),f158(x42031)),f120(x42031)),x42032),f335(f175(x42031),x42032)) % 186.01/186.01 [4252]P1(f335(f335(f243(f934(f933(f928(x42521),f928(x42521)),a922)),f165(x42521,x42522)),f315(f928(x42521),f164(x42521,x42522)))) % 186.01/186.01 [4281]P1(f335(f54(x42811,x42812),f335(f335(f260(a927,a927),f335(f335(f42(a927),x42811),x42812)),f51(a927,x42811,x42812)))) % 186.01/186.01 [4293]P1(f335(f335(f243(f934(f933(f928(x42931),f928(x42931)),a922)),f164(x42931,f315(x42931,x42932))),f315(f928(x42931),f164(x42931,x42932)))) % 186.01/186.01 [4511]E(f335(f335(f267(f933(a106,a106),a106,f933(a106,a106),f933(x45111,f933(a106,a106))),f275(f335(f172(a106),f335(f335(f161(f933(a106,x45111),a106),f259(a106,x45111)),x45112)))),f335(f335(f8(x45111,f934(f933(a106,a106),f933(x45111,f933(a106,a106))),a106),f260(x45111,f933(a106,a106))),f276(x45111,x45112))),f274(x45111,x45112)) % 186.01/186.01 [4588]E(f232(a927,f933(x45881,f929(x45881)),f2(a927),f335(f265(x45881,f929(x45881),a927),f335(f16(f934(f929(x45881),a927),x45881),f335(f335(f7(f929(x45881),a927,a927),f335(f335(f8(a927,f934(a927,a927),f929(x45881)),f86(a927)),f196(f929(x45881)))),f84(a927)))),f335(f142(x45881),x45882)),f335(f196(f929(x45881)),x45882)) % 186.01/186.01 [4696]E(f335(f265(f934(f933(x46961,x46961),a922),f934(f933(x46961,x46961),a922),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f335(f335(f7(f934(f933(x46961,x46961),a922),f934(f934(f933(x46961,x46961),a922),f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922))),f934(f934(f933(x46961,x46961),a922),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922))))),f335(f335(f8(f934(f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922)),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f934(f934(f934(f933(x46961,x46961),a922),f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922))),f934(f934(f933(x46961,x46961),a922),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922))))),f934(f933(x46961,x46961),a922)),f8(f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922)),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922))),f934(f933(x46961,x46961),a922))),f335(f335(f8(f934(f934(x46962,x46961),f934(f934(f933(x46962,x46962),a922),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f934(f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922)),f934(f934(x46962,x46961),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f934(f933(x46961,x46961),a922)),f18(f934(x46962,x46961),f934(f933(x46962,x46962),a922),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f335(f335(f8(f934(f934(x46962,x46961),f934(f933(x46962,x46962),a922)),f934(f934(x46962,x46961),f934(f934(f933(x46962,x46962),a922),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f934(f933(x46961,x46961),a922)),f335(f8(f934(f933(x46962,x46962),a922),f934(f934(f933(x46962,x46962),a922),f933(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922))),f934(x46962,x46961)),f260(f934(f933(x46962,x46962),a922),f934(f933(x46962,x46962),a922)))),f296(x46961,x46962))))),f296(x46961,x46962))),f79(x46961,x46962)) % 186.01/186.01 [4771]~E(f335(f316(x47711),x47712),f195(f934(f934(x47711,a922),a922))) % 186.01/186.01 [4782]~P1(f335(f335(f179(x47821),f120(x47821)),x47822)) % 186.01/186.01 [4786]~P1(f335(f335(f337(x47861),x47862),f195(f934(x47861,a922)))) % 186.01/186.01 [4794]~P1(f335(f335(f244(f934(x47941,a922)),x47942),f195(f934(x47941,a922)))) % 186.01/186.01 [3614]E(f335(f335(f23(a927),x36141),f335(f335(f86(a927),x36141),x36142)),f2(a927)) % 186.01/186.01 [3617]E(f335(f335(f108(f934(x36171,a922)),x36172),x36172),x36172) % 186.01/186.01 [3618]E(f335(f335(f117(f934(x36181,a922)),x36182),x36182),x36182) % 186.01/186.01 [3646]E(f335(f335(f23(f934(x36461,a922)),x36462),x36462),f195(f934(x36461,a922))) % 186.01/186.01 [3649]E(f335(f150(x36491,x36492),f2(a927)),f195(f934(f933(f928(x36491),f928(x36491)),a922))) % 186.01/186.01 [3650]E(f335(f335(f86(a927),x36501),f335(a119,x36502)),f335(a119,f335(f335(f86(a927),x36501),x36502))) % 186.01/186.01 [3662]E(f201(f335(f107(a1),x36621),f335(f107(a1),x36622)),f335(f107(a1),f335(f335(f23(a927),x36621),x36622))) % 186.01/186.01 [3665]E(f335(f335(f42(a1),f335(f85(a1),x36651)),x36652),f335(f335(f42(a1),x36651),f335(f85(a1),x36652))) % 186.01/186.01 [3669]E(f335(f41(a1),f335(f310(a1,x36691),x36692)),f335(a111,f335(f335(f23(a1),x36692),x36691))) % 186.01/186.01 [3672]E(f335(f335(f86(a927),f335(a119,x36721)),x36722),f335(a119,f335(f335(f86(a927),x36721),x36722))) % 186.01/186.01 [3675]E(f335(f85(f934(x36751,a922)),f335(f85(f934(x36751,a922)),x36752)),x36752) % 186.01/186.01 [3688]E(f186(x36881,f335(f335(f158(f928(x36881)),f120(x36881)),x36882)),f186(x36881,x36882)) % 186.01/186.01 [3692]E(f335(f335(f86(a927),x36921),f335(f335(f87(a927),x36921),x36922)),f335(f335(f87(a927),x36921),f335(a119,x36922))) % 186.01/186.01 [3699]E(f335(f335(a24,f335(a3,x36991)),f335(a3,x36992)),f335(a3,f335(f335(f23(a927),x36991),x36992))) % 186.01/186.01 [3714]E(f335(f335(f87(a1),f335(f85(a1),x37141)),x37142),f335(f85(a1),f335(f335(f87(a1),x37141),x37142))) % 186.01/186.01 [3716]E(f335(f335(f252(a1),f335(f107(a1),x37161)),x37162),f335(f107(a1),f335(f335(f252(a927),x37161),x37162))) % 186.01/186.01 [3717]E(f335(f335(f87(a106),f335(a3,x37171)),f335(a3,x37172)),f335(a3,f335(f335(f87(a927),x37171),x37172))) % 186.01/186.01 [3718]E(f335(f335(f86(a106),f335(a3,x37181)),f335(a3,x37182)),f335(a3,f335(f335(f86(a927),x37181),x37182))) % 186.01/186.01 [3719]E(f335(f335(f241(a927),f335(a119,x37191)),f335(a119,x37192)),f335(a119,f335(f335(f241(a927),x37191),x37192))) % 186.01/186.01 [3720]E(f335(f335(f242(a927),f335(a119,x37201)),f335(a119,x37202)),f335(a119,f335(f335(f242(a927),x37201),x37202))) % 186.01/186.01 [3725]E(f335(f179(a927),f146(a927,f335(f310(a927,x37251),x37252))),f335(f310(a927,x37251),x37252)) % 186.01/186.01 [3726]E(f320(x37261,f335(f335(f317(x37261),x37262),f195(f934(x37261,a922)))),x37262) % 186.01/186.01 [3730]E(f335(f292(x37301,x37302),f195(f934(f933(x37301,x37302),a922))),f195(f934(x37302,a922))) % 186.01/186.01 [3731]E(f335(f272(x37311,x37312),f195(f934(f933(x37311,x37312),a922))),f195(f934(x37311,a922))) % 186.01/186.01 [3735]E(f335(a111,f335(f335(f23(a1),x37351),x37352)),f335(f41(a1),f313(a1,x37352,x37351))) % 186.01/186.01 [3740]E(f335(f335(f86(a927),x37401),f335(f335(f87(a927),x37402),x37401)),f335(f335(f87(a927),f335(a119,x37402)),x37401)) % 186.01/186.01 [3742]E(f335(f335(f66(x37421),f195(f934(x37421,a922))),x37422),f195(f934(f934(x37421,a922),a922))) % 186.01/186.01 [3751]E(f335(f196(f928(a927)),f146(a927,f335(f310(a927,x37511),x37512))),f335(f335(f23(a927),x37512),x37511)) % 186.01/186.01 [3766]E(f335(f335(f108(f934(x37661,a922)),f250(f934(x37661,a922))),x37662),x37662) % 186.01/186.01 [3767]E(f335(f335(f117(f934(x37671,a922)),f195(f934(x37671,a922))),x37672),x37672) % 186.01/186.01 [3768]E(f335(f335(f86(a1),f335(f85(a1),x37681)),f335(f85(a1),x37682)),f335(f85(a1),f335(f335(f86(a1),x37681),x37682))) % 186.01/186.01 [3773]E(f335(f335(f87(a1),f335(f107(a1),x37731)),f335(f107(a1),x37732)),f335(f107(a1),f335(f335(f87(a927),x37731),x37732))) % 186.01/186.01 [3774]E(f335(f335(f87(a1),f335(f110(a1),x37741)),f335(f110(a1),x37742)),f335(f110(a1),f335(f335(f87(a1),x37741),x37742))) % 186.01/186.01 [3776]E(f335(f335(f86(a1),f335(f107(a1),x37761)),f335(f107(a1),x37762)),f335(f107(a1),f335(f335(f86(a927),x37761),x37762))) % 186.01/186.01 [3777]E(f335(f335(f86(a1),f335(f110(a1),x37771)),f335(f110(a1),x37772)),f335(f110(a1),f335(f335(f86(a1),x37771),x37772))) % 186.01/186.01 [3778]E(f335(f335(f42(a1),f335(f107(a1),x37781)),f335(f107(a1),x37782)),f335(f107(a1),f335(f335(f42(a927),x37781),x37782))) % 186.01/186.01 [3797]E(f335(f335(f6(x37971,a927),f335(f16(a927,x37971),f84(a927))),x37972),f335(f41(x37971),x37972)) % 186.01/186.01 [3807]E(f335(f85(a1),f51(a1,f335(f85(a1),x38071),x38072)),f51(a1,x38071,f335(f85(a1),x38072))) % 186.01/186.01 [3809]E(f335(f179(a1),f185(x38091,f335(f335(f23(a1),x38092),f84(a1)))),f335(f310(a1,x38091),x38092)) % 186.01/186.01 [3814]P1(f335(f335(f243(a927),x38141),f335(f335(f86(a927),x38142),x38141))) % 186.01/186.01 [3815]P1(f335(f335(f243(a927),x38151),f335(f335(f86(a927),x38151),x38152))) % 186.01/186.01 [3817]E(f335(f335(f23(f934(x38171,a922)),f195(f934(x38171,a922))),x38172),f195(f934(x38171,a922))) % 186.01/186.01 [3818]E(f335(f335(f108(f934(x38181,a922)),f195(f934(x38181,a922))),x38182),f195(f934(x38181,a922))) % 186.01/186.01 [3819]E(f335(f335(f117(f934(x38191,a922)),f250(f934(x38191,a922))),x38192),f250(f934(x38191,a922))) % 186.01/186.01 [3826]E(f335(f335(f260(a1,a1),x38261),f335(f85(a1),x38262)),f335(a57,f335(f335(f260(a1,a1),x38261),x38262))) % 186.01/186.01 [3827]E(f335(f310(a1,f335(f335(f86(a1),x38271),f84(a1))),x38272),f314(a1,x38271,x38272)) % 186.01/186.01 [3838]E(f335(f335(f87(a927),x38381),f335(f335(f42(a927),x38382),x38381)),f335(f335(f23(a927),x38382),f51(a927,x38382,x38381))) % 186.01/186.01 [3839]E(f335(f335(f87(a1),x38391),f335(f335(f42(a1),x38392),x38391)),f335(f335(f23(a1),x38392),f51(a1,x38392,x38391))) % 186.01/186.01 [3842]E(f335(f179(a1),f185(f335(f335(f86(a1),x38421),f84(a1)),x38422)),f313(a1,x38421,x38422)) % 186.01/186.01 [3846]P1(f335(f335(f243(f934(x38461,a922)),x38462),x38462)) % 186.01/186.01 [3849]E(f335(f335(f108(f934(x38491,a922)),x38492),f335(f85(f934(x38491,a922)),x38492)),f195(f934(x38491,a922))) % 186.01/186.01 [3850]E(f335(f335(f117(f934(x38501,a922)),x38502),f335(f85(f934(x38501,a922)),x38502)),f250(f934(x38501,a922))) % 186.01/186.01 [3858]E(f335(f335(f23(a927),f335(f335(f23(a927),x38581),f84(a927))),x38582),f335(f335(f23(a927),x38581),f335(a119,x38582))) % 186.01/186.01 [3864]E(f335(f335(f23(f934(x38641,a922)),f250(f934(x38641,a922))),x38642),f335(f85(f934(x38641,a922)),x38642)) % 186.01/186.01 [3865]E(f335(f335(f23(a1),f335(f110(a1),x38651)),f335(f110(a1),x38652)),f335(f110(a1),f335(f335(f86(a1),x38651),f335(f85(a1),x38652)))) % 186.01/186.01 [3878]E(f335(f179(a927),f146(a927,f335(f310(a927,x38781),f335(a119,x38782)))),f311(a927,x38781,x38782)) % 186.01/186.01 [3894]E(f335(f196(f928(f928(x38941))),f60(x38941,x38942)),f335(f335(f252(a927),f335(a119,f335(a119,f2(a927)))),f335(f196(f928(x38941)),x38942))) % 186.01/186.01 [3913]E(f335(f335(f190(f933(x39131,x39131),a922),f2(a927)),x39132),f315(x39131,f195(f934(f933(x39131,x39131),a922)))) % 186.01/186.01 [3917]P1(f335(f144(a927),f146(a927,f335(f310(a927,x39171),x39172)))) % 186.01/186.01 [3933]E(f335(f318(a1,a927,a111),f311(a1,f335(f107(a1),x39331),f335(f107(a1),x39332))),f311(a927,x39331,x39332)) % 186.01/186.01 [3942]E(f192(a927,f2(a927),f5(a927),f335(f335(f23(a927),x39421),x39422)),f335(f335(f23(a927),x39421),f335(a119,x39422))) % 186.01/186.01 [3943]E(f335(a111,f335(f335(f23(a1),x39431),f335(f335(f86(a1),x39432),f84(a1)))),f335(f41(a1),f314(a1,x39432,x39431))) % 186.01/186.01 [3979]E(f335(f335(f161(a927,a927),a119),f146(a927,f335(f310(a927,x39791),x39792))),f146(a927,f335(f310(a927,f335(a119,x39791)),f335(a119,x39792)))) % 186.01/186.01 [3987]E(f335(f179(a1),f185(f335(f335(f86(a1),x39871),f84(a1)),f335(f335(f23(a1),x39872),f84(a1)))),f314(a1,x39871,x39872)) % 186.01/186.01 [3999]P1(f335(f335(f243(f934(x39991,a922)),f195(f934(x39991,a922))),x39992)) % 186.01/186.01 [4003]E(f91(x40031,f335(f335(f7(x40031,x40031,a922),a332),x40032)),x40032) % 186.01/186.01 [4004]E(f96(x40041,f335(f335(f7(x40041,x40041,a922),a332),x40042)),x40042) % 186.01/186.01 [4008]E(f335(f179(a927),f146(a927,f335(f310(a927,f335(a119,x40081)),f335(a119,x40082)))),f313(a927,x40081,x40082)) % 186.01/186.01 [4035]E(f335(f335(f262(x40351,x40352),f250(f934(x40351,a922))),f335(f16(f934(x40352,a922),x40351),f250(f934(x40352,a922)))),f250(f934(f933(x40351,x40352),a922))) % 186.01/186.01 [4069]E(f335(f270(x40691),f335(f335(f8(a922,a922,x40691),a330),x40692)),f335(f85(f934(x40691,a922)),f335(f270(x40691),x40692))) % 186.01/186.01 [4072]E(f335(f270(x40721),f335(f335(f7(x40721,x40721,a922),a332),x40722)),f335(f335(f317(x40721),x40722),f195(f934(x40721,a922)))) % 186.01/186.01 [4079]E(f335(f335(f86(a1),f335(f335(f23(a1),x40791),x40792)),f335(f335(f23(a1),x40791),x40792)),f335(f335(f23(a1),f335(f335(f86(a1),x40791),x40791)),f335(f335(f86(a1),x40792),x40792))) % 186.01/186.01 [4080]E(f335(f335(f86(a1),f335(f335(f86(a1),x40801),x40801)),f335(f335(f86(a1),x40802),x40802)),f335(f335(f86(a1),f335(f335(f86(a1),x40801),x40802)),f335(f335(f86(a1),x40801),x40802))) % 186.01/186.01 [4096]P1(f335(f335(f243(a927),f335(f41(x40961),f335(f179(x40961),x40962))),f335(f196(f928(x40961)),x40962))) % 186.01/186.01 [4097]P1(f335(f335(f243(a927),f335(f196(f928(x40971)),f159(x40971,x40972))),f335(f196(f928(x40971)),x40972))) % 186.01/186.01 [4108]E(f335(f270(x41081),f335(f335(f7(x41081,f934(x41081,a922),a922),f337(x41081)),x41082)),x41082) % 186.01/186.01 [4122]E(f335(f335(f182(x41221),f335(f335(f23(a927),f335(f196(f928(x41221)),x41222)),f84(a927))),x41222),f121(x41221,x41222)) % 186.01/186.01 [4145]E(f192(a927,f2(a927),f335(f335(f8(a927,a927,a927),a119),f335(f241(a927),x41451)),x41452),f335(f335(f241(a927),f335(a119,x41451)),x41452)) % 186.01/186.01 [4150]E(f43(f934(x41501,a922),f335(f318(f934(f933(x41501,x41501),a922),f934(x41501,a922),f289(x41501)),x41502)),f335(f289(x41501),f43(f934(f933(x41501,x41501),a922),x41502))) % 186.01/186.01 [4151]E(f192(a927,f335(a119,x41511),f335(f335(f8(a927,a927,a927),a119),f335(f242(a927),x41511)),x41512),f335(f335(f242(a927),f335(a119,x41511)),x41512)) % 186.01/186.01 [4153]E(f335(f335(f260(a1,a1),f335(f335(f42(a1),f335(f81(a1),x41531)),f335(f81(a1),x41532))),f51(a1,f335(f81(a1),x41531),f335(f81(a1),x41532))),f59(x41531,x41532)) % 186.01/186.01 [4176]P1(f335(f335(f243(f934(f934(x41761,a922),a922)),x41762),f335(f316(x41761),f43(f934(x41761,a922),x41762)))) % 186.01/186.01 [4208]E(f335(f335(f45(x42081,f934(x42081,a922)),x42082),f335(f335(f7(x42081,f934(x42081,a922),f934(x42081,a922)),f317(x42081)),f195(f934(x42081,a922)))),x42082) % 186.01/186.01 [4209]E(f335(f335(f297(x42091,x42091,x42091),f335(f294(x42091,x42091),x42092)),f315(x42091,f335(f294(x42091,x42091),x42092))),f335(f294(x42091,x42091),f335(f335(f297(x42091,x42091,x42091),x42092),f315(x42091,x42092)))) % 186.01/186.01 [4273]E(f335(f179(x42731),f335(f149(f928(x42731),f928(x42731),f141(x42731),f120(x42731)),x42732)),f335(f335(f45(f928(x42731),f934(x42731,a922)),f335(f179(f928(x42731)),x42732)),f179(x42731))) % 186.01/186.01 [4304]E(f335(f335(f117(f934(f933(x43041,x43041),a922)),f315(x43041,f195(f934(f933(x43041,x43041),a922)))),f335(f335(f297(x43041,x43041,x43041),f315(x43041,x43042)),x43042)),f315(x43041,x43042)) % 186.01/186.01 [4340]E(f335(f335(f188(x43401,x43401),x43402),x43402),f335(f335(f161(x43401,f933(x43401,x43401)),f335(f335(f18(x43401,x43401,f933(x43401,x43401)),f260(x43401,x43401)),f5(x43401))),x43402)) % 186.01/186.01 [4453]E(f335(f149(a927,f928(x44531),f335(f7(f928(x44531),a927,a927),f335(f335(f8(a927,f934(a927,a927),f928(x44531)),f242(a927)),f196(f928(x44531)))),f2(a927)),f335(f175(f928(x44531)),x44532)),f335(f196(f928(f928(x44531))),f186(x44531,x44532))) % 186.01/186.01 [4525]E(f335(f335(f296(f933(a927,f928(x45251)),f928(x45251)),f328(a927,f928(x45251),a248,f152(x45251,x45252))),f335(f335(f18(f928(x45251),f928(x45251),f933(a927,f928(x45251))),f335(f335(f8(a927,f934(f928(x45251),f933(a927,f928(x45251))),f928(x45251)),f260(a927,f928(x45251))),f196(f928(x45251)))),f5(f928(x45251)))),f153(x45251,x45252)) % 186.01/186.01 [4652]E(f335(f270(x46521),f335(f335(f8(f934(f934(x46521,a922),a922),a922,x46521),f94(f934(x46521,a922))),f335(f335(f8(f934(f934(x46521,a922),a922),f934(f934(x46521,a922),a922),x46521),f335(f18(f934(x46521,a922),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x46521,a922)),a338),f335(f335(f7(f934(x46521,a922),f934(f934(x46521,a922),a922),a922),f337(f934(x46521,a922))),x46522)))),f337(x46521)))),f44(f934(x46521,a922),x46522)) % 186.01/186.01 [4653]E(f335(f270(x46531),f335(f335(f8(f934(f934(x46531,a922),a922),a922,x46531),f93(f934(x46531,a922))),f335(f335(f8(f934(f934(x46531,a922),a922),f934(f934(x46531,a922),a922),x46531),f335(f18(f934(x46531,a922),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x46531,a922)),a333),f335(f335(f7(f934(x46531,a922),f934(f934(x46531,a922),a922),a922),f337(f934(x46531,a922))),x46532)))),f337(x46531)))),f43(f934(x46531,a922),x46532)) % 186.01/186.01 [4795]~P1(f335(f335(f244(a1),f335(f107(a1),x47951)),f335(f85(a1),f335(f107(a1),x47952)))) % 186.01/186.01 [3738]E(f335(f335(f23(a927),f335(f335(f86(a927),x37381),x37382)),x37382),x37381) % 186.01/186.01 [3739]E(f335(f335(f23(a927),f335(f335(f86(a927),x37391),x37392)),x37391),x37392) % 186.01/186.01 [3808]E(f335(f335(f86(a927),f335(f335(f23(a927),x38081),x38082)),x38082),f335(f335(f242(a927),x38081),x38082)) % 186.01/186.01 [3920]E(f335(f335(f87(a927),f335(f335(f42(a927),x39201),x39202)),x39202),f335(f335(f23(a927),x39201),f51(a927,x39201,x39202))) % 186.01/186.01 [3947]E(f335(f179(a927),f146(a927,f335(f310(a927,f335(a119,x39471)),x39472))),f314(a927,x39471,x39472)) % 186.01/186.01 [3955]E(f335(f107(a1),f225(f335(a111,f335(f81(a1),x39551)),f335(a111,f335(f81(a1),x39552)))),f335(f335(a226,x39551),x39552)) % 186.01/186.01 [3957]E(f335(f335(f108(f934(x39571,a922)),f335(f85(f934(x39571,a922)),x39572)),x39572),f195(f934(x39571,a922))) % 186.01/186.01 [3958]E(f335(f335(f117(f934(x39581,a922)),f335(f85(f934(x39581,a922)),x39582)),x39582),f250(f934(x39581,a922))) % 186.01/186.01 [3975]P1(f335(f335(f243(a927),f335(f335(f23(a927),x39751),x39752)),x39751)) % 186.01/186.01 [3976]P1(f335(f335(f243(a927),f335(f335(f42(a927),x39761),x39762)),x39761)) % 186.01/186.01 [4000]P1(f335(f335(f244(a927),x40001),f335(a119,f335(f335(f86(a927),x40002),x40001)))) % 186.01/186.01 [4001]P1(f335(f335(f244(a927),x40011),f335(a119,f335(f335(f86(a927),x40011),x40012)))) % 186.01/186.01 [4019]E(f335(f335(f87(a927),f335(a111,f335(f81(a1),x40191))),f335(a111,f335(f81(a1),x40192))),f335(a111,f335(f81(a1),f335(f335(f87(a1),x40191),x40192)))) % 186.01/186.01 [4031]P1(f335(f335(f243(a1),f2(a1)),f335(f335(f252(a1),f335(f81(a1),x40311)),x40312))) % 186.01/186.01 [4101]E(f335(f293(f928(x41011),f928(x41011),f165(x41011,x41012)),f335(f335(f317(f928(x41011)),f120(x41011)),f195(f934(f928(x41011),a922)))),f335(f335(f317(f928(x41011)),f120(x41011)),f195(f934(f928(x41011),a922)))) % 186.01/186.01 [4120]E(f335(f335(f117(f934(f933(x41201,x41201),a922)),f315(x41201,x41202)),f315(x41201,f195(f934(f933(x41201,x41201),a922)))),f315(x41201,x41202)) % 186.01/186.01 [4133]E(f335(f335(f42(a1),f335(f110(a1),f335(f335(f86(a1),x41331),x41331))),f335(f110(a1),f335(f335(f86(a1),x41332),x41332))),f335(f335(f42(a1),f335(f110(a1),x41331)),f335(f110(a1),x41332))) % 186.01/186.01 [4198]E(f335(f335(f252(a1),x41981),f335(f110(a927),f335(f335(f86(a1),x41982),x41982))),f335(f335(f92(a1,a1),f335(f335(f252(a1),x41981),f335(f110(a927),x41982))),f335(f335(f18(a1,a1,a1),f87(a1)),f5(a1)))) % 186.01/186.01 [4204]E(f335(f270(f934(x42041,a922)),f335(f335(f7(f934(x42041,a922),f934(x42041,a922),a922),f243(f934(x42041,a922))),x42042)),f335(f316(x42041),x42042)) % 186.01/186.01 [4220]E(f335(f335(f161(a1,a927),a111),f335(f335(f141(a1),f335(f335(f161(a927,a1),f107(a1)),x42201)),f335(f335(f161(a927,a1),f107(a1)),x42202))),f335(f335(f141(a927),x42201),x42202)) % 186.01/186.01 [4251]E(f335(f318(a1,a1,f335(f335(f7(a1,a1,a1),f86(a1)),x42511)),f335(f310(a1,f2(a1)),f335(f335(f23(a1),x42512),x42511))),f335(f310(a1,x42511),x42512)) % 186.01/186.01 [4253]P55(x42531,f335(f335(f23(f934(f933(x42531,x42531),a922)),x42532),f315(x42531,f195(f934(f933(x42531,x42531),a922))))) % 186.01/186.01 [4271]E(f335(f196(f928(x42711)),f335(f149(f928(x42711),f928(x42711),f141(x42711),f120(x42711)),x42712)),f335(f172(a927),f335(f335(f161(f928(x42711),a927),f196(f928(x42711))),x42712))) % 186.01/186.01 [4275]P54(x42751,f250(f934(x42751,a922)),f335(f335(f117(f934(f933(x42751,x42751),a922)),x42752),f315(x42751,f195(f934(f933(x42751,x42751),a922))))) % 186.01/186.01 [4320]E(f192(a927,f2(a927),f335(f335(f8(a927,a927,a927),a119),f335(f335(f7(a927,a927,a927),f241(a927)),x43201)),x43202),f335(f335(f241(a927),x43202),f335(a119,x43201))) % 186.01/186.01 [4323]E(f192(a927,f335(a119,x43231),f335(f335(f8(a927,a927,a927),a119),f335(f335(f7(a927,a927,a927),f242(a927)),x43231)),x43232),f335(f335(f242(a927),x43232),f335(a119,x43231))) % 186.01/186.01 [4326]E(f335(f318(x43261,f928(x43261),f335(f335(f7(x43261,f928(x43261),f928(x43261)),f158(x43261)),f120(x43261))),x43262),f181(x43261,x43262,f335(f335(f317(f928(x43261)),f120(x43261)),f195(f934(f928(x43261),a922))))) % 186.01/186.01 [4328]E(f335(f335(f117(f934(f933(x43281,x43281),a922)),f335(f335(f297(x43281,x43281,x43281),x43282),f315(x43281,x43282))),f315(x43281,f195(f934(f933(x43281,x43281),a922)))),f315(x43281,x43282)) % 186.01/186.01 [4335]P1(f335(f335(f243(f934(f933(x43351,x43351),a922)),f271(x43351,x43352)),f335(f335(f262(x43351,x43351),x43352),f335(f16(f934(x43351,a922),x43351),x43352)))) % 186.01/186.01 [4338]E(f335(f318(a1,a927,a111),f335(f335(f108(f934(a1,a922)),f335(f318(a927,a1,f107(a1)),x43381)),f335(f318(a927,a1,f107(a1)),x43382))),f335(f335(f108(f934(a927,a922)),x43381),x43382)) % 186.01/186.01 [4339]E(f335(f318(a1,a927,a111),f335(f335(f117(f934(a1,a922)),f335(f318(a927,a1,f107(a1)),x43391)),f335(f318(a927,a1,f107(a1)),x43392))),f335(f335(f117(f934(a927,a922)),x43391),x43392)) % 186.01/186.01 [4342]E(f335(f270(x43421),f335(f335(f8(a922,a922,x43421),a330),f335(f335(f7(x43421,f934(x43421,a922),a922),f337(x43421)),x43422))),f335(f85(f934(x43421,a922)),x43422)) % 186.01/186.01 [4369]E(f335(f149(f928(x43691),f928(x43691),f141(x43691),f120(x43691)),f335(f335(f161(f928(x43691),f928(x43691)),f175(x43691)),f335(f175(f928(x43691)),x43692))),f335(f175(x43691),f335(f149(f928(x43691),f928(x43691),f141(x43691),f120(x43691)),x43692))) % 186.01/186.01 [4397]E(f335(f335(f45(a927,f934(f933(x43971,x43971),a922)),f250(f934(a927,a922))),f335(f335(f7(a927,f934(f933(x43971,x43971),a922),f934(f933(x43971,x43971),a922)),f190(f933(x43971,x43971),a922)),x43972)),f315(x43971,x43972)) % 186.01/186.01 [4415]E(f91(x44151,f335(f335(f8(f934(x44151,a922),a922,x44151),f335(a332,x44152)),f335(f335(f7(x44151,f934(x44151,a922),f934(x44151,a922)),f317(x44151)),f195(f934(x44151,a922))))),f320(x44151,x44152)) % 186.01/186.01 [4423]E(f335(f196(f928(x44231)),f159(x44231,f335(f149(f928(x44231),f928(x44231),f141(x44231),f120(x44231)),x44232))),f335(f41(x44231),f335(f335(f45(f928(x44231),f934(x44231,a922)),f335(f179(f928(x44231)),x44232)),f179(x44231)))) % 186.01/186.01 [4437]E(f335(f335(f117(f934(f933(x44371,x44371),a922)),x44372),f335(f335(f297(x44371,x44371,x44371),f335(f335(f297(x44371,x44371,x44371),x44372),f315(x44371,x44372))),x44372)),f335(f335(f297(x44371,x44371,x44371),x44372),f315(x44371,x44372))) % 186.01/186.01 [4461]P1(f335(f335(f243(f934(f933(x44611,x44611),a922)),f335(f335(f297(x44611,x44611,x44611),x44612),f315(x44611,x44612))),f335(f335(f262(x44611,x44611),f335(f289(x44611),x44612)),f335(f16(f934(x44611,a922),x44611),f335(f289(x44611),x44612))))) % 186.01/186.01 [4502]E(f335(f270(f928(x45021)),f335(f335(f7(f928(x45021),f934(x45021,a922),a922),f335(f335(f8(f934(x45021,a922),f934(f934(x45021,a922),a922),f928(x45021)),f243(f934(x45021,a922))),f179(x45021))),x45022)),f168(x45021,x45022)) % 186.01/186.01 [4513]E(f335(f163(f928(x45131),x45131,f120(x45131),f335(f335(f8(f928(x45131),f934(f928(x45131),f928(x45131)),x45131),f335(f7(f928(x45131),f928(x45131),f928(x45131)),f141(x45131))),f335(f335(f7(x45131,f928(x45131),f928(x45131)),f158(x45131)),f120(x45131)))),x45132),f335(f174(x45131),x45132)) % 186.01/186.01 [4553]P26(f934(x45531,x45532),f934(f933(x45531,x45532),a922),f335(f335(f8(f934(f933(x45531,x45532),a922),f934(f933(x45531,x45532),a922),f934(x45531,x45532)),f270(f933(x45531,x45532))),f335(f335(f8(f934(x45531,f934(x45532,a922)),f934(f933(x45531,x45532),a922),f934(x45531,x45532)),f265(x45531,x45532,a922)),f335(f8(x45532,f934(x45532,a922),x45531),f335(f7(x45532,x45532,a922),a332)))),f250(f934(f934(x45531,x45532),a922))) % 186.01/186.01 [4558]E(f51(a1,f335(f110(a1),f335(f335(f86(a1),x45581),x45581)),f335(f110(a1),f335(f335(f86(a1),x45582),x45582))),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a1,f335(f110(a1),x45581),f335(f110(a1),x45582)))) % 186.01/186.01 [4602]E(f335(f335(f45(x46021,f934(f933(x46021,x46021),a922)),x46022),f335(f335(f7(x46021,f934(f933(x46021,x46021),a922),f934(f933(x46021,x46021),a922)),f335(f335(f8(f933(x46021,x46021),f934(f934(f933(x46021,x46021),a922),f934(f933(x46021,x46021),a922)),x46021),f317(f933(x46021,x46021))),f335(f335(f18(x46021,x46021,f933(x46021,x46021)),f260(x46021,x46021)),f5(x46021)))),f195(f934(f933(x46021,x46021),a922)))),f271(x46021,x46022)) % 186.01/186.01 [4610]E(f211(x46101,f335(f335(f260(a1,a1),f335(f85(a1),f335(f335(f78(f933(a1,a1),a1,x46101,f259(a1,a1)),f221(x46101)),x46102))),f335(f335(f78(f933(a1,a1),a1,x46101,f264(a1,a1)),f221(x46101)),x46102))),f236(x46101,x46102)) % 186.01/186.01 [4693]E(f335(f270(f934(x46931,a922)),f335(f335(f8(f934(f934(x46931,a922),a922),a922,f934(x46931,a922)),f93(f934(x46931,a922))),f335(f335(f7(f934(x46931,a922),f934(f934(x46931,a922),a922),f934(f934(x46931,a922),a922)),f335(f335(f8(f934(f934(x46931,a922),f934(a922,a922)),f934(f934(f934(x46931,a922),a922),f934(f934(x46931,a922),a922)),f934(x46931,a922)),f18(f934(x46931,a922),a922,a922)),f335(f335(f8(f934(f934(x46931,a922),a922),f934(f934(x46931,a922),f934(a922,a922)),f934(x46931,a922)),f335(f8(a922,f934(a922,a922),f934(x46931,a922)),a333)),f335(f335(f7(f934(x46931,a922),f934(f934(x46931,a922),f934(x46931,a922)),f934(f934(x46931,a922),a922)),f335(f335(f8(f934(f934(x46931,a922),a922),f934(f934(f934(x46931,a922),f934(x46931,a922)),f934(f934(x46931,a922),a922)),f934(x46931,a922)),f8(f934(x46931,a922),a922,f934(x46931,a922))),a332)),f85(f934(x46931,a922)))))),f335(f335(f8(f934(f934(x46931,a922),a922),a922,f934(x46931,a922)),f335(f337(f934(x46931,a922)),x46932)),f316(x46931))))),f335(f316(x46931),f335(f85(f934(x46931,a922)),x46932))) % 186.01/186.01 [4793]~E(f335(f335(f86(a1),x47931),x47931),f335(f335(f23(a1),f335(f335(f86(a1),x47932),x47932)),a104)) % 186.01/186.01 [4797]~P1(f335(f335(f244(a927),f335(f335(f86(a927),x47971),x47972)),x47972)) % 186.01/186.01 [4798]~P1(f335(f335(f244(a927),f335(f335(f86(a927),x47981),x47982)),x47981)) % 186.01/186.01 [4036]E(f335(f335(f23(a927),x40361),f335(f335(f87(a927),f335(f335(f42(a927),x40361),x40362)),x40362)),f51(a927,x40361,x40362)) % 186.01/186.01 [4037]E(f335(f335(f23(a1),x40371),f335(f335(f87(a1),f335(f335(f42(a1),x40371),x40372)),x40372)),f51(a1,x40371,x40372)) % 186.01/186.01 [4070]E(f335(f335(f161(a927,x40701),f335(f171(x40701),x40702)),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(x40701)),x40702)))),x40702) % 186.01/186.01 [4129]E(f335(f293(x41291,x41291,f315(x41291,f195(f934(f933(x41291,x41291),a922)))),x41292),x41292) % 186.01/186.01 [4256]E(f315(x42561,f335(f335(f23(f934(f933(x42561,x42561),a922)),x42562),f315(x42561,f195(f934(f933(x42561,x42561),a922))))),f315(x42561,x42562)) % 186.01/186.01 [4257]E(f315(x42571,f335(f335(f117(f934(f933(x42571,x42571),a922)),x42572),f315(x42571,f195(f934(f933(x42571,x42571),a922))))),f315(x42571,x42572)) % 186.01/186.01 [4307]E(f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f86(a1),x43071),x43071)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x43072),x43072)),a104)),f335(f335(f86(a1),f335(f335(f23(a1),x43071),x43072)),f335(f335(f23(a1),x43071),x43072))) % 186.01/186.01 [4347]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f86(a1),x43471),x43472)),f335(f335(f86(a1),x43471),x43472))),a104),f335(f335(f86(a1),f335(f335(f86(a1),x43471),x43471)),f335(f335(f23(a1),f335(f335(f86(a1),x43472),x43472)),a104))) % 186.01/186.01 [4372]E(f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),x43721),x43721)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x43722),x43722)),a104)),f335(f335(f86(a1),f335(f335(f86(a1),x43721),f335(f335(f23(a1),x43722),a104))),f335(f335(f86(a1),x43721),f335(f335(f23(a1),x43722),a104)))) % 186.01/186.01 [4385]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),x43851),x43852)),f335(f335(f23(a1),x43851),x43852))),a104),f335(f335(f23(a1),f335(f335(f23(a1),f335(f335(f86(a1),x43851),x43851)),a104)),f335(f335(f86(a1),x43852),x43852))) % 186.01/186.01 [4386]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f86(a1),x43861),x43862)),f335(f335(f86(a1),x43861),x43862))),a104),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),x43861),x43861)),a104)),f335(f335(f86(a1),x43862),x43862))) % 186.01/186.01 [4434]E(f335(f107(a1),f335(f335(f42(a927),f335(f335(f87(a927),f335(a111,f335(f81(a1),x44341))),f335(a111,f335(f81(a1),x44342)))),f225(f335(a111,f335(f81(a1),x44341)),f335(a111,f335(f81(a1),x44342))))),f227(x44341,x44342)) % 186.01/186.01 [4479]E(f335(f335(f267(f933(a106,a106),a106,f933(a106,a106),f933(x44791,f933(a106,a106))),f275(f335(a3,f335(f196(f928(x44791)),x44792)))),f335(f335(f8(x44791,f934(f933(a106,a106),f933(x44791,f933(a106,a106))),a106),f260(x44791,f933(a106,a106))),f335(f335(f8(a927,x44791,a106),f335(f171(x44791),x44792)),a20))),f283(x44791,x44792)) % 186.01/186.01 [4559]E(f335(f149(a927,f928(x45591),f335(f7(f928(x45591),a927,a927),f335(f335(f8(a927,f934(a927,a927),f928(x45591)),f242(a927)),f196(f928(x45591)))),f2(a927)),f335(f175(f928(x45591)),f186(x45591,x45592))),f335(f196(f928(f928(x45591))),f335(f143(f928(x45591),f335(f335(f8(a922,a922,f928(x45591)),a330),f335(f335(f7(f928(x45591),f928(x45591),a922),a332),f120(x45591)))),x45592))) % 186.01/186.01 [4565]E(f335(f335(f45(a927,f934(x45651,a922)),f250(f934(a927,a922))),f335(f335(f7(a927,f934(a927,f934(x45651,a922)),f934(x45651,a922)),f335(f335(f8(f934(a927,a922),f934(f934(a927,f934(x45651,a922)),f934(x45651,a922)),a927),f45(a927,f934(x45651,a922))),f310(a927,f2(a927)))),x45652)),f335(f335(f45(a927,f934(x45651,a922)),f250(f934(a927,a922))),x45652)) % 186.01/186.01 [4587]P1(f335(f67(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),x45871)),f335(f335(f7(a927,a927,a922),f244(a927)),x45872))))) % 186.01/186.01 [4701]E(f335(f270(f933(f928(x47011),f928(x47011))),f335(f265(f928(x47011),f928(x47011),a922),f335(f335(f18(f928(x47011),f934(f928(x47011),a922),f934(f928(x47011),a922)),f335(f335(f8(f934(f928(x47011),f934(a922,a922)),f934(f934(f928(x47011),a922),f934(f928(x47011),a922)),f928(x47011)),f18(f928(x47011),a922,a922)),f335(f335(f8(f934(f928(x47011),a922),f934(f928(x47011),f934(a922,a922)),f928(x47011)),f335(f8(a922,f934(a922,a922),f928(x47011)),a334)),f335(f335(f7(f928(x47011),f934(f928(x47011),a927),f934(f928(x47011),a922)),f335(f335(f8(f934(a927,a922),f934(f934(f928(x47011),a927),f934(f928(x47011),a922)),f928(x47011)),f8(a927,a922,f928(x47011))),f335(f335(f8(a927,f934(a927,a922),f928(x47011)),f244(a927)),f196(f928(x47011))))),f196(f928(x47011)))))),f335(f335(f18(f928(x47011),f934(f928(x47011),a922),f934(f928(x47011),a922)),f335(f335(f8(f934(f928(x47011),f934(a922,a922)),f934(f934(f928(x47011),a922),f934(f928(x47011),a922)),f928(x47011)),f18(f928(x47011),a922,a922)),f335(f335(f8(f934(f928(x47011),a922),f934(f928(x47011),f934(a922,a922)),f928(x47011)),f335(f8(a922,f934(a922,a922),f928(x47011)),a333)),f335(f335(f7(f928(x47011),f934(f928(x47011),a927),f934(f928(x47011),a922)),f335(f335(f8(f934(a927,a922),f934(f934(f928(x47011),a927),f934(f928(x47011),a922)),f928(x47011)),f8(a927,a922,f928(x47011))),f335(f335(f8(a927,f934(a927,a922),f928(x47011)),a332),f196(f928(x47011))))),f196(f928(x47011)))))),f335(f335(f7(f928(x47011),f934(f933(f928(x47011),f928(x47011)),a922),f934(f928(x47011),a922)),f335(f335(f8(f934(f928(x47011),f934(f934(f933(f928(x47011),f928(x47011)),a922),a922)),f934(f934(f933(f928(x47011),f928(x47011)),a922),f934(f928(x47011),a922)),f928(x47011)),f7(f928(x47011),f934(f933(f928(x47011),f928(x47011)),a922),a922)),f335(f335(f8(f934(f928(x47011),f933(f928(x47011),f928(x47011))),f934(f928(x47011),f934(f934(f933(f928(x47011),f928(x47011)),a922),a922)),f928(x47011)),f335(f8(f933(f928(x47011),f928(x47011)),f934(f934(f933(f928(x47011),f928(x47011)),a922),a922),f928(x47011)),f337(f933(f928(x47011),f928(x47011))))),f260(f928(x47011),f928(x47011))))),f152(x47011,x47012)))))),f153(x47011,x47012)) % 186.01/186.01 [4375]E(f335(f335(f86(a1),f335(f335(f86(a1),f335(f335(f87(a1),x43751),x43752)),f335(f335(f87(a1),x43751),x43752))),x43752),f335(f335(f87(a1),f335(f335(f23(a1),f335(f335(f86(a1),x43751),x43751)),a104)),x43752)) % 186.01/186.01 [4478]E(f335(a111,f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x44781),x44782)),f195(f934(f933(a927,a927),a922)))))),f335(f335(f23(a927),x44781),x44782)) % 186.01/186.01 [4482]E(f335(f335(f297(x44821,x44821,x44821),f335(f335(f117(f934(f933(x44821,x44821),a922)),x44822),f315(x44821,f195(f934(f933(x44821,x44821),a922))))),f315(x44821,f335(f335(f117(f934(f933(x44821,x44821),a922)),x44822),f315(x44821,f195(f934(f933(x44821,x44821),a922)))))),f315(x44821,x44822)) % 186.01/186.01 [4519]E(f276(x45191,f335(f143(f933(a106,x45191),f335(f265(a106,x45191,a922),f335(f335(f8(a922,f934(x45191,a922),a106),f16(a922,x45191)),f335(f244(a106),f2(a106))))),x45192)),f276(x45191,x45192)) % 186.01/186.01 [4520]E(f274(x45201,f335(f143(f933(a106,x45201),f335(f265(a106,x45201,a922),f335(f335(f8(a922,f934(x45201,a922),a106),f16(a922,x45201)),f335(f244(a106),f2(a106))))),x45202)),f274(x45201,x45202)) % 186.01/186.01 [4522]E(f335(f85(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x45221),x45222)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x45222),x45221)),f195(f934(f933(a927,a927),a922)))))) % 186.01/186.01 [4578]E(f335(f335(f296(f928(a927),x45781),f152(a927,a248)),f335(f335(f7(x45781,f928(f934(x45781,a927)),f928(a927)),f335(f335(f8(f934(f934(x45781,a927),a927),f934(f928(f934(x45781,a927)),f928(a927)),x45781),f161(f934(x45781,a927),a927)),f335(f7(f934(x45781,a927),x45781,a927),f5(f934(x45781,a927))))),x45782)),f160(x45781,x45782)) % 186.01/186.01 [4599]E(f335(f335(f92(a1,a927),f335(f110(a1),f335(f335(f86(a1),x45991),a104))),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f2(a927))),f335(f335(f8(a927,a927,a1),a119),f335(f335(f8(a927,a927,a1),f335(f241(a927),x45992)),a111)))),f335(f335(f241(a927),f335(a119,x45992)),f335(f110(a927),x45991))) % 186.01/186.01 [4600]E(f335(f335(f92(a1,a927),f335(f110(a1),f335(f335(f86(a1),x46001),a104))),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f335(a119,x46002))),f335(f335(f8(a927,a927,a1),a119),f335(f335(f8(a927,a927,a1),f335(f242(a927),x46002)),a111)))),f335(f335(f242(a927),f335(a119,x46002)),f335(f110(a927),x46001))) % 186.01/186.01 [4620]E(f335(f149(f928(x46201),f928(x46201),f141(x46201),f120(x46201)),f335(f335(f161(f928(x46201),f928(x46201)),f163(f928(x46201),x46201,f120(x46201),f335(f335(f8(f928(x46201),f934(f928(x46201),f928(x46201)),x46201),f16(f928(x46201),f928(x46201))),f335(f335(f7(x46201,f928(x46201),f928(x46201)),f158(x46201)),f120(x46201))))),x46202)),f335(f335(f161(f928(x46201),x46201),f148(x46201)),f335(f143(f928(x46201),f335(f335(f8(a922,a922,f928(x46201)),a330),f335(f335(f7(f928(x46201),f928(x46201),a922),a332),f120(x46201)))),x46202))) % 186.01/186.01 [4684]E(f335(f265(a1,a1,a922),f335(f335(f7(a1,f934(a1,a922),f934(a1,a922)),f335(f335(f8(f934(a1,f934(a922,a922)),f934(f934(a1,a922),f934(a1,a922)),a1),f18(a1,a922,a922)),f335(f335(f8(f934(a1,a922),f934(a1,f934(a922,a922)),a1),f335(f8(a922,f934(a922,a922),a1),a333)),f335(f335(f8(f934(a1,a1),f934(a1,a922),a1),f335(f8(a1,a922,a1),f335(a332,x46841))),f335(f335(f8(a1,f934(a1,a1),a1),f86(a1)),f335(f87(a1),x46842)))))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),f335(a338,f335(f335(f244(a1),f2(a1)),x46842))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),f335(f335(f7(a1,a1,a922),f244(a1)),x46842))))),f335(f335(f8(a922,a922,a1),f335(a338,f335(a330,f335(f335(f244(a1),f2(a1)),x46842)))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f244(a1),x46842))),f335(f335(f7(a1,a1,a922),f243(a1)),f2(a1))))))),f55(x46841,x46842)) % 186.01/186.01 [4687]E(f335(f270(x46871),f335(f335(f8(f934(a927,a922),a922,x46871),f93(a927)),f335(f335(f7(x46871,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),x46871),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),x46871),f335(f8(a922,f934(a922,a922),a927),a333)),f335(f335(f7(x46871,f934(a927,x46871),f934(a927,a922)),f335(f335(f8(f934(x46871,a922),f934(f934(a927,x46871),f934(a927,a922)),x46871),f8(x46871,a922,a927)),a332)),f335(f171(x46871),x46872))))),f335(f335(f7(a927,a927,a922),f244(a927)),f335(f196(f928(x46871)),x46872))))),f335(f179(x46871),x46872)) % 186.01/186.01 [4492]E(f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),x44921),a104)),x44922)),f335(f335(f23(a1),f335(f335(f86(a1),x44921),a104)),x44922))),a104),f335(f335(f23(a1),f335(f335(f86(a1),x44921),x44921)),f335(f335(f23(a1),f335(f335(f86(a1),x44922),x44922)),a104))) % 186.01/186.01 [4615]E(f335(f149(f928(f928(x46151)),f928(f928(x46151)),f141(f928(x46151)),f120(f928(x46151))),f335(f335(f161(f928(x46151),f928(f928(x46151))),f163(f928(f928(x46151)),x46151,f120(f928(x46151)),f335(f16(f934(f928(x46151),f928(f928(x46151))),x46151),f335(f335(f7(f928(x46151),f928(f928(x46151)),f928(f928(x46151))),f158(f928(x46151))),f120(f928(x46151)))))),x46152)),f335(f335(f161(f928(x46151),f928(x46151)),f178(x46151)),f335(f143(f928(x46151),f335(f335(f8(a922,a922,f928(x46151)),a330),f335(f335(f7(f928(x46151),f928(x46151),a922),a332),f120(x46151)))),x46152))) % 186.01/186.01 [4625]E(f335(f335(f92(a1,a927),f335(f110(a1),f335(f335(f86(a1),x46251),a104))),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f2(a927))),f335(f335(f8(a927,a927,a1),a119),f335(f335(f7(a1,a927,a927),f335(f335(f8(a927,f934(a927,a927),a1),f241(a927)),a111)),x46252)))),f335(f335(f241(a927),f335(f110(a927),x46251)),f335(a119,x46252))) % 186.01/186.01 [4626]E(f335(f335(f92(a1,a927),f335(f110(a1),f335(f335(f86(a1),x46261),a104))),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f335(a119,x46262))),f335(f335(f8(a927,a927,a1),a119),f335(f335(f7(a1,a927,a927),f335(f335(f8(a927,f934(a927,a927),a1),f242(a927)),a111)),x46262)))),f335(f335(f242(a927),f335(f110(a927),x46261)),f335(a119,x46262))) % 186.01/186.01 [4614]E(f335(f265(x46141,x46141,a922),f335(f335(f18(x46141,a922,f934(x46141,a922)),f335(f335(f8(f934(x46141,f934(a922,a922)),f934(a922,f934(x46141,a922)),x46141),f7(x46141,a922,a922)),f335(f335(f8(f934(x46141,a922),f934(x46141,f934(a922,a922)),x46141),f335(f8(a922,f934(a922,a922),x46141),a333)),a332))),x46142)),f271(x46141,x46142)) % 186.01/186.01 [4659]E(f335(f335(f42(a927),x46591),f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46592)),f335(f335(f42(a927),x46591),f335(a119,f335(a119,f335(a119,x46592))))) % 186.01/186.01 [4660]E(f51(a927,x46601,f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46602)),f51(a927,x46601,f335(a119,f335(a119,f335(a119,x46602))))) % 186.01/186.01 [4661]E(f51(a927,f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46611),x46612),f51(a927,f335(a119,f335(a119,f335(a119,x46611))),x46612)) % 186.01/186.01 [4675]E(f130(f335(x46751,f335(f335(f87(a106),f335(f110(a106),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46752))),f335(f209(x46751),x46752)) % 186.01/186.01 [4676]E(f335(f335(f42(a927),f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),x46761)),x46762),f335(f335(f42(a927),f335(a119,f335(a119,f335(a119,x46761)))),x46762)) % 186.01/186.01 [4741]~E(f29(x47411,x47412,x47413),a26) % 186.01/186.01 [4742]~E(f28(x47421,x47422,x47423),a26) % 186.01/186.01 [4746]~E(f133(x47461,x47462,x47463),f126(x47461)) % 186.01/186.01 [3463]E(f335(f199(x34631,x34632),x34633),f128(x34631,x34632)) % 186.01/186.01 [3482]E(f335(f208(x34821,x34822),x34823),f335(f136(x34821),x34822)) % 186.01/186.01 [3558]E(f335(f335(f161(x35581,x35582),x35583),f120(x35581)),f120(x35582)) % 186.01/186.01 [3598]E(f335(f191(x35981,x35982,x35983),f2(a927)),x35982) % 186.01/186.01 [3600]E(f335(f335(f188(x36001,x36002),x36003),f120(x36002)),f120(f933(x36001,x36002))) % 186.01/186.01 [3615]E(f335(f196(f928(x36151)),f176(x36151,x36152,x36153)),x36152) % 186.01/186.01 [3634]E(f91(x36341,f68(x36341,x36342,x36343)),f335(f69(x36341,x36342),x36343)) % 186.01/186.01 [3638]E(f251(x36381,x36382,f251(x36382,x36381,x36383)),x36383) % 186.01/186.01 [3658]E(f335(f175(x36581),f176(x36581,x36582,x36583)),f176(x36581,x36582,x36583)) % 186.01/186.01 [3685]E(f147(x36851,x36852,f159(x36851,x36853)),f159(x36851,f147(x36851,x36852,x36853))) % 186.01/186.01 [3704]E(f335(f259(f928(x37041),f928(x37041)),f173(x37041,x37042,x37043)),f335(f143(x37041,x37042),x37043)) % 186.01/186.01 [3747]E(f335(f335(f158(x37471),x37472),f176(x37471,x37473,x37472)),f176(x37471,f335(a119,x37473),x37472)) % 186.01/186.01 [3779]E(f192(x37791,x37792,x37793,f2(a927)),x37792) % 186.01/186.01 [3780]E(f17(x37801,x37802,x37803,f2(a106)),x37802) % 186.01/186.01 [3781]E(f19(x37811,x37812,x37813,f2(a106)),x37812) % 186.01/186.01 [3788]E(f170(x37881,x37882,x37883,f120(x37881)),f120(x37882)) % 186.01/186.01 [3789]E(f137(x37891,x37892,x37893,f126(x37891)),f126(x37892)) % 186.01/186.01 [3795]E(f335(f335(f171(x37951),f335(f335(f158(x37951),x37952),x37953)),f2(a927)),x37952) % 186.01/186.01 [3828]E(f65(x38281,x38282,f120(x38281),x38283),f120(f933(x38281,x38282))) % 186.01/186.01 [3848]P26(x38481,x38482,x38483,f195(f934(x38481,a922))) % 186.01/186.01 [3951]E(f273(x39511,x39512,x39513),f335(f260(f934(a106,f934(a922,f931(f929(x39511)))),f933(a106,a106)),f47(x39511))) % 186.01/186.01 [4009]E(f335(f78(x40091,x40092,x40091,x40093),f25(x40091)),x40093) % 186.01/186.01 [4190]P1(f335(f335(f337(f933(x41901,x41901)),f335(f335(f260(x41901,x41901),x41902),x41902)),f315(x41901,x41903))) % 186.01/186.01 [4802]~P1(f335(f335(f337(f933(f928(x48021),f928(x48021))),f335(f335(f260(f928(x48021),f928(x48021)),x48022),f120(x48021))),f152(x48021,x48023))) % 186.01/186.01 [4803]~P1(f335(f335(f337(f933(f928(x48031),f928(x48031))),f335(f335(f260(f928(x48031),f928(x48031)),x48032),f120(x48031))),f154(x48031,x48033))) % 186.01/186.01 [4804]~P1(f335(f335(f337(f933(f928(x48041),f928(x48041))),f335(f335(f260(f928(x48041),f928(x48041)),x48042),f120(x48041))),f164(x48041,x48043))) % 186.01/186.01 [4805]~P1(f335(f335(f337(f933(f928(x48051),f928(x48051))),f335(f335(f260(f928(x48051),f928(x48051)),f120(x48051)),x48052)),f152(x48051,x48053))) % 186.01/186.01 [4806]~P1(f335(f335(f337(f933(f928(x48061),f928(x48061))),f335(f335(f260(f928(x48061),f928(x48061)),f120(x48061)),x48062)),f164(x48061,x48063))) % 186.01/186.01 [3533]E(f335(f335(f210(x35331),x35332),x35333),f211(x35331,f224(x35332,x35333))) % 186.01/186.01 [3587]E(f335(f294(x35871,x35872),f335(f294(x35872,x35871),x35873)),x35873) % 186.01/186.01 [3610]E(f335(f335(f188(x36101,x36102),f120(x36101)),x36103),f120(f933(x36101,x36102))) % 186.01/186.01 [3613]E(f183(x36131,x36132,f335(f290(a927),x36133)),f335(f335(f182(x36131),x36133),x36132)) % 186.01/186.01 [3631]E(f159(x36311,f335(f143(x36311,x36312),x36313)),f335(f143(x36311,x36312),f159(x36311,x36313))) % 186.01/186.01 [3632]E(f335(f292(x36321,x36322),f335(f294(x36322,x36321),x36323)),f335(f272(x36322,x36321),x36323)) % 186.01/186.01 [3633]E(f335(f272(x36331,x36332),f335(f294(x36332,x36331),x36333)),f335(f292(x36332,x36331),x36333)) % 186.01/186.01 [3651]E(f335(f143(x36511,x36512),f335(f175(x36511),x36513)),f335(f175(x36511),f335(f143(x36511,x36512),x36513))) % 186.01/186.01 [3664]E(f335(f335(f145(x36641),x36642),f335(f178(x36641),x36643)),f335(f335(f145(x36641),f335(a119,x36642)),x36643)) % 186.01/186.01 [3680]E(f30(f28(x36801,x36802,x36803)),f335(f335(f86(a927),f30(x36803)),f335(a119,f2(a927)))) % 186.01/186.01 [3681]E(f335(f318(x36811,x36812,x36813),f195(f934(x36811,a922))),f195(f934(x36812,a922))) % 186.01/186.01 [3682]E(f335(f319(x36821,x36822,x36823),f195(f934(x36822,a922))),f195(f934(x36821,a922))) % 186.01/186.01 [3683]E(f335(f319(x36831,x36832,x36833),f250(f934(x36832,a922))),f250(f934(x36831,a922))) % 186.01/186.01 [3684]E(f335(f293(x36841,x36842,x36843),f195(f934(x36841,a922))),f195(f934(x36842,a922))) % 186.01/186.01 [3710]E(f127(x37101,f133(f929(x37101),x37102,x37103)),f123(x37101,x37102,f127(x37101,x37103))) % 186.01/186.01 [3712]E(f335(f335(f317(x37121),x37122),f335(f179(x37121),x37123)),f335(f179(x37121),f147(x37121,x37122,x37123))) % 186.01/186.01 [3799]E(f335(f196(a924),f28(x37991,x37992,x37993)),f335(f335(f86(a927),f335(f196(a924),x37993)),f335(a119,f2(a927)))) % 186.01/186.01 [3800]E(f335(f318(f933(x38001,x38002),x38002,f264(x38001,x38002)),x38003),f335(f292(x38001,x38002),x38003)) % 186.01/186.01 [3801]E(f335(f318(f933(x38011,x38012),x38011,f259(x38011,x38012)),x38013),f335(f272(x38011,x38012),x38013)) % 186.01/186.01 [3820]E(f335(f179(x38201),f176(x38201,f335(a119,x38202),x38203)),f335(f335(f317(x38201),x38203),f195(f934(x38201,a922)))) % 186.01/186.01 [3877]E(f335(f335(f260(x38771,x38772),f335(f259(x38771,x38772),x38773)),f335(f264(x38771,x38772),x38773)),x38773) % 186.01/186.01 [3884]E(f335(f196(f929(x38841)),f133(x38841,x38842,x38843)),f335(f335(f86(a927),f335(f196(f929(x38841)),x38843)),f335(a119,f2(a927)))) % 186.01/186.01 [3886]E(f335(f335(f265(x38861,x38862,x38861),f16(x38861,x38862)),x38863),f335(f259(x38861,x38862),x38863)) % 186.01/186.01 [3964]E(f30(f29(x39641,x39642,x39643)),f335(f335(f86(a927),f335(f335(f86(a927),f30(x39642)),f30(x39643))),f335(a119,f2(a927)))) % 186.01/186.01 [4014]E(f335(f78(x40141,x40141,x40142,f25(x40141)),x40143),x40143) % 186.01/186.01 [4022]E(f335(f335(f141(x40221),f176(x40221,x40222,x40223)),f335(f335(f158(x40221),x40223),f120(x40221))),f335(f335(f158(x40221),x40223),f176(x40221,x40222,x40223))) % 186.01/186.01 [4123]E(f335(f196(a924),f29(x41231,x41232,x41233)),f335(f335(f86(a927),f335(f335(f86(a927),f335(f196(a924),x41232)),f335(f196(a924),x41233))),f335(a119,f2(a927)))) % 186.01/186.01 [4199]P1(f335(f335(f243(f934(x41991,a922)),f335(f179(x41991),f335(f143(x41991,x41992),x41993))),f335(f179(x41991),x41993))) % 186.01/186.01 [4242]P1(f335(f335(f243(f934(x42421,a922)),f335(f179(x42421),f335(f335(f182(x42421),x42422),x42423))),f335(f179(x42421),x42423))) % 186.01/186.01 [4243]P1(f335(f335(f243(f934(x42431,a922)),f335(f179(x42431),f335(f335(f145(x42431),x42432),x42433))),f335(f179(x42431),x42433))) % 186.01/186.01 [4247]P1(f335(f335(f243(f934(x42471,a922)),f335(f179(x42471),f183(x42471,x42472,x42473))),f335(f179(x42471),x42472))) % 186.01/186.01 [4248]P1(f335(f335(f243(f934(x42481,a922)),f335(f179(x42481),f177(x42481,x42482,x42483))),f335(f179(x42481),x42483))) % 186.01/186.01 [4269]P26(f933(x42691,x42692),f933(x42692,x42691),f335(f265(x42691,x42692,f933(x42692,x42691)),f335(f7(x42692,x42691,f933(x42692,x42691)),f260(x42692,x42691))),x42693) % 186.01/186.01 [4280]E(f335(f335(f335(f190(f928(x42801),f928(x42801)),f51(a927,x42802,f335(f196(f928(x42801)),x42803))),f174(x42801)),x42803),f335(f335(f335(f190(f928(x42801),f928(x42801)),x42802),f174(x42801)),x42803)) % 186.01/186.01 [4324]P1(f335(f335(f337(f933(f928(x43241),f928(x43241))),f335(f335(f260(f928(x43241),f928(x43241)),x43242),x43242)),f165(x43241,f315(x43241,x43243)))) % 186.01/186.01 [4465]E(f91(f933(x44651,x44652),f335(f335(f18(f933(x44651,x44652),x44652,a922),f335(f335(f8(x44651,f934(x44652,a922),f933(x44651,x44652)),x44653),f259(x44651,x44652))),f264(x44651,x44652))),f91(f933(x44651,x44652),f335(f265(x44651,x44652,a922),x44653))) % 186.01/186.01 [4466]E(f96(f933(x44661,x44662),f335(f335(f18(f933(x44661,x44662),x44662,a922),f335(f335(f8(x44661,f934(x44662,a922),f933(x44661,x44662)),x44663),f259(x44661,x44662))),f264(x44661,x44662))),f96(f933(x44661,x44662),f335(f265(x44661,x44662,a922),x44663))) % 186.01/186.01 [4499]E(f335(f335(f296(f933(a927,x44991),x44991),f328(a927,x44991,a248,x44992)),f335(f335(f18(x44991,x44991,f933(a927,x44991)),f335(f335(f8(a927,f934(x44991,f933(a927,x44991)),x44991),f260(a927,x44991)),x44993)),f5(x44991))),f329(x44991,x44993,x44992)) % 186.01/186.01 [4561]E(f335(f266(x45611,x45611,x45612,x45612,f5(x45611),f5(x45612)),x45613),x45613) % 186.01/186.01 [4634]E(f335(f149(f928(f928(x46341)),f928(f928(x46341)),f141(f928(x46341)),f120(f928(x46341))),f335(f335(f161(f928(x46341),f928(f928(x46341))),f335(f335(f7(f928(x46341),f928(x46341),f928(f928(x46341))),f335(f335(f8(f934(x46341,f928(x46341)),f934(f928(x46341),f928(f928(x46341))),f928(x46341)),f161(x46341,f928(x46341))),f335(f7(x46341,f928(x46341),f928(x46341)),f158(x46341)))),x46342)),f61(x46341,x46343,x46342))),f61(x46341,f335(a119,x46343),x46342)) % 186.01/186.01 [4692]E(f232(a927,f933(x46921,f929(x46921)),f2(a927),f335(f265(x46921,f929(x46921),a927),f335(f335(f7(x46921,a927,f934(f929(x46921),a927)),f335(f335(f8(f934(f929(x46921),f934(a927,a927)),f934(a927,f934(f929(x46921),a927)),x46921),f7(f929(x46921),a927,a927)),f335(f335(f8(f934(f929(x46921),a927),f934(f929(x46921),f934(a927,a927)),x46921),f335(f8(a927,f934(a927,a927),f929(x46921)),f86(a927))),f335(f335(f7(x46921,f934(f929(x46921),a927),f934(f929(x46921),a927)),f335(f335(f8(f934(a927,a927),f934(f934(f929(x46921),a927),f934(f929(x46921),a927)),x46921),f8(a927,a927,f929(x46921))),f335(f335(f8(a927,f934(a927,a927),x46921),f86(a927)),x46922))),f132(x46921,x46922))))),f84(a927))),f335(f142(x46921),x46923)),f335(f132(x46921,x46922),x46923)) % 186.01/186.01 [4700]E(f335(f335(f92(a1,x47001),f227(f335(f335(f78(f933(a1,a1),a1,x47001,f264(a1,a1)),f221(x47001)),x47002),f335(f335(f78(f933(a1,a1),a1,x47001,f264(a1,a1)),f221(x47001)),x47003))),f335(f335(f18(a1,a1,x47001),f335(f335(f8(a1,f934(a1,x47001),a1),f210(x47001)),f335(f335(f18(a1,a1,a1),f335(f335(f8(a1,f934(a1,a1),a1),f86(a1)),f335(f335(f8(a1,a1,a1),f335(f87(a1),f335(f335(f78(f933(a1,a1),a1,x47001,f259(a1,a1)),f221(x47001)),x47002))),f335(f335(f7(a1,a1,a1),f42(a1)),f335(f335(f78(f933(a1,a1),a1,x47001,f264(a1,a1)),f221(x47001)),x47002))))),f335(f335(f8(a1,a1,a1),f335(f87(a1),f335(f335(f78(f933(a1,a1),a1,x47001,f259(a1,a1)),f221(x47001)),x47003))),f335(f335(f7(a1,a1,a1),f42(a1)),f335(f335(f78(f933(a1,a1),a1,x47001,f264(a1,a1)),f221(x47001)),x47003)))))),f5(a1))),f239(x47001,x47002,x47003)) % 186.01/186.01 [4737]~E(f335(f335(f158(x47371),x47372),x47373),x47373) % 186.01/186.01 [4744]~E(f335(f335(f158(x47441),x47442),x47443),f120(x47441)) % 186.01/186.01 [4762]~E(f335(f335(f317(x47621),x47622),x47623),f195(f934(x47621,a922))) % 186.01/186.01 [4784]~E(f335(f318(x47841,f934(x47841,a922),x47842),x47843),f335(f316(x47841),x47843)) % 186.01/186.01 [3592]E(f335(f335(f166(x35921,f120(x35921)),x35922),x35923),f120(x35921)) % 186.01/186.01 [3593]E(f335(f148(x35931),f335(f335(f158(x35931),x35932),x35933)),x35932) % 186.01/186.01 [3594]E(f335(f178(x35941),f335(f335(f158(x35941),x35942),x35943)),x35943) % 186.01/186.01 [3637]E(f335(f335(f145(x36371),f84(a927)),f335(f335(f158(x36371),x36372),x36373)),x36373) % 186.01/186.01 [3671]E(f121(x36711,f335(f335(f145(x36711),x36712),x36713)),f335(f335(f145(x36711),x36712),f121(x36711,x36713))) % 186.01/186.01 [3673]E(f335(f335(f166(x36731,x36732),x36733),f335(f335(f171(x36731),x36732),x36733)),x36732) % 186.01/186.01 [3694]E(f335(f335(f317(x36941),x36942),f335(f335(f317(x36941),x36942),x36943)),f335(f335(f317(x36941),x36942),x36943)) % 186.01/186.01 [3707]E(f335(f335(f317(x37071),x37072),f335(f179(x37071),x37073)),f335(f179(x37071),f335(f335(f158(x37071),x37072),x37073))) % 186.01/186.01 [3709]E(f335(f335(f145(x37091),x37092),f335(f178(x37091),x37093)),f335(f178(x37091),f335(f335(f145(x37091),x37092),x37093))) % 186.01/186.01 [3721]E(f335(f335(f182(x37211),f84(a927)),f335(f335(f158(x37211),x37212),x37213)),f335(f335(f158(x37211),x37212),f120(x37211))) % 186.01/186.01 [3764]E(f335(f69(x37641,x37642),f335(f335(f317(x37641),x37643),f195(f934(x37641,a922)))),x37643) % 186.01/186.01 [3810]E(f335(f335(f86(a927),x38101),f335(f335(f86(a927),x38102),x38103)),f335(f335(f86(a927),x38102),f335(f335(f86(a927),x38101),x38103))) % 186.01/186.01 [3811]E(f335(f335(f86(a1),x38111),f335(f335(f86(a1),x38112),x38113)),f335(f335(f86(a1),x38112),f335(f335(f86(a1),x38111),x38113))) % 186.01/186.01 [3816]E(f335(f335(f262(x38161,x38162),f195(f934(x38161,a922))),x38163),f195(f934(f933(x38161,x38162),a922))) % 186.01/186.01 [3840]E(f335(f335(f108(f934(x38401,a922)),x38402),x38403),f335(f335(f108(f934(x38401,a922)),x38403),x38402)) % 186.01/186.01 [3841]E(f335(f335(f117(f934(x38411,a922)),x38412),x38413),f335(f335(f117(f934(x38411,a922)),x38413),x38412)) % 186.01/186.01 [3843]E(f335(f335(f141(x38431),x38432),f335(f335(f158(x38431),x38433),f120(x38431))),f335(f174(x38431),f335(f335(f158(x38431),x38433),x38432))) % 186.01/186.01 [3844]E(f335(f335(f141(x38441),f335(f175(x38441),x38442)),f335(f175(x38441),x38443)),f335(f175(x38441),f335(f335(f141(x38441),x38443),x38442))) % 186.01/186.01 [3854]E(f335(f178(x38541),f335(f335(f182(x38541),f335(a119,x38542)),x38543)),f335(f335(f182(x38541),x38542),f335(f178(x38541),x38543))) % 186.01/186.01 [3862]P1(f335(f335(f337(x38621),x38622),f335(f335(f317(x38621),x38622),x38623))) % 186.01/186.01 [3866]E(f335(f335(f46(x38661,f934(x38662,a922)),f195(f934(x38661,a922))),x38663),f250(f934(x38662,a922))) % 186.01/186.01 [3869]E(f335(f293(x38691,x38691,f271(x38691,x38692)),x38693),f335(f335(f108(f934(x38691,a922)),x38692),x38693)) % 186.01/186.01 [3883]E(f335(f196(f928(x38831)),f335(f335(f158(x38831),x38832),x38833)),f335(f335(f86(a927),f335(f196(f928(x38831)),x38833)),f335(a119,f2(a927)))) % 186.01/186.01 [3888]E(f121(x38881,f335(f335(f141(x38881),x38882),f335(f335(f158(x38881),x38883),f120(x38881)))),x38882) % 186.01/186.01 [3889]E(f151(x38891,f335(f335(f141(x38891),x38892),f335(f335(f158(x38891),x38893),f120(x38891)))),x38893) % 186.01/186.01 [3898]E(f335(f335(f141(x38981),f335(f335(f182(x38981),x38982),x38983)),f335(f335(f145(x38981),x38982),x38983)),x38983) % 186.01/186.01 [3907]E(f335(f335(f23(a927),f335(f335(f86(a927),x39071),x39072)),f335(f335(f86(a927),x39073),x39072)),f335(f335(f23(a927),x39071),x39073)) % 186.01/186.01 [3908]E(f335(f335(f23(a927),f335(f335(f86(a927),x39081),x39082)),f335(f335(f86(a927),x39081),x39083)),f335(f335(f23(a927),x39082),x39083)) % 186.01/186.01 [3914]E(f335(f335(f141(x39141),f335(f175(x39141),x39142)),f335(f335(f158(x39141),x39143),f120(x39141))),f335(f175(x39141),f335(f335(f158(x39141),x39143),x39142))) % 186.01/186.01 [3916]E(f335(f335(f86(a927),f335(f196(f928(x39161)),x39162)),f335(f196(f928(x39161)),x39163)),f335(f196(f928(x39161)),f335(f335(f141(x39161),x39162),x39163))) % 186.01/186.01 [3919]E(f335(f335(f86(a927),f335(f196(f928(x39191)),x39192)),f335(f196(f928(x39191)),x39193)),f335(f196(f928(x39191)),f180(x39191,x39192,x39193))) % 186.01/186.01 [3926]E(f335(f335(f117(f934(x39261,a922)),f335(f179(x39261),x39262)),f335(f179(x39261),x39263)),f335(f179(x39261),f335(f335(f141(x39261),x39262),x39263))) % 186.01/186.01 [3927]E(f51(a927,f335(f335(f87(a927),x39271),x39272),f335(f335(f87(a927),x39271),x39273)),f335(f335(f87(a927),x39271),f51(a927,x39272,x39273))) % 186.01/186.01 [3939]E(f335(f335(f182(x39391),f335(f335(f23(a927),x39392),f84(a927))),f335(f178(x39391),x39393)),f335(f178(x39391),f335(f335(f182(x39391),x39392),x39393))) % 186.01/186.01 [3944]E(f335(f335(f108(f934(x39441,a922)),x39442),f335(f85(f934(x39441,a922)),x39443)),f335(f335(f23(f934(x39441,a922)),x39442),x39443)) % 186.01/186.01 [3945]E(f335(f335(f23(f934(x39451,a922)),x39452),f335(f85(f934(x39451,a922)),x39453)),f335(f335(f108(f934(x39451,a922)),x39452),x39453)) % 186.01/186.01 [3968]E(f335(f335(f262(x39681,x39682),x39683),f335(f16(f934(x39682,a922),x39681),f195(f934(x39682,a922)))),f195(f934(f933(x39681,x39682),a922))) % 186.01/186.01 [3970]E(f335(f335(f23(a927),f335(f335(f87(a927),x39701),x39702)),f335(f335(f87(a927),x39701),x39703)),f335(f335(f87(a927),x39701),f335(f335(f23(a927),x39702),x39703))) % 186.01/186.01 [3971]E(f335(f335(f86(a927),f335(f335(f87(a927),x39711),x39712)),f335(f335(f87(a927),x39711),x39713)),f335(f335(f87(a927),x39711),f335(f335(f86(a927),x39712),x39713))) % 186.01/186.01 [3972]E(f335(f335(f23(a1),f335(f335(f87(a1),x39721),x39722)),f335(f335(f87(a1),x39721),x39723)),f335(f335(f87(a1),x39721),f335(f335(f23(a1),x39722),x39723))) % 186.01/186.01 [3973]E(f335(f335(f86(a1),f335(f335(f87(a1),x39731),x39732)),f335(f335(f87(a1),x39731),x39733)),f335(f335(f87(a1),x39731),f335(f335(f86(a1),x39732),x39733))) % 186.01/186.01 [3974]E(f335(f335(f87(a1),f335(f335(f252(a1),x39741),x39742)),f335(f335(f252(a1),x39741),x39743)),f335(f335(f252(a1),x39741),f335(f335(f86(a927),x39742),x39743))) % 186.01/186.01 [3988]E(f335(f335(f45(x39881,f934(x39882,a922)),x39883),f335(f16(f934(x39882,a922),x39881),f195(f934(x39882,a922)))),f195(f934(x39882,a922))) % 186.01/186.01 [3990]E(f51(a927,f335(f335(f87(a927),x39901),x39902),f335(f335(f87(a927),x39903),x39902)),f335(f335(f87(a927),f51(a927,x39901,x39903)),x39902)) % 186.01/186.01 [3995]E(f51(a1,f335(f335(f23(a1),x39951),f51(a1,x39952,x39953)),x39953),f51(a1,f335(f335(f23(a1),x39951),x39952),x39953)) % 186.01/186.01 [3996]E(f51(a1,f335(f335(f87(a1),x39961),f51(a1,x39962,x39963)),x39963),f51(a1,f335(f335(f87(a1),x39961),x39962),x39963)) % 186.01/186.01 [3997]P1(f335(f335(f243(f934(x39971,a922)),x39972),f335(f335(f317(x39971),x39973),x39972))) % 186.01/186.01 [4074]E(f335(f335(f45(f934(x40741,a922),f934(x40741,a922)),x40742),f335(f108(f934(x40741,a922)),x40743)),f335(f335(f108(f934(x40741,a922)),x40743),f43(f934(x40741,a922),x40742))) % 186.01/186.01 [4075]E(f335(f335(f46(f934(x40751,a922),f934(x40751,a922)),x40752),f335(f117(f934(x40751,a922)),x40753)),f335(f335(f117(f934(x40751,a922)),x40753),f44(f934(x40751,a922),x40752))) % 186.01/186.01 [4087]E(f335(f179(x40871),f335(f335(f335(f190(f928(x40871),f928(x40871)),x40872),f174(x40871)),x40873)),f335(f179(x40871),x40873)) % 186.01/186.01 [4091]E(f335(f335(f182(x40911),f335(f196(f928(x40911)),f184(x40911,x40912,x40913))),x40913),f184(x40911,x40912,x40913)) % 186.01/186.01 [4095]E(f335(f196(f928(x40951)),f335(f335(f335(f190(f928(x40951),f928(x40951)),x40952),f174(x40951)),x40953)),f335(f196(f928(x40951)),x40953)) % 186.01/186.01 [4098]E(f335(f335(f265(x40981,x40982,x40982),f335(f16(f934(x40982,x40982),x40981),f5(x40982))),x40983),f335(f264(x40981,x40982),x40983)) % 186.01/186.01 [4105]E(f51(a1,f335(f335(f23(a1),f51(a1,x41051,x41052)),x41053),x41052),f51(a1,f335(f335(f23(a1),x41051),x41053),x41052)) % 186.01/186.01 [4106]E(f51(a1,f335(f335(f252(a1),f51(a1,x41061,x41062)),x41063),x41062),f51(a1,f335(f335(f252(a1),x41061),x41063),x41062)) % 186.01/186.01 [4109]E(f335(f335(f45(f934(f933(x41091,x41092),a922),f934(x41092,a922)),x41093),f292(x41091,x41092)),f335(f292(x41091,x41092),f43(f934(f933(x41091,x41092),a922),x41093))) % 186.01/186.01 [4110]E(f335(f335(f45(f934(f933(x41101,x41102),a922),f934(x41101,a922)),x41103),f272(x41101,x41102)),f335(f272(x41101,x41102),f43(f934(f933(x41101,x41102),a922),x41103))) % 186.01/186.01 [4134]E(f335(f78(x41341,x41341,x41341,x41342),f335(f335(f190(x41341,x41341),x41343),x41342)),f335(f335(f190(x41341,x41341),f335(a119,x41343)),x41342)) % 186.01/186.01 [4154]E(f335(f335(f145(x41541),f335(f335(f23(a927),f335(f196(f928(x41541)),x41542)),x41543)),f335(f175(x41541),x41542)),f335(f175(x41541),f335(f335(f182(x41541),x41543),x41542))) % 186.01/186.01 [4155]E(f335(f335(f182(x41551),f335(f335(f23(a927),f335(f196(f928(x41551)),x41552)),x41553)),f335(f175(x41551),x41552)),f335(f175(x41551),f335(f335(f145(x41551),x41553),x41552))) % 186.01/186.01 [4157]E(f335(f335(f86(a927),f335(f172(a927),f335(f335(f161(x41571,a927),x41572),x41573))),f335(f196(f928(x41571)),x41573)),f162(x41571,x41572,x41573)) % 186.01/186.01 [4177]E(f335(f174(x41771),f335(f335(f335(f190(f928(x41771),f928(x41771)),x41772),f174(x41771)),x41773)),f335(f335(f335(f190(f928(x41771),f928(x41771)),f335(a119,x41772)),f174(x41771)),x41773)) % 186.01/186.01 [4191]P1(f335(f335(f243(a927),f335(f196(f928(x41911)),f335(f143(x41911,x41912),x41913))),f335(f196(f928(x41911)),x41913))) % 186.01/186.01 [4207]E(f335(f335(f117(f934(f934(x42071,a922),a922)),f335(f316(x42071),x42072)),f335(f318(f934(x42071,a922),f934(x42071,a922),f335(f317(x42071),x42073)),f335(f316(x42071),x42072))),f335(f316(x42071),f335(f335(f317(x42071),x42073),x42072))) % 186.01/186.01 [4239]P1(f335(f335(f243(a927),f335(f196(f928(x42391)),f184(x42391,x42392,x42393))),f335(f196(f928(x42391)),x42393))) % 186.01/186.01 [4246]E(f335(f272(x42461,x42462),f335(f270(f933(x42461,x42462)),f335(f265(x42461,x42462,a922),x42463))),f335(f270(x42461),f335(f335(f8(f934(x42462,a922),a922,x42461),f93(x42462)),x42463))) % 186.01/186.01 [4258]E(f335(f318(a927,a927,f335(f335(f7(a927,a927,a927),f86(a927)),x42581)),f311(a927,x42582,x42583)),f311(a927,f335(f335(f86(a927),x42582),x42581),f335(f335(f86(a927),x42583),x42581))) % 186.01/186.01 [4272]E(f335(f318(a927,a927,f335(f335(f7(a927,a927,a927),f86(a927)),x42721)),f335(f310(a927,x42722),x42723)),f335(f310(a927,f335(f335(f86(a927),x42722),x42721)),f335(f335(f86(a927),x42723),x42721))) % 186.01/186.01 [4290]E(f335(f335(f188(x42901,x42902),f335(f335(f161(f933(x42901,x42902),x42901),f259(x42901,x42902)),x42903)),f335(f335(f161(f933(x42901,x42902),x42902),f264(x42901,x42902)),x42903)),x42903) % 186.01/186.01 [4295]E(f335(f335(f86(a927),f335(f335(f87(a927),x42951),f51(a927,f335(f335(f42(a927),x42952),x42951),x42953))),f51(a927,x42952,x42951)),f51(a927,x42952,f335(f335(f87(a927),x42951),x42953))) % 186.01/186.01 [4308]E(f335(f335(f141(x43081),x43082),f335(f149(f928(x43081),f928(x43081),f141(x43081),f120(x43081)),x43083)),f335(f149(f928(x43081),f928(x43081),f141(x43081),x43082),x43083)) % 186.01/186.01 [4329]P1(f335(f335(f337(f933(x43291,x43291)),f335(f335(f260(x43291,x43291),x43292),x43292)),f335(f335(f190(f933(x43291,x43291),a922),f2(a927)),x43293))) % 186.01/186.01 [4334]E(f335(f270(x43341),f335(f335(f8(f934(x43342,a922),a922,x43341),f93(x43342)),f335(f7(x43342,x43341,a922),x43343))),f335(f292(x43342,x43341),f335(f270(f933(x43342,x43341)),f335(f265(x43342,x43341,a922),x43343)))) % 186.01/186.01 [4351]E(f335(f335(f117(f934(x43511,a922)),f335(f335(f45(a927,f934(x43511,a922)),f311(a927,f84(a927),x43512)),x43513)),f335(x43513,f2(a927))),f335(f335(f45(a927,f934(x43511,a922)),f335(f309(a927),x43512)),x43513)) % 186.01/186.01 [4366]E(f335(f149(f928(x43661),f928(x43661),f141(x43661),f120(x43661)),f335(f335(f161(f928(x43661),f928(x43661)),f143(x43661,x43662)),x43663)),f335(f143(x43661,x43662),f335(f149(f928(x43661),f928(x43661),f141(x43661),f120(x43661)),x43663))) % 186.01/186.01 [4370]E(f335(f264(f928(x43701),f928(x43701)),f173(x43701,x43702,x43703)),f335(f143(x43701,f335(f78(a922,a922,x43701,a330),x43702)),x43703)) % 186.01/186.01 [4380]P25(x43801,x43802,f335(f335(f317(f926(x43801)),f98(x43801,x43803,a26,x43803)),f195(f934(f926(x43801),a922)))) % 186.01/186.01 [4417]E(f335(f335(f86(a1),f335(f335(f86(a1),f335(f335(f87(a1),x44171),f335(f335(f42(a1),x44172),x44171))),f51(a1,x44172,x44171))),x44173),f335(f335(f86(a1),x44172),x44173)) % 186.01/186.01 [4454]E(f335(f335(f86(a1),f335(f335(f86(a1),f335(f335(f87(a1),f335(f335(f42(a1),x44541),x44542)),x44542)),f51(a1,x44541,x44542))),x44543),f335(f335(f86(a1),x44541),x44543)) % 186.01/186.01 [4480]E(f91(f933(x44801,x44802),f335(f265(x44801,x44802,a922),f335(f335(f8(f934(x44802,f933(x44801,x44802)),f934(x44802,a922),x44801),f335(f8(f933(x44801,x44802),a922,x44802),x44803)),f260(x44801,x44802)))),f91(f933(x44801,x44802),x44803)) % 186.01/186.01 [4481]E(f96(f933(x44811,x44812),f335(f265(x44811,x44812,a922),f335(f335(f8(f934(x44812,f933(x44811,x44812)),f934(x44812,a922),x44811),f335(f8(f933(x44811,x44812),a922,x44812),x44813)),f260(x44811,x44812)))),f96(f933(x44811,x44812),x44813)) % 186.01/186.01 [4508]P1(f335(f335(f243(f934(x45081,a922)),f43(f934(x45081,a922),f335(f335(f108(f934(f934(x45081,a922),a922)),x45082),x45083))),f335(f335(f108(f934(x45081,a922)),f43(f934(x45081,a922),x45082)),f43(f934(x45081,a922),x45083)))) % 186.01/186.01 [4509]E(f335(f175(x45091),f335(f335(f335(f190(f928(x45091),f928(x45091)),f335(f335(f23(a927),f335(f196(f928(x45091)),x45092)),f51(a927,x45093,f335(f196(f928(x45091)),x45092)))),f174(x45091)),x45092)),f335(f335(f335(f190(f928(x45091),f928(x45091)),x45093),f174(x45091)),f335(f175(x45091),x45092))) % 186.01/186.01 [4546]P1(f335(f335(f243(a927),f335(f196(f928(x45461)),f335(f335(f145(x45461),f335(f196(f928(x45461)),f184(x45461,x45462,x45463))),x45463))),f335(f196(f928(x45461)),x45463))) % 186.01/186.01 [4796]~P1(f335(f68(x47961,x47962,f195(f934(x47961,a922))),x47963)) % 186.01/186.01 [4801]~P1(f335(f335(f337(f933(x48011,x48011)),f335(f335(f260(x48011,x48011),x48012),x48013)),f160(x48011,f120(f934(x48011,a927))))) % 186.01/186.01 [3855]E(f335(f196(f928(x38551)),f335(f335(f182(x38551),x38552),x38553)),f335(f335(f241(a927),f335(f196(f928(x38551)),x38553)),x38552)) % 186.01/186.01 [3856]E(f335(f196(f928(x38561)),f335(f335(f145(x38561),x38562),x38563)),f335(f335(f23(a927),f335(f196(f928(x38561)),x38563)),x38562)) % 186.01/186.01 [3882]E(f335(f196(f928(f928(x38821))),f61(x38821,x38822,x38823)),f335(f335(f252(a927),f335(f196(f928(x38821)),x38823)),x38822)) % 186.01/186.01 [3900]E(f335(f335(f42(a927),f335(f335(f42(a927),x39001),x39002)),x39003),f335(f335(f42(a927),x39001),f335(f335(f87(a927),x39002),x39003))) % 186.01/186.01 [3901]E(f335(f335(f23(a927),f335(f335(f23(a927),x39011),x39012)),x39013),f335(f335(f23(a927),x39011),f335(f335(f86(a927),x39012),x39013))) % 186.01/186.01 [3902]E(f335(f335(f87(a927),f335(f335(f87(a927),x39021),x39022)),x39023),f335(f335(f87(a927),x39021),f335(f335(f87(a927),x39022),x39023))) % 186.01/186.01 [3903]E(f335(f335(f87(a1),f335(f335(f87(a1),x39031),x39032)),x39033),f335(f335(f87(a1),x39031),f335(f335(f87(a1),x39032),x39033))) % 186.01/186.01 [3904]E(f335(f335(f86(a927),f335(f335(f86(a927),x39041),x39042)),x39043),f335(f335(f86(a927),x39041),f335(f335(f86(a927),x39042),x39043))) % 186.01/186.01 [3905]E(f335(f335(f86(a1),f335(f335(f86(a1),x39051),x39052)),x39053),f335(f335(f86(a1),x39051),f335(f335(f86(a1),x39052),x39053))) % 186.01/186.01 [3906]E(f335(f335(f252(a1),f335(f335(f252(a1),x39061),x39062)),x39063),f335(f335(f252(a1),x39061),f335(f335(f87(a927),x39062),x39063))) % 186.01/186.01 [3925]E(f169(x39251,f335(f335(f158(f934(x39251,a922)),x39252),x39253)),f181(x39251,x39252,f169(x39251,x39253))) % 186.01/186.01 [3969]E(f335(f335(f23(a927),f335(f335(f23(a927),x39691),x39692)),x39693),f335(f335(f23(a927),f335(f335(f23(a927),x39691),x39693)),x39692)) % 186.01/186.01 [3977]E(f335(f335(f108(f934(x39771,a922)),x39772),f335(f335(f23(f934(x39771,a922)),x39773),x39772)),f195(f934(x39771,a922))) % 186.01/186.01 [3981]E(f335(f335(f161(a927,x39811),f335(f16(x39811,a927),x39812)),f146(a927,f335(f310(a927,f2(a927)),x39813))),f176(x39811,x39813,x39812)) % 186.01/186.01 [4020]E(f44(f934(x40201,a922),f335(f335(f317(f934(x40201,a922)),x40202),x40203)),f335(f335(f108(f934(x40201,a922)),x40202),f44(f934(x40201,a922),x40203))) % 186.01/186.01 [4021]E(f43(f934(x40211,a922),f335(f335(f317(f934(x40211,a922)),x40212),x40213)),f335(f335(f117(f934(x40211,a922)),x40212),f43(f934(x40211,a922),x40213))) % 186.01/186.01 [4023]E(f176(x40231,f335(f196(f928(x40231)),f335(f143(x40231,f335(a332,x40232)),x40233)),x40232),f335(f143(x40231,f335(a332,x40232)),x40233)) % 186.01/186.01 [4025]E(f335(f335(f23(a927),f335(f335(f87(a927),x40251),x40252)),f335(f335(f87(a927),x40253),x40252)),f335(f335(f87(a927),f335(f335(f23(a927),x40251),x40253)),x40252)) % 186.01/186.01 [4026]E(f335(f335(f86(a927),f335(f335(f87(a927),x40261),x40262)),f335(f335(f87(a927),x40263),x40262)),f335(f335(f87(a927),f335(f335(f86(a927),x40261),x40263)),x40262)) % 186.01/186.01 [4027]E(f335(f335(f23(a1),f335(f335(f87(a1),x40271),x40272)),f335(f335(f87(a1),x40273),x40272)),f335(f335(f87(a1),f335(f335(f23(a1),x40271),x40273)),x40272)) % 186.01/186.01 [4028]E(f335(f335(f86(a1),f335(f335(f87(a1),x40281),x40282)),f335(f335(f87(a1),x40283),x40282)),f335(f335(f87(a1),f335(f335(f86(a1),x40281),x40283)),x40282)) % 186.01/186.01 [4030]E(f335(f335(f241(a927),f335(f335(f23(a927),x40301),x40302)),f335(f335(f23(a927),x40303),x40302)),f335(f335(f23(a927),f335(f335(f241(a927),x40301),x40303)),x40302)) % 186.01/186.01 [4051]E(f335(f335(f108(f934(f928(x40511),a922)),f167(x40511,x40512)),f167(x40511,x40513)),f167(x40511,f335(f335(f108(f934(x40511,a922)),x40512),x40513))) % 186.01/186.01 [4054]E(f335(f335(f108(f934(x40541,a922)),x40542),f335(f335(f108(f934(x40541,a922)),x40542),x40543)),f335(f335(f108(f934(x40541,a922)),x40542),x40543)) % 186.01/186.01 [4055]E(f335(f335(f117(f934(x40551,a922)),x40552),f335(f335(f23(f934(x40551,a922)),x40553),x40552)),f335(f335(f117(f934(x40551,a922)),x40552),x40553)) % 186.01/186.01 [4056]E(f335(f335(f117(f934(x40561,a922)),x40562),f335(f335(f117(f934(x40561,a922)),x40562),x40563)),f335(f335(f117(f934(x40561,a922)),x40562),x40563)) % 186.01/186.01 [4068]E(f335(f335(f297(x40681,x40682,x40682),x40683),f315(x40682,f195(f934(f933(x40682,x40682),a922)))),x40683) % 186.01/186.01 [4071]E(f335(f335(f117(f934(x40711,a922)),f335(f335(f317(x40711),x40712),f195(f934(x40711,a922)))),x40713),f335(f335(f317(x40711),x40712),x40713)) % 186.01/186.01 [4090]E(f335(f335(f23(a927),f335(f335(f23(a927),f335(a119,x40901)),x40902)),f335(a119,x40903)),f335(f335(f23(a927),f335(f335(f23(a927),x40901),x40902)),x40903)) % 186.01/186.01 [4118]E(f335(f335(f108(f934(f934(x41181,a922),a922)),f335(f316(x41181),x41182)),f335(f316(x41181),x41183)),f335(f316(x41181),f335(f335(f108(f934(x41181,a922)),x41182),x41183))) % 186.01/186.01 [4121]E(f335(f335(f117(f934(x41211,a922)),f335(f85(f934(x41211,a922)),x41212)),x41213),f335(f85(f934(x41211,a922)),f335(f335(f23(f934(x41211,a922)),x41212),x41213))) % 186.01/186.01 [4131]E(f335(f335(f317(x41311),x41312),f335(f335(f23(f934(x41311,a922)),x41313),f335(f335(f317(x41311),x41312),f195(f934(x41311,a922))))),f335(f335(f317(x41311),x41312),x41313)) % 186.01/186.01 [4143]P1(f335(f335(f243(f934(x41431,a922)),x41432),f335(f335(f117(f934(x41431,a922)),x41433),x41432))) % 186.01/186.01 [4144]P1(f335(f335(f243(f934(x41441,a922)),x41442),f335(f335(f117(f934(x41441,a922)),x41442),x41443))) % 186.01/186.01 [4148]E(f335(f335(f117(f934(x41481,a922)),f335(f85(f934(x41481,a922)),x41482)),f335(f85(f934(x41481,a922)),x41483)),f335(f85(f934(x41481,a922)),f335(f335(f108(f934(x41481,a922)),x41482),x41483))) % 186.01/186.01 [4149]E(f335(f335(f108(f934(x41491,a922)),f335(f85(f934(x41491,a922)),x41492)),f335(f85(f934(x41491,a922)),x41493)),f335(f85(f934(x41491,a922)),f335(f335(f117(f934(x41491,a922)),x41492),x41493))) % 186.01/186.01 [4163]P1(f335(f335(f243(f934(x41631,a922)),f335(f179(x41631),x41632)),f335(f179(x41631),f335(f335(f158(x41631),x41633),x41632)))) % 186.01/186.01 [4175]E(f335(f335(f117(f934(x41751,a922)),f335(f335(f23(f934(x41751,a922)),x41752),x41753)),f335(f335(f108(f934(x41751,a922)),x41752),x41753)),x41752) % 186.01/186.01 [4226]E(f335(f335(f6(x42261,a1),f335(f335(f8(a927,a1,x42261),f107(a1)),x42262)),x42263),f335(f107(a1),f335(f335(f6(x42261,a927),x42262),x42263))) % 186.01/186.01 [4227]E(f335(f335(f9(x42271,a1),f335(f335(f8(a927,a1,x42271),f107(a1)),x42272)),x42273),f335(f107(a1),f335(f335(f9(x42271,a927),x42272),x42273))) % 186.01/186.01 [4274]E(f335(f335(f141(x42741),f184(x42741,x42742,x42743)),f335(f335(f145(x42741),f335(f196(f928(x42741)),f184(x42741,x42742,x42743))),x42743)),x42743) % 186.01/186.01 [4278]E(f335(f85(f934(f933(x42781,x42782),a922)),f335(f335(f262(x42781,x42782),x42783),f335(f16(f934(x42782,a922),x42781),f250(f934(x42782,a922))))),f335(f335(f262(x42781,x42782),f335(f85(f934(x42781,a922)),x42783)),f335(f16(f934(x42782,a922),x42781),f250(f934(x42782,a922))))) % 186.01/186.01 [4279]E(f335(f85(f934(f933(x42791,x42792),a922)),f335(f335(f262(x42791,x42792),f250(f934(x42791,a922))),f335(f16(f934(x42792,a922),x42791),x42793))),f335(f335(f262(x42791,x42792),f250(f934(x42791,a922))),f335(f16(f934(x42792,a922),x42791),f335(f85(f934(x42792,a922)),x42793)))) % 186.01/186.01 [4330]E(f335(f335(f45(f934(x43301,a922),f934(x43301,a922)),x43302),f335(f335(f7(f934(x43301,a922),f934(x43301,a922),f934(x43301,a922)),f108(f934(x43301,a922))),x43303)),f335(f335(f108(f934(x43301,a922)),f43(f934(x43301,a922),x43302)),x43303)) % 186.01/186.01 [4336]E(f335(f149(f928(x43361),f928(x43361),f141(x43361),f120(x43361)),f335(f335(f158(f928(x43361)),x43362),x43363)),f335(f335(f141(x43361),x43362),f335(f149(f928(x43361),f928(x43361),f141(x43361),f120(x43361)),x43363))) % 186.01/186.01 [4357]E(f335(f335(f317(f934(x43571,a922)),f335(f293(x43571,x43571,x43572),f335(f335(f317(x43571),x43573),f195(f934(x43571,a922))))),f195(f934(f934(x43571,a922),a922))),f335(f335(f66(x43571),f335(f335(f317(x43571),x43573),f195(f934(x43571,a922)))),x43572)) % 186.01/186.01 [4367]E(f335(f335(f86(a927),f335(f335(f87(a927),x43671),f335(f335(f42(a927),x43672),x43673))),f335(f335(f42(a927),f335(f335(f87(a927),x43671),f51(a927,x43672,x43673))),x43673)),f335(f335(f42(a927),f335(f335(f87(a927),x43671),x43672)),x43673)) % 186.01/186.01 [4368]E(f335(f335(f86(a1),f335(f335(f87(a1),x43681),f335(f335(f42(a1),x43682),x43683))),f335(f335(f42(a1),f335(f335(f87(a1),x43681),f51(a1,x43682,x43683))),x43683)),f335(f335(f42(a1),f335(f335(f87(a1),x43681),x43682)),x43683)) % 186.01/186.01 [4402]E(f335(f335(f23(f934(x44021,a922)),f335(f179(x44021),x44022)),f335(f335(f317(x44021),x44023),f195(f934(x44021,a922)))),f335(f179(x44021),f335(f143(x44021,f335(f335(f8(a922,a922,x44021),a330),f335(a332,x44023))),x44022))) % 186.01/186.01 [4452]E(f335(f335(f141(x44521),f335(f149(f928(x44521),f928(x44521),f141(x44521),f120(x44521)),x44522)),f335(f149(f928(x44521),f928(x44521),f141(x44521),f120(x44521)),x44523)),f335(f149(f928(x44521),f928(x44521),f141(x44521),f120(x44521)),f335(f335(f141(f928(x44521)),x44522),x44523))) % 186.01/186.01 [4455]E(f335(f335(f260(f928(x44551),f928(x44551)),f335(f143(x44551,x44552),x44553)),f335(f143(x44551,f335(f78(a922,a922,x44551,a330),x44552)),x44553)),f173(x44551,x44552,x44553)) % 186.01/186.01 [4458]E(f335(f335(f86(a927),f335(f335(f86(a927),f335(f335(f42(a927),x44581),x44582)),f335(f335(f42(a927),x44583),x44582))),f335(f335(f42(a927),f335(f335(f86(a927),f51(a927,x44581,x44582)),f51(a927,x44583,x44582))),x44582)),f335(f335(f42(a927),f335(f335(f86(a927),x44581),x44583)),x44582)) % 186.01/186.01 [4459]E(f335(f335(f86(a1),f335(f335(f86(a1),f335(f335(f42(a1),x44591),x44592)),f335(f335(f42(a1),x44593),x44592))),f335(f335(f42(a1),f335(f335(f86(a1),f51(a1,x44591,x44592)),f51(a1,x44593,x44592))),x44592)),f335(f335(f42(a1),f335(f335(f86(a1),x44591),x44593)),x44592)) % 186.01/186.01 [4512]E(f335(f335(f108(f934(f928(x45121),a922)),f335(f335(f7(f928(x45121),f934(f928(x45121),a922),a922),f337(f928(x45121))),f168(x45121,x45122))),f335(f335(f7(f928(x45121),f934(f928(x45121),a922),a922),f337(f928(x45121))),f168(x45121,x45123))),f167(x45121,f335(f335(f108(f934(x45121,a922)),f335(f335(f7(x45121,f934(x45121,a922),a922),f337(x45121)),x45122)),f335(f335(f7(x45121,f934(x45121,a922),a922),f337(x45121)),x45123)))) % 186.01/186.01 [4524]E(f335(f270(x45241),f335(f335(f18(x45241,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45241),a334),f335(f335(f7(x45241,x45241,a922),a332),x45242))),f335(f335(f7(x45241,f934(x45241,a922),a922),f337(x45241)),x45243))),f335(f335(f317(x45241),x45242),x45243)) % 186.01/186.01 [4544]E(f335(f335(f92(f928(f928(x45441)),f928(f928(x45441))),f60(x45441,x45442)),f335(f335(f18(f928(f928(x45441)),f928(f928(x45441)),f928(f928(x45441))),f335(f335(f8(f928(f928(x45441)),f934(f928(f928(x45441)),f928(f928(x45441))),f928(f928(x45441))),f141(f928(x45441))),f335(f161(f928(x45441),f928(x45441)),f335(f158(x45441),x45443)))),f5(f928(f928(x45441))))),f60(x45441,f335(f335(f158(x45441),x45443),x45442))) % 186.01/186.01 [4547]E(f335(f270(x45471),f335(f335(f18(x45471,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45471),a333),f335(f335(f7(x45471,f934(x45471,a922),a922),f337(x45471)),x45472))),f335(f335(f7(x45471,f934(x45471,a922),a922),f337(x45471)),x45473))),f335(f335(f108(f934(x45471,a922)),x45472),x45473)) % 186.01/186.01 [4548]E(f335(f270(x45481),f335(f335(f18(x45481,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45481),a334),f335(f335(f7(x45481,f934(x45481,a922),a922),f337(x45481)),x45482))),f335(f335(f7(x45481,f934(x45481,a922),a922),f337(x45481)),x45483))),f335(f335(f117(f934(x45481,a922)),x45482),x45483)) % 186.01/186.01 [4637]E(f335(f335(f45(x46371,f934(f934(x46371,a922),a922)),x46372),f335(f335(f7(x46371,f934(f934(x46371,a922),a922),f934(f934(x46371,a922),a922)),f335(f335(f8(f934(x46371,a922),f934(f934(f934(x46371,a922),a922),f934(f934(x46371,a922),a922)),x46371),f317(f934(x46371,a922))),f335(f335(f8(f934(x46371,a922),f934(x46371,a922),x46371),f293(x46371,x46371,x46373)),f335(f335(f7(x46371,f934(x46371,a922),f934(x46371,a922)),f317(x46371)),f195(f934(x46371,a922)))))),f195(f934(f934(x46371,a922),a922)))),f335(f335(f66(x46371),x46372),x46373)) % 186.01/186.01 [4639]E(f335(f335(f210(x46391),f335(f335(f87(a1),f335(f335(f78(f933(a1,a1),a1,x46391,f259(a1,a1)),f221(x46391)),x46392)),f335(f335(f78(f933(a1,a1),a1,x46391,f259(a1,a1)),f221(x46391)),x46393))),f335(f335(f87(a1),f335(f335(f78(f933(a1,a1),a1,x46391,f264(a1,a1)),f221(x46391)),x46392)),f335(f335(f78(f933(a1,a1),a1,x46391,f264(a1,a1)),f221(x46391)),x46393))),f237(x46391,x46392,x46393)) % 186.01/186.01 [4642]E(f335(f270(f928(x46421)),f335(f335(f18(f928(x46421),a922,a922),f335(f335(f8(a922,f934(a922,a922),f928(x46421)),a333),f335(f335(f7(f928(x46421),a927,a922),f335(f335(f8(a927,f934(a927,a922),f928(x46421)),a332),f196(f928(x46421)))),x46422))),f335(f335(f7(f928(x46421),f934(x46421,a922),a922),f335(f335(f8(f934(x46421,a922),f934(f934(x46421,a922),a922),f928(x46421)),f243(f934(x46421,a922))),f179(x46421))),f335(f179(x46421),x46423)))),f335(f179(f928(x46421)),f61(x46421,x46422,x46423))) % 186.01/186.01 [4044]E(f51(a927,f335(f335(f86(a927),f335(f335(f87(a927),x40441),x40442)),x40443),x40442),f51(a927,x40443,x40442)) % 186.01/186.01 [4089]E(f146(a927,f335(f310(a927,f335(f335(f86(a927),x40891),x40892)),x40893)),f335(f335(f145(a927),x40892),f146(a927,f335(f310(a927,x40891),x40893)))) % 186.01/186.01 [4130]E(f335(f335(f86(a1),f335(f107(a1),x41301)),f335(f335(f86(a1),f335(f107(a1),x41302)),x41303)),f335(f335(f86(a1),f335(f107(a1),f335(f335(f86(a927),x41301),x41302))),x41303)) % 186.01/186.01 [4139]E(f335(f335(f23(f934(x41391,a922)),f335(f335(f23(f934(x41391,a922)),x41392),x41393)),x41393),f335(f335(f23(f934(x41391,a922)),x41392),x41393)) % 186.01/186.01 [4140]E(f335(f335(f117(f934(x41401,a922)),f335(f335(f23(f934(x41401,a922)),x41402),x41403)),x41403),f335(f335(f117(f934(x41401,a922)),x41402),x41403)) % 186.01/186.01 [4164]E(f335(f335(f297(x41641,x41641,x41642),f315(x41641,f195(f934(f933(x41641,x41641),a922)))),x41643),x41643) % 186.01/186.01 [4172]E(f335(f335(f117(f934(x41721,a922)),f335(f289(x41721),x41722)),f335(f289(x41721),x41723)),f335(f289(x41721),f335(f335(f117(f934(f933(x41721,x41721),a922)),x41722),x41723))) % 186.01/186.01 [4182]E(f274(x41821,f335(f335(f158(f933(a106,x41821)),f335(f335(f260(a106,x41821),f2(a106)),x41822)),x41823)),f274(x41821,x41823)) % 186.01/186.01 [4184]E(f335(f335(f108(f934(x41841,a922)),f44(f934(x41841,a922),x41842)),f44(f934(x41841,a922),x41843)),f44(f934(x41841,a922),f335(f335(f117(f934(f934(x41841,a922),a922)),x41842),x41843))) % 186.01/186.01 [4185]E(f335(f335(f117(f934(x41851,a922)),f43(f934(x41851,a922),x41852)),f43(f934(x41851,a922),x41853)),f43(f934(x41851,a922),f335(f335(f117(f934(f934(x41851,a922),a922)),x41852),x41853))) % 186.01/186.01 [4222]E(f335(f335(f297(x42221,x42221,x42221),f335(f335(f190(f933(x42221,x42221),a922),x42222),x42223)),x42223),f335(f335(f190(f933(x42221,x42221),a922),f335(a119,x42222)),x42223)) % 186.01/186.01 [4266]P1(f335(f335(f243(f934(x42661,a922)),f335(f335(f23(f934(x42661,a922)),x42662),x42663)),x42662)) % 186.01/186.01 [4267]P1(f335(f335(f243(f934(x42671,a922)),f335(f335(f108(f934(x42671,a922)),x42672),x42673)),x42673)) % 186.01/186.01 [4268]P1(f335(f335(f243(f934(x42681,a922)),f335(f335(f108(f934(x42681,a922)),x42682),x42683)),x42682)) % 186.01/186.01 [4292]E(f315(x42921,f335(f335(f117(f934(f933(x42921,x42921),a922)),f315(x42921,x42922)),f315(x42921,x42923))),f315(x42921,f335(f335(f117(f934(f933(x42921,x42921),a922)),x42922),x42923))) % 186.01/186.01 [4296]E(f44(f934(x42961,a922),f335(f335(f317(f934(x42961,a922)),x42962),f335(f335(f317(f934(x42961,a922)),x42963),f195(f934(f934(x42961,a922),a922))))),f335(f335(f108(f934(x42961,a922)),x42962),x42963)) % 186.01/186.01 [4297]E(f43(f934(x42971,a922),f335(f335(f317(f934(x42971,a922)),x42972),f335(f335(f317(f934(x42971,a922)),x42973),f195(f934(f934(x42971,a922),a922))))),f335(f335(f117(f934(x42971,a922)),x42972),x42973)) % 186.01/186.01 [4302]E(f335(f335(f297(x43021,x43021,x43021),f335(f335(f190(f933(x43021,x43021),a922),x43022),x43023)),x43023),f335(f335(f297(x43021,x43021,x43021),x43023),f335(f335(f190(f933(x43021,x43021),a922),x43022),x43023))) % 186.01/186.01 [4371]E(f335(f335(f117(f934(x43711,a922)),f335(f270(x43711),f335(f335(f7(x43711,x43711,a922),a332),x43712))),x43713),f335(f335(f317(x43711),x43712),x43713)) % 186.01/186.01 [4373]E(f335(a111,f335(f335(f6(x43731,a1),f335(f335(f8(a927,a1,x43731),f107(a1)),x43732)),x43733)),f335(f335(f6(x43731,a927),x43732),x43733)) % 186.01/186.01 [4374]E(f335(a111,f335(f335(f9(x43741,a1),f335(f335(f8(a927,a1,x43741),f107(a1)),x43742)),x43743)),f335(f335(f9(x43741,a927),x43742),x43743)) % 186.01/186.01 [4449]E(f335(f163(f928(x44491),x44491,f335(f178(x44491),x44492),f335(f16(f934(f928(x44491),f928(x44491)),x44491),f335(f335(f7(f928(x44491),f928(x44491),f928(x44491)),f141(x44491)),x44492))),x44493),f335(f178(x44491),f335(f335(f141(x44491),x44493),x44492))) % 186.01/186.01 [4477]P1(f335(f335(f243(f934(f934(x44771,a922),a922)),f335(f335(f117(f934(f934(x44771,a922),a922)),f335(f316(x44771),x44772)),f335(f316(x44771),x44773))),f335(f316(x44771),f335(f335(f117(f934(x44771,a922)),x44772),x44773)))) % 186.01/186.01 [4566]E(f335(f270(x45661),f335(f335(f18(x45661,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45661),a333),f335(f335(f7(x45661,f934(x45661,a922),a922),f337(x45661)),x45662))),f335(f335(f8(a922,a922,x45661),a330),f335(f335(f7(x45661,f934(x45661,a922),a922),f337(x45661)),x45663)))),f335(f335(f23(f934(x45661,a922)),x45662),x45663)) % 186.01/186.01 [4590]E(f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,a927,a922),f244(a927)),f335(f196(f928(x45901)),x45902)))),f335(f335(f8(x45901,a922,a927),x45903),f335(f171(x45901),x45902))))),f335(f196(f928(x45901)),f335(f143(x45901,x45903),x45902))) % 186.01/186.01 [4592]E(f335(f196(f928(x45921)),f183(x45921,x45922,x45923)),f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,a927,a922),f244(a927)),f335(f196(f928(x45921)),x45922)))),f335(f335(f7(a927,f934(a927,a922),a922),f337(a927)),x45923))))) % 186.01/186.01 [4690]E(f335(f335(f108(f934(f933(f928(x46901),f928(x46901)),a922)),f335(f318(f933(f933(x46901,f928(x46901)),f933(x46901,f928(x46901))),f933(f928(x46901),f928(x46901)),f266(f933(x46901,f928(x46901)),f928(x46901),f933(x46901,f928(x46901)),f928(x46901),f335(f265(x46901,f928(x46901),f928(x46901)),f158(x46901)),f335(f265(x46901,f928(x46901),f928(x46901)),f158(x46901)))),f328(x46901,f928(x46901),x46902,f335(f150(x46901,x46902),x46903)))),f335(f270(f933(f928(x46901),f928(x46901))),f335(f265(f928(x46901),f928(x46901),a922),f335(f335(f7(f928(x46901),f934(f928(x46901),a922),f934(f928(x46901),a922)),f335(f335(f8(f934(a922,a922),f934(f934(f928(x46901),a922),f934(f928(x46901),a922)),f928(x46901)),f8(a922,a922,f928(x46901))),f335(f335(f8(a922,f934(a922,a922),f928(x46901)),a333),f335(f335(f7(f928(x46901),a927,a922),f335(f335(f8(a927,f934(a927,a922),f928(x46901)),a332),f196(f928(x46901)))),f335(a119,x46903))))),f335(f335(f7(f928(x46901),a927,a922),f335(f335(f8(a927,f934(a927,a922),f928(x46901)),a332),f196(f928(x46901)))),f335(a119,x46903)))))),f335(f150(x46901,x46902),f335(a119,x46903))) % 186.01/186.01 [4186]E(f51(a927,f335(a119,f335(f335(f86(a927),f335(f335(f87(a927),x41861),x41862)),x41863)),x41862),f51(a927,f335(a119,x41863),x41862)) % 186.01/186.01 [4435]E(f335(f270(x44351),f335(f335(f18(x44351,a922,a922),f335(f335(f8(a922,f934(a922,a922),x44351),a333),x44352)),x44353)),f335(f335(f108(f934(x44351,a922)),f335(f270(x44351),x44352)),f335(f270(x44351),x44353))) % 186.01/186.01 [4436]E(f335(f270(x44361),f335(f335(f18(x44361,a922,a922),f335(f335(f8(a922,f934(a922,a922),x44361),a334),x44362)),x44363)),f335(f335(f117(f934(x44361,a922)),f335(f270(x44361),x44362)),f335(f270(x44361),x44363))) % 186.01/186.01 [4438]E(f335(f335(f141(x44381),f335(f335(f145(x44381),f51(a927,x44382,f335(f196(f928(x44381)),x44383))),x44383)),f335(f335(f182(x44381),f51(a927,x44382,f335(f196(f928(x44381)),x44383))),x44383)),f335(f335(f335(f190(f928(x44381),f928(x44381)),x44382),f174(x44381)),x44383)) % 186.01/186.01 [4444]E(f335(f270(x44441),f335(f335(f18(x44441,a922,a922),f335(f335(f8(a922,f934(a922,a922),x44441),a338),x44442)),x44443)),f335(f335(f117(f934(x44441,a922)),f335(f85(f934(x44441,a922)),f335(f270(x44441),x44442))),f335(f270(x44441),x44443))) % 186.01/186.01 [4460]E(f335(f335(f86(a927),f335(f196(f928(x44601)),f335(f143(x44601,x44602),x44603))),f335(f196(f928(x44601)),f335(f143(x44601,f335(f335(f8(a922,a922,x44601),a330),x44602)),x44603))),f335(f196(f928(x44601)),x44603)) % 186.01/186.01 [4483]P1(f335(f335(f243(f934(x44831,a922)),f335(f335(f117(f934(x44831,a922)),f44(f934(x44831,a922),x44832)),f44(f934(x44831,a922),x44833))),f44(f934(x44831,a922),f335(f335(f108(f934(f934(x44831,a922),a922)),x44832),x44833)))) % 186.01/186.01 [4497]E(f335(f179(x44971),f335(f143(x44971,f335(f335(f8(a922,a922,x44971),a330),f335(f335(f7(x44971,x44971,a922),a332),x44972))),x44973)),f335(f335(f23(f934(x44971,a922)),f335(f179(x44971),x44973)),f335(f335(f317(x44971),x44972),f195(f934(x44971,a922))))) % 186.01/186.01 [4506]P1(f335(f335(f243(f934(f933(x45061,x45061),a922)),f335(f335(f117(f934(f933(x45061,x45061),a922)),f315(x45061,x45062)),f315(x45061,x45063))),f315(x45061,f335(f335(f117(f934(f933(x45061,x45061),a922)),x45062),x45063)))) % 186.01/186.01 [4529]E(f335(f335(f87(a927),f335(a119,f335(a119,f2(a927)))),f335(f335(f6(a927,a927),f335(f335(f8(a927,a927,a927),f335(f86(a927),x45291)),f335(f335(f7(a927,a927,a927),f87(a927)),x45292))),f335(f290(a927),x45293))),f335(f335(f87(a927),x45293),f335(f335(f86(a927),x45291),f335(f335(f86(a927),x45291),f335(f335(f87(a927),f335(f335(f23(a927),x45293),f84(a927))),x45292))))) % 186.01/186.01 [4539]E(f335(f270(x45391),f335(f335(f18(x45391,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45391),a333),f335(f335(f7(x45391,f934(x45391,a922),a922),f337(x45391)),f335(f179(x45391),x45392)))),x45393)),f335(f179(x45391),f335(f143(x45391,x45393),x45392))) % 186.01/186.01 [4689]E(f335(f270(x46891),f335(f335(f8(f934(a927,a922),a922,x46891),f93(a927)),f335(f335(f7(x46891,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),x46891),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),x46891),f335(f8(a922,f934(a922,a922),a927),a333)),f335(f335(f7(x46891,f934(a927,x46891),f934(a927,a922)),f335(f335(f8(f934(x46891,a922),f934(f934(a927,x46891),f934(a927,a922)),x46891),f8(x46891,a922,a927)),a332)),f335(f171(x46891),x46892))))),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,a927,a922),f244(a927)),f335(f196(f928(x46891)),x46892)))),f335(f335(f7(a927,f934(a927,a922),a922),f337(a927)),x46893))))),f335(f179(x46891),f183(x46891,x46892,x46893))) % 186.01/186.01 [4579]E(f335(f270(x45791),f335(f335(f18(x45791,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45791),a338),f335(f335(f8(a922,a922,x45791),a330),f335(f335(f7(x45791,x45791,a922),a332),x45792)))),x45793)),f335(f335(f317(x45791),x45792),f335(f270(x45791),x45793))) % 186.01/186.01 [4611]E(f335(f335(f161(f933(x46111,a927),x46111),f259(x46111,a927)),f335(f143(f933(x46111,a927),f335(f335(f7(f933(x46111,a927),f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),f933(x46111,a927)),f337(a927)),f264(x46111,a927))),x46112)),f335(f335(f188(x46111,a927),x46113),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(x46111)),x46113)))))),f183(x46111,x46113,x46112)) % 186.01/186.01 [4638]E(f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f6(a927,a1),f335(f335(f8(a1,a1,a927),f335(f86(a1),x46381)),f335(f335(f7(a927,a1,a1),f335(f335(f8(a1,f934(a1,a1),a927),f87(a1)),f107(a1))),x46382))),f335(f290(a927),x46383))),f335(f335(f87(a1),f335(f107(a1),x46383)),f335(f335(f86(a1),x46381),f335(f335(f86(a1),x46381),f335(f335(f87(a1),f335(f107(a1),f335(f335(f23(a927),x46383),f84(a927)))),x46382))))) % 186.01/186.01 [4682]E(f335(f270(f933(x46821,x46822)),f335(f265(x46821,x46822,a922),f335(f335(f7(x46821,f934(f933(x46822,x46821),a922),f934(x46822,a922)),f335(f335(f8(f934(x46822,f934(f934(f933(x46822,x46821),a922),a922)),f934(f934(f933(x46822,x46821),a922),f934(x46822,a922)),x46821),f7(x46822,f934(f933(x46822,x46821),a922),a922)),f335(f335(f8(f934(x46822,f933(x46822,x46821)),f934(x46822,f934(f934(f933(x46822,x46821),a922),a922)),x46821),f335(f8(f933(x46822,x46821),f934(f934(f933(x46822,x46821),a922),a922),x46822),f337(f933(x46822,x46821)))),f335(f7(x46822,x46821,f933(x46822,x46821)),f260(x46822,x46821))))),x46823))),f335(f294(x46822,x46821),x46823)) % 186.01/186.01 [4702]E(f335(f270(f928(x47021)),f335(f335(f8(f934(x47021,a922),a922,f928(x47021)),f93(x47021)),f335(f335(f8(f934(x47021,f934(f928(x47021),a922)),f934(x47021,a922),f928(x47021)),f335(f8(f934(f928(x47021),a922),a922,x47021),f93(f928(x47021)))),f335(f335(f7(f928(x47021),f934(x47021,f934(f928(x47021),a922)),f934(x47021,f934(f928(x47021),a922))),f335(f335(f8(f934(x47021,f934(f934(f928(x47021),a922),f934(f928(x47021),a922))),f934(f934(x47021,f934(f928(x47021),a922)),f934(x47021,f934(f928(x47021),a922))),f928(x47021)),f18(x47021,f934(f928(x47021),a922),f934(f928(x47021),a922))),f335(f335(f8(f934(x47021,f934(f928(x47021),f934(a922,a922))),f934(x47021,f934(f934(f928(x47021),a922),f934(f928(x47021),a922))),f928(x47021)),f335(f8(f934(f928(x47021),f934(a922,a922)),f934(f934(f928(x47021),a922),f934(f928(x47021),a922)),x47021),f18(f928(x47021),a922,a922))),f335(f335(f8(f934(x47021,f934(f928(x47021),a922)),f934(x47021,f934(f928(x47021),f934(a922,a922))),f928(x47021)),f335(f8(f934(f928(x47021),a922),f934(f928(x47021),f934(a922,a922)),x47021),f335(f8(a922,f934(a922,a922),f928(x47021)),a333))),f335(f335(f7(f928(x47021),f934(x47021,f934(f928(x47021),f928(x47021))),f934(x47021,f934(f928(x47021),a922))),f335(f335(f8(f934(f934(f928(x47021),f928(x47021)),f934(f928(x47021),a922)),f934(f934(x47021,f934(f928(x47021),f928(x47021))),f934(x47021,f934(f928(x47021),a922))),f928(x47021)),f8(f934(f928(x47021),f928(x47021)),f934(f928(x47021),a922),x47021)),f335(f335(f8(f934(f928(x47021),a922),f934(f934(f928(x47021),f928(x47021)),f934(f928(x47021),a922)),f928(x47021)),f8(f928(x47021),a922,f928(x47021))),a332))),f158(x47021)))))),f335(f335(f7(x47021,f934(f928(x47021),a922),f934(f928(x47021),a922)),f335(f335(f8(f934(a922,a922),f934(f934(f928(x47021),a922),f934(f928(x47021),a922)),x47021),f8(a922,a922,f928(x47021))),f335(f335(f8(a922,f934(a922,a922),x47021),a333),f335(f335(f7(x47021,f934(x47021,a922),a922),f337(x47021)),x47022)))),f335(f335(f7(f928(x47021),f934(f928(x47021),a922),a922),f337(f928(x47021))),x47023)))))),f181(x47021,x47022,x47023)) % 186.01/186.01 [4699]E(f335(f335(f92(a1,f933(a1,a1)),f335(f335(f23(a1),x46991),x46992)),f335(f335(f7(a1,f933(a1,a1),f933(a1,a1)),f335(f335(f18(a1,f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),f335(f335(f8(a922,f934(f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),a1),f103(f933(a1,a1))),f335(f243(a1),f2(a1)))),f335(f260(a1,a1),f335(f335(f86(a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x46993)),f84(a1))))),f335(f335(f260(a1,a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x46993)),x46991))),f335(f49(x46992),f335(f335(f260(a1,a1),x46993),x46991))) % 186.01/186.01 [4726]~E(f31(x47261,x47262),f32(x47263,x47264)) % 186.01/186.01 [4729]~E(f27(x47291,x47292),f32(x47293,x47294)) % 186.01/186.01 [4730]~E(f27(x47301,x47302),f31(x47303,x47304)) % 186.01/186.01 [3737]E(f123(x37371,f335(x37372,x37373),f335(x37374,x37373)),f335(f212(x37371,x37372,x37374),x37373)) % 186.01/186.01 [3790]E(f335(f335(f253(x37901,x37902,x37903),x37904),f2(a927)),x37902) % 186.01/186.01 [3803]E(f36(x38031,x38032,x38033,f33(x38034)),f335(x38033,x38034)) % 186.01/186.01 [3804]E(f36(x38041,x38042,x38043,f34(x38044)),f335(x38042,x38044)) % 186.01/186.01 [3805]E(f37(x38051,x38052,x38053,f33(x38054)),f335(x38053,x38054)) % 186.01/186.01 [3806]E(f37(x38061,x38062,x38063,f34(x38064)),f335(x38062,x38064)) % 186.01/186.01 [3833]E(f192(x38331,x38332,x38333,f335(a119,x38334)),f335(x38333,x38334)) % 186.01/186.01 [3874]E(f177(x38741,x38742,f177(x38741,x38743,x38744)),f177(x38741,x38743,f177(x38741,x38742,x38744))) % 186.01/186.01 [3875]E(f133(x38751,x38752,f123(x38751,x38753,x38754)),f123(x38751,f133(x38751,x38752,x38753),x38754)) % 186.01/186.01 [4010]E(f335(f163(x40101,x40102,x40103,x40104),f120(x40102)),x40103) % 186.01/186.01 [4011]E(f335(f149(x40111,x40112,x40113,x40114),f120(x40112)),x40114) % 186.01/186.01 [4018]E(f335(f196(f926(x40181)),f98(x40181,x40182,x40183,x40184)),f2(a927)) % 186.01/186.01 [4050]E(f335(f196(f932(x40501,x40502)),f229(x40501,x40502,x40503,x40504)),f2(a927)) % 186.01/186.01 [4073]E(f335(f265(x40731,x40732,x40733),f263(x40731,x40732,x40733,x40734)),x40734) % 186.01/186.01 [4117]E(f335(f335(f141(x41171),f176(x41171,x41172,x41173)),f176(x41171,x41174,x41173)),f335(f335(f141(x41171),f176(x41171,x41174,x41173)),f176(x41171,x41172,x41173))) % 186.01/186.01 [4205]E(f335(f335(f267(x42051,x42052,x42053,f933(x42052,x42053)),x42054),f260(x42052,x42053)),x42054) % 186.01/186.01 [4215]E(f134(x42151,x42152,x42153,x42154,f126(x42152)),x42153) % 186.01/186.01 [4221]E(f80(x42211,x42212,x42213,x42214,f335(x42213,x42214)),x42213) % 186.01/186.01 [4490]P43(x44901,x44902,x44903,x44904,f195(f934(x44901,a922)),x44904) % 186.01/186.01 [3539]E(f335(f335(f16(x35391,x35392),x35393),x35394),x35393) % 186.01/186.01 [3823]E(f177(x38231,x38232,f335(f143(x38231,x38233),x38234)),f335(f143(x38231,x38233),f177(x38231,x38232,x38234))) % 186.01/186.01 [3857]E(f335(f335(f70(x38571,x38572,x38573),x38574),f195(f934(x38571,a922))),x38574) % 186.01/186.01 [3881]E(f335(f335(f171(x38811),f335(f335(f158(x38811),x38812),x38813)),f335(a119,x38814)),f335(f335(f171(x38811),x38813),x38814)) % 186.01/186.01 [3949]E(f335(f335(x39491,x39492),f335(f191(x39493,x39494,x39491),x39492)),f335(f191(x39493,x39494,x39491),f335(a119,x39492))) % 186.01/186.01 [3991]E(f263(x39911,x39912,x39913,f335(f265(x39911,x39912,x39913),x39914)),x39914) % 186.01/186.01 [4048]E(f335(f335(f166(x40481,f335(f335(f158(x40481),x40482),x40483)),f2(a927)),x40484),f335(f335(f158(x40481),x40484),x40483)) % 186.01/186.01 [4058]E(f335(f335(f45(f934(x40581,a922),f934(x40582,a922)),x40583),f318(x40581,x40582,x40584)),f335(f318(x40581,x40582,x40584),f43(f934(x40581,a922),x40583))) % 186.01/186.01 [4059]E(f335(f335(f45(f934(x40591,a922),f934(x40592,a922)),x40593),f319(x40592,x40591,x40594)),f335(f319(x40592,x40591,x40594),f43(f934(x40591,a922),x40593))) % 186.01/186.01 [4084]E(f127(x40841,f137(x40842,f929(x40841),x40843,x40844)),f335(f125(x40842,x40841,x40844),x40843)) % 186.01/186.01 [4160]E(f335(f132(x41601,x41602),f133(x41601,x41603,x41604)),f335(f335(f86(a927),f335(f335(f86(a927),f335(x41602,x41603)),f335(f132(x41601,x41602),x41604))),f335(a119,f2(a927)))) % 186.01/186.01 [4181]E(f335(f149(x41811,x41812,f335(f7(x41812,x41811,x41811),x41813),x41814),f335(f175(x41812),f120(x41812))),x41814) % 186.01/186.01 [4225]E(f82(x42251,x42252,x42253,x42254,f195(f934(x42251,a922))),x42253) % 186.01/186.01 [4286]E(f232(x42861,f933(x42862,f929(x42862)),x42863,f335(f265(x42862,f929(x42862),x42861),x42864),f335(f142(x42862),f126(x42862))),x42863) % 186.01/186.01 [4420]E(f335(f265(x44201,x44202,x44203),f335(f335(f8(f934(x44202,f933(x44201,x44202)),f934(x44202,x44203),x44201),f335(f8(f933(x44201,x44202),x44203,x44202),x44204)),f260(x44201,x44202))),x44204) % 186.01/186.01 [3728]E(f335(f264(x37281,x37282),f335(f335(f260(x37281,x37282),x37283),x37284)),x37284) % 186.01/186.01 [3729]E(f335(f259(x37291,x37292),f335(f335(f260(x37291,x37292),x37293),x37294)),x37293) % 186.01/186.01 [3762]E(f335(f196(f928(x37621)),f335(f335(f166(x37621,x37622),x37623),x37624)),f335(f196(f928(x37621)),x37622)) % 186.01/186.01 [3763]E(f335(f196(f928(x37631)),f335(f335(f161(x37632,x37631),x37633),x37634)),f335(f196(f928(x37632)),x37634)) % 186.01/186.01 [3784]E(f335(f335(f145(x37841),f335(a119,x37842)),f335(f335(f158(x37841),x37843),x37844)),f335(f335(f145(x37841),x37842),x37844)) % 186.01/186.01 [3852]E(f335(f335(f182(x38521),x38522),f176(x38521,x38523,x38524)),f176(x38521,f335(f335(f241(a927),x38522),x38523),x38524)) % 186.01/186.01 [3853]E(f335(f335(f145(x38531),x38532),f176(x38531,x38533,x38534)),f176(x38531,f335(f335(f23(a927),x38533),x38532),x38534)) % 186.01/186.01 [3859]E(f335(f335(f317(x38591),x38592),f335(f335(f317(x38591),x38593),x38594)),f335(f335(f317(x38591),x38593),f335(f335(f317(x38591),x38592),x38594))) % 186.01/186.01 [3863]E(f335(f335(f161(x38631,x38632),x38633),f121(x38631,x38634)),f121(x38632,f335(f335(f161(x38631,x38632),x38633),x38634))) % 186.01/186.01 [3879]E(f335(f175(x38791),f335(f335(f161(x38792,x38791),x38793),x38794)),f335(f335(f161(x38792,x38791),x38793),f335(f175(x38792),x38794))) % 186.01/186.01 [3880]E(f335(f335(f161(x38801,x38802),x38803),f335(f178(x38801),x38804)),f335(f178(x38802),f335(f335(f161(x38801,x38802),x38803),x38804))) % 186.01/186.01 [3895]E(f335(f335(f182(x38951),f335(a119,x38952)),f335(f335(f158(x38951),x38953),x38954)),f335(f335(f158(x38951),x38953),f335(f335(f182(x38951),x38952),x38954))) % 186.01/186.01 [3899]E(f335(f179(x38991),f335(f335(f161(x38992,x38991),x38993),x38994)),f335(f318(x38992,x38991,x38993),f335(f179(x38992),x38994))) % 186.01/186.01 [3912]E(f335(f335(f161(x39121,x39122),f335(f16(x39122,x39121),x39123)),x39124),f176(x39122,f335(f196(f928(x39121)),x39124),x39123)) % 186.01/186.01 [3948]E(f17(x39481,x39482,x39483,f335(a3,f335(a119,f335(a20,x39484)))),f335(x39483,x39484)) % 186.01/186.01 [3952]E(f335(f335(f141(x39521),f335(f143(x39521,x39522),x39523)),f335(f143(x39521,x39522),x39524)),f335(f143(x39521,x39522),f335(f335(f141(x39521),x39523),x39524))) % 186.01/186.01 [3965]E(f159(x39651,f335(f335(f161(x39652,x39651),x39653),f159(x39652,x39654))),f159(x39651,f335(f335(f161(x39652,x39651),x39653),x39654))) % 186.01/186.01 [3980]E(f335(f294(x39801,x39801),f335(f335(f296(x39802,x39801),x39803),x39804)),f335(f335(f296(x39802,x39801),f335(f294(x39802,x39802),x39803)),x39804)) % 186.01/186.01 [3992]E(f335(f335(f297(x39921,x39922,x39923),x39924),f195(f934(f933(x39922,x39923),a922))),f195(f934(f933(x39921,x39923),a922))) % 186.01/186.01 [3993]E(f335(f335(f182(x39931),f335(f335(f23(a927),x39932),x39933)),f335(f335(f145(x39931),x39933),x39934)),f335(f335(f145(x39931),x39933),f335(f335(f182(x39931),x39932),x39934))) % 186.01/186.01 [4012]E(f335(f335(f141(x40121),f176(x40121,x40122,x40123)),f176(x40121,x40124,x40123)),f176(x40121,f335(f335(f86(a927),x40122),x40124),x40123)) % 186.01/186.01 [4013]E(f335(f335(f335(f286(x40131),x40132),x40133),x40134),f335(f260(f934(a106,f934(a922,f931(f929(x40131)))),f933(a106,a106)),f335(f48(x40131),x40132))) % 186.01/186.01 [4041]E(f44(f934(x40411,a922),f335(f318(x40412,f934(x40411,a922),x40413),x40414)),f335(f335(f46(x40412,f934(x40411,a922)),x40414),x40413)) % 186.01/186.01 [4042]E(f43(f934(x40421,a922),f335(f318(x40422,f934(x40421,a922),x40423),x40424)),f335(f335(f45(x40422,f934(x40421,a922)),x40424),x40423)) % 186.01/186.01 [4043]E(f335(f196(f928(f933(x40431,x40432))),f335(f335(f188(x40431,x40432),x40433),x40434)),f335(f335(f241(a927),f335(f196(f928(x40431)),x40433)),f335(f196(f928(x40432)),x40434))) % 186.01/186.01 [4045]E(f335(f319(x40451,x40452,x40453),f335(f85(f934(x40452,a922)),x40454)),f335(f85(f934(x40451,a922)),f335(f319(x40451,x40452,x40453),x40454))) % 186.01/186.01 [4094]E(f335(f319(x40941,x40942,x40943),f335(f270(x40942),x40944)),f335(f270(x40941),f335(f335(f8(x40942,a922,x40941),x40944),x40943))) % 186.01/186.01 [4112]E(f335(f335(f171(x41121),f335(f335(f141(x41121),x41122),f335(f335(f158(x41121),x41123),x41124))),f335(f196(f928(x41121)),x41122)),x41123) % 186.01/186.01 [4137]E(f335(f318(x41371,x41372,x41373),f335(f319(x41371,x41372,x41373),x41374)),f335(f335(f108(f934(x41372,a922)),x41374),f335(f318(x41371,x41372,x41373),f250(f934(x41371,a922))))) % 186.01/186.01 [4156]P1(f335(f335(f337(x41561),f335(x41562,x41563)),f335(f318(x41564,x41561,x41562),f250(f934(x41564,a922))))) % 186.01/186.01 [4165]E(f19(x41651,x41652,x41653,f335(a3,f335(a119,f335(a20,x41654)))),f335(f335(x41653,x41654),f19(x41651,x41652,x41653,x41654))) % 186.01/186.01 [4169]E(f335(f335(f141(x41691),f176(x41691,x41692,x41693)),f335(f335(f158(x41691),x41693),x41694)),f335(f335(f158(x41691),x41693),f335(f335(f141(x41691),f176(x41691,x41692,x41693)),x41694))) % 186.01/186.01 [4171]E(f335(f335(f262(x41711,x41712),f335(f179(x41711),x41713)),f335(f16(f934(x41712,a922),x41711),f335(f179(x41712),x41714))),f335(f179(f933(x41711,x41712)),f65(x41711,x41712,x41713,x41714))) % 186.01/186.01 [4183]E(f162(x41831,x41832,f335(f335(f158(x41831),x41833),x41834)),f335(f335(f86(a927),f335(f335(f86(a927),f335(x41832,x41833)),f162(x41831,x41832,x41834))),f335(a119,f2(a927)))) % 186.01/186.01 [4196]E(f192(f928(x41961),f335(f335(f158(x41961),x41962),x41963),f335(f335(f7(a927,f928(x41961),f928(x41961)),f145(x41961)),x41963),x41964),f335(f335(f145(x41961),x41964),f335(f335(f158(x41961),x41962),x41963))) % 186.01/186.01 [4197]P26(x41971,f933(x41972,x41971),f339(x41973,x41974,x41972,x41971),f335(f335(f45(x41972,f934(x41971,a922)),x41974),x41973)) % 186.01/186.01 [4206]E(f335(f335(f23(f934(x42061,a922)),f335(f335(f23(f934(x42061,a922)),x42062),x42063)),f335(f335(f317(x42061),x42064),f195(f934(x42061,a922)))),f335(f335(f23(f934(x42061,a922)),x42062),f335(f335(f317(x42061),x42064),x42063))) % 186.01/186.01 [4219]E(f335(f335(f190(f934(x42191,x42192),f934(x42191,x42192)),x42193),f78(x42192,x42192,x42191,x42194)),f78(x42192,x42192,x42191,f335(f335(f190(x42192,x42192),x42193),x42194))) % 186.01/186.01 [4291]E(f335(f335(f335(f190(f928(x42911),f928(x42911)),x42912),f174(x42911)),f335(f335(f335(f190(f928(x42911),f928(x42911)),x42913),f174(x42911)),x42914)),f335(f335(f335(f190(f928(x42911),f928(x42911)),f335(f335(f86(a927),x42912),x42913)),f174(x42911)),x42914)) % 186.01/186.01 [4376]P1(f335(f335(f243(f934(x43761,a922)),f335(f179(x43761),f335(f335(f166(x43761,x43762),x43763),x43764))),f335(f335(f317(x43761),x43764),f335(f179(x43761),x43762)))) % 186.01/186.01 [4410]E(f335(f335(f45(f934(x44101,a922),f934(f933(x44101,x44102),a922)),x44103),f335(f335(f7(f934(x44101,a922),f934(x44101,f934(x44102,a922)),f934(f933(x44101,x44102),a922)),f262(x44101,x44102)),x44104)),f335(f335(f262(x44101,x44102),f43(f934(x44101,a922),x44103)),x44104)) % 186.01/186.01 [4448]E(f218(x44481,x44482,x44483,f335(f78(x44482,f934(a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(x44482))))),x44481,f217(x44482)),x44484)),f219(x44481,x44482,x44484,x44483)) % 186.01/186.01 [4463]E(f214(x44631,x44632,x44633,f335(f78(x44632,f934(a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(f931(x44632)))))),x44631,f213(x44632)),x44634)),f215(x44631,x44632,x44634,x44633)) % 186.01/186.01 [4468]P1(f335(f72(x44681,x44682,x44683,x44684,f195(f934(x44681,a922))),x44684)) % 186.01/186.01 [4507]E(f335(f335(f45(x45071,f934(x45072,a922)),x45073),f335(f335(f7(x45071,f934(x45072,a922),f934(x45072,a922)),f335(f335(f8(x45072,f934(f934(x45072,a922),f934(x45072,a922)),x45071),f317(x45072)),x45074)),f195(f934(x45072,a922)))),f335(f318(x45071,x45072,x45074),x45073)) % 186.01/186.01 [4514]P1(f335(f335(f243(f934(x45141,a922)),f335(f292(x45142,x45141),f335(f335(f108(f934(f933(x45142,x45141),a922)),x45143),x45144))),f335(f335(f108(f934(x45141,a922)),f335(f292(x45142,x45141),x45143)),f335(f292(x45142,x45141),x45144)))) % 186.01/186.01 [4515]P1(f335(f335(f243(f934(x45151,a922)),f335(f272(x45151,x45152),f335(f335(f108(f934(f933(x45151,x45152),a922)),x45153),x45154))),f335(f335(f108(f934(x45151,a922)),f335(f272(x45151,x45152),x45153)),f335(f272(x45151,x45152),x45154)))) % 186.01/186.01 [4575]P1(f335(f335(f243(f934(f933(x45751,x45752),a922)),f335(f318(x45752,f933(x45751,x45752),f339(x45753,x45754,x45751,x45752)),f335(f335(f45(x45751,f934(x45752,a922)),x45754),x45753))),f335(f335(f262(x45751,x45752),x45754),x45753))) % 186.01/186.01 [4576]E(f335(f125(x45761,f933(x45761,x45762),x45763),f335(f335(f8(f934(x45762,f929(f933(x45761,x45762))),f929(f933(x45761,x45762)),x45761),f125(x45762,f933(x45761,x45762),x45764)),f335(f335(f8(f934(x45762,f933(x45761,x45762)),f934(x45762,f929(f933(x45761,x45762))),x45761),f335(f8(f933(x45761,x45762),f929(f933(x45761,x45762)),x45762),f136(f933(x45761,x45762)))),f260(x45761,x45762)))),f138(x45761,x45762,x45763,x45764)) % 186.01/186.01 [4577]E(f284(x45771,x45772,x45773,f335(f78(x45772,f934(a106,f934(a106,f934(f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x45772)))),f933(a106,a106))))),x45771,f286(x45772)),x45774)),f287(x45771,x45772,x45774,x45773)) % 186.01/186.01 [4617]E(f91(f933(x46171,x46172),f335(f265(x46171,x46172,a922),f335(f335(f7(x46171,f934(x46172,a922),f934(x46172,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46172,a922),f934(x46172,a922)),x46171),f8(a922,a922,x46172)),f335(f335(f8(a922,f934(a922,a922),x46171),a333),f335(a332,x46173)))),f335(a332,x46174)))),f335(f335(f260(x46171,x46172),x46173),x46174)) % 186.01/186.02 [4618]E(f96(f933(x46181,x46182),f335(f265(x46181,x46182,a922),f335(f335(f7(x46181,f934(x46182,a922),f934(x46182,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46182,a922),f934(x46182,a922)),x46181),f8(a922,a922,x46182)),f335(f335(f8(a922,f934(a922,a922),x46181),a333),f335(a332,x46183)))),f335(a332,x46184)))),f335(f335(f260(x46181,x46182),x46183),x46184)) % 186.01/186.02 [4691]E(f335(f335(f265(f928(x46911),f928(x46911),f933(f928(x46911),f928(x46911))),f335(f335(f18(f928(x46911),f934(f928(x46911),f933(f928(x46911),f928(x46911))),f934(f928(x46911),f933(f928(x46911),f928(x46911)))),f335(f335(f8(f934(f928(x46911),f934(f933(f928(x46911),f928(x46911)),f933(f928(x46911),f928(x46911)))),f934(f934(f928(x46911),f933(f928(x46911),f928(x46911))),f934(f928(x46911),f933(f928(x46911),f928(x46911)))),f928(x46911)),f18(f928(x46911),f933(f928(x46911),f928(x46911)),f933(f928(x46911),f928(x46911)))),f335(f335(f8(f934(f928(x46911),f933(f928(x46911),f928(x46911))),f934(f928(x46911),f934(f933(f928(x46911),f928(x46911)),f933(f928(x46911),f928(x46911)))),f928(x46911)),f335(f8(f933(f928(x46911),f928(x46911)),f934(f933(f928(x46911),f928(x46911)),f933(f928(x46911),f928(x46911))),f928(x46911)),f335(f103(f933(f928(x46911),f928(x46911))),f335(x46912,x46913)))),f335(f335(f8(f928(x46911),f934(f928(x46911),f933(f928(x46911),f928(x46911))),f928(x46911)),f260(f928(x46911),f928(x46911))),f335(f158(x46911),x46913))))),f335(f335(f7(f928(x46911),f934(f928(x46911),f928(x46911)),f934(f928(x46911),f933(f928(x46911),f928(x46911)))),f335(f335(f8(f934(f928(x46911),f933(f928(x46911),f928(x46911))),f934(f934(f928(x46911),f928(x46911)),f934(f928(x46911),f933(f928(x46911),f928(x46911)))),f928(x46911)),f8(f928(x46911),f933(f928(x46911),f928(x46911)),f928(x46911))),f260(f928(x46911),f928(x46911)))),f335(f158(x46911),x46913)))),f173(x46911,x46912,x46914)),f173(x46911,x46912,f335(f335(f158(x46911),x46913),x46914))) % 186.01/186.02 [3928]E(f335(f335(f182(x39281),x39282),f335(f335(f182(x39281),x39283),x39284)),f335(f335(f182(x39281),f335(f335(f241(a927),x39282),x39283)),x39284)) % 186.01/186.02 [3929]E(f335(f335(f145(x39291),x39292),f335(f335(f145(x39291),x39293),x39294)),f335(f335(f145(x39291),f335(f335(f86(a927),x39292),x39293)),x39294)) % 186.01/186.02 [3940]E(f335(f335(f141(x39401),f335(f335(f158(x39401),x39402),x39403)),x39404),f335(f335(f158(x39401),x39402),f335(f335(f141(x39401),x39403),x39404))) % 186.01/186.02 [3941]E(f335(f335(f141(x39411),f335(f335(f141(x39411),x39412),x39413)),x39414),f335(f335(f141(x39411),x39412),f335(f335(f141(x39411),x39413),x39414))) % 186.01/186.02 [4024]E(f335(f335(f171(x40241),f335(f335(f158(x40241),x40242),x40243)),x40244),f192(x40241,x40242,f335(f171(x40241),x40243),x40244)) % 186.01/186.02 [4033]E(f335(f335(f190(x40331,x40331),x40332),f335(f335(f190(x40331,x40331),x40333),x40334)),f335(f335(f190(x40331,x40331),f335(f335(f87(a927),x40333),x40332)),x40334)) % 186.01/186.02 [4061]E(f335(f335(f117(f934(x40611,a922)),x40612),f335(f335(f317(x40611),x40613),x40614)),f335(f335(f317(x40611),x40613),f335(f335(f117(f934(x40611,a922)),x40612),x40614))) % 186.01/186.02 [4076]E(f335(f335(f335(f190(x40761,x40761),x40762),x40763),f335(x40763,x40764)),f335(x40763,f335(f335(f335(f190(x40761,x40761),x40762),x40763),x40764))) % 186.01/186.02 [4085]E(f335(f335(f297(x40851,x40852,x40853),f195(f934(f933(x40851,x40852),a922))),x40854),f195(f934(f933(x40851,x40853),a922))) % 186.01/186.02 [4100]E(f335(f335(f117(f934(x41001,a922)),f335(f335(f317(x41001),x41002),x41003)),x41004),f335(f335(f317(x41001),x41002),f335(f335(f117(f934(x41001,a922)),x41003),x41004))) % 186.01/186.02 [4119]E(f335(f41(f933(x41191,x41192)),f335(f335(f262(x41191,x41192),x41193),f335(f16(f934(x41192,a922),x41191),x41194))),f335(f335(f87(a927),f335(f41(x41191),x41193)),f335(f41(x41192),x41194))) % 186.01/186.02 [4126]E(f335(f335(f108(f934(x41261,a922)),f335(f335(f317(x41261),x41262),x41263)),f335(f335(f317(x41261),x41262),x41264)),f335(f335(f317(x41261),x41262),f335(f335(f108(f934(x41261,a922)),x41263),x41264))) % 186.01/186.02 [4141]E(f335(f335(f108(f934(x41411,a922)),x41412),f335(f335(f108(f934(x41411,a922)),x41413),x41414)),f335(f335(f108(f934(x41411,a922)),x41413),f335(f335(f108(f934(x41411,a922)),x41412),x41414))) % 186.01/186.02 [4142]E(f335(f335(f117(f934(x41421,a922)),x41422),f335(f335(f117(f934(x41421,a922)),x41423),x41424)),f335(f335(f117(f934(x41421,a922)),x41423),f335(f335(f117(f934(x41421,a922)),x41422),x41424))) % 186.01/186.02 [4152]E(f70(x41521,x41522,f335(f335(f8(x41522,f934(x41522,x41522),x41521),x41523),x41524)),f335(f71(x41522,x41521,x41523),x41524)) % 186.01/186.02 [4161]E(f186(x41611,f335(f335(f161(f928(x41612),f928(x41611)),f335(f161(x41612,x41611),x41613)),x41614)),f335(f335(f161(f928(x41612),f928(x41611)),f335(f161(x41612,x41611),x41613)),f186(x41612,x41614))) % 186.01/186.02 [4180]E(f335(f149(f928(x41801),f928(x41801),f141(x41801),f120(x41801)),f335(f335(f161(x41802,f928(x41801)),x41803),x41804)),f170(x41802,x41801,x41803,x41804)) % 186.01/186.02 [4238]E(f335(f78(x42381,x42381,x42381,f335(f335(f190(x42381,x42381),x42382),x42383)),f335(f335(f190(x42381,x42381),x42384),x42383)),f335(f335(f190(x42381,x42381),f335(f335(f86(a927),x42382),x42384)),x42383)) % 186.01/186.02 [4261]E(f335(f335(f117(f934(x42611,a922)),f335(f335(f23(f934(x42611,a922)),x42612),x42613)),f335(f335(f23(f934(x42611,a922)),x42612),x42614)),f335(f335(f23(f934(x42611,a922)),x42612),f335(f335(f108(f934(x42611,a922)),x42613),x42614))) % 186.01/186.02 [4262]E(f335(f335(f108(f934(x42621,a922)),f335(f335(f23(f934(x42621,a922)),x42622),x42623)),f335(f335(f23(f934(x42621,a922)),x42622),x42624)),f335(f335(f23(f934(x42621,a922)),x42622),f335(f335(f117(f934(x42621,a922)),x42623),x42624))) % 186.01/186.02 [4263]E(f335(f335(f23(f934(x42631,a922)),f335(f335(f108(f934(x42631,a922)),x42632),x42633)),f335(f335(f108(f934(x42631,a922)),x42632),x42634)),f335(f335(f108(f934(x42631,a922)),x42632),f335(f335(f23(f934(x42631,a922)),x42633),x42634))) % 186.01/186.02 [4264]E(f335(f335(f117(f934(x42641,a922)),f335(f335(f108(f934(x42641,a922)),x42642),x42643)),f335(f335(f108(f934(x42641,a922)),x42642),x42644)),f335(f335(f108(f934(x42641,a922)),x42642),f335(f335(f117(f934(x42641,a922)),x42643),x42644))) % 186.01/186.02 [4265]E(f335(f335(f108(f934(x42651,a922)),f335(f335(f117(f934(x42651,a922)),x42652),x42653)),f335(f335(f117(f934(x42651,a922)),x42652),x42654)),f335(f335(f117(f934(x42651,a922)),x42652),f335(f335(f108(f934(x42651,a922)),x42653),x42654))) % 186.01/186.02 [4270]E(f335(f41(f933(x42701,x42702)),f335(f335(f262(x42701,x42702),f335(f335(f317(x42701),x42703),f195(f934(x42701,a922)))),f335(f16(f934(x42702,a922),x42701),x42704))),f335(f41(x42702),x42704)) % 186.01/186.02 [4305]E(f335(f335(f46(x43051,f934(x43052,a922)),x43053),f335(f335(f8(f934(x43052,a922),f934(x43052,a922),x43051),f85(f934(x43052,a922))),x43054)),f335(f85(f934(x43052,a922)),f335(f335(f45(x43051,f934(x43052,a922)),x43053),x43054))) % 186.01/186.02 [4306]E(f335(f335(f45(x43061,f934(x43062,a922)),x43063),f335(f335(f8(f934(x43062,a922),f934(x43062,a922),x43061),f85(f934(x43062,a922))),x43064)),f335(f85(f934(x43062,a922)),f335(f335(f46(x43061,f934(x43062,a922)),x43063),x43064))) % 186.01/186.02 [4322]E(f335(f335(f297(x43221,x43221,x43221),f335(f335(f190(f933(x43221,x43221),a922),x43222),x43223)),f335(f335(f190(f933(x43221,x43221),a922),x43224),x43223)),f335(f335(f190(f933(x43221,x43221),a922),f335(f335(f86(a927),x43222),x43224)),x43223)) % 186.01/186.02 [4352]E(f335(f335(f46(x43521,f934(f934(x43522,a922),a922)),x43523),f335(f335(f8(f934(x43522,a922),f934(f934(x43522,a922),a922),x43521),f316(x43522)),x43524)),f335(f316(x43522),f335(f335(f46(x43521,f934(x43522,a922)),x43523),x43524))) % 186.01/186.02 [4383]E(f335(f335(f45(f934(x43831,a922),f934(x43832,a922)),x43833),f335(f335(f7(f934(x43831,a922),f934(x43831,f934(x43832,a922)),f934(x43832,a922)),f45(x43831,f934(x43832,a922))),x43834)),f335(f335(f45(x43831,f934(x43832,a922)),f43(f934(x43831,a922),x43833)),x43834)) % 186.01/186.02 [4384]E(f335(f335(f46(f934(x43841,a922),f934(x43842,a922)),x43843),f335(f335(f7(f934(x43841,a922),f934(x43841,f934(x43842,a922)),f934(x43842,a922)),f46(x43841,f934(x43842,a922))),x43844)),f335(f335(f46(x43841,f934(x43842,a922)),f43(f934(x43841,a922),x43843)),x43844)) % 186.01/186.02 [4389]E(f335(f335(f161(x43891,x43892),x43893),f335(f149(f928(x43891),f928(x43891),f141(x43891),f120(x43891)),x43894)),f335(f149(f928(x43892),f928(x43892),f141(x43892),f120(x43892)),f335(f335(f161(f928(x43891),f928(x43892)),f335(f161(x43891,x43892),x43893)),x43894))) % 186.01/186.02 [4391]E(f192(f928(x43911),f120(x43911),f335(f335(f8(f928(x43911),f928(x43911),a927),f335(f158(x43911),x43912)),f335(f335(f7(a927,f928(x43911),f928(x43911)),f182(x43911)),x43913)),x43914),f335(f335(f182(x43911),x43914),f335(f335(f158(x43911),x43912),x43913))) % 186.01/186.02 [4429]P1(f335(f335(f243(f934(x44291,a922)),f335(f318(x44292,x44291,x44293),f335(f319(x44292,x44291,x44293),x44294))),x44294)) % 186.01/186.02 [4431]E(f335(f318(f933(x44311,x44312),f933(x44312,x44311),f335(f265(x44311,x44312,f933(x44312,x44311)),f335(f7(x44312,x44311,f933(x44312,x44311)),f260(x44312,x44311)))),f335(f335(f262(x44311,x44312),x44313),f335(f16(f934(x44312,a922),x44311),x44314))),f335(f335(f262(x44312,x44311),x44314),f335(f16(f934(x44311,a922),x44312),x44313))) % 186.01/186.02 [4440]E(f335(f335(f45(x44401,f934(x44402,a922)),x44403),f335(f335(f8(f934(x44401,a922),f934(x44402,a922),x44401),f319(x44402,x44401,x44404)),f335(f335(f7(x44401,f934(x44401,a922),f934(x44401,a922)),f317(x44401)),f195(f934(x44401,a922))))),f335(f319(x44402,x44401,x44404),x44403)) % 186.01/186.02 [4441]E(f335(f335(f45(x44411,f934(x44412,a922)),x44413),f335(f335(f8(f934(x44411,a922),f934(x44412,a922),x44411),f293(x44411,x44412,x44414)),f335(f335(f7(x44411,f934(x44411,a922),f934(x44411,a922)),f317(x44411)),f195(f934(x44411,a922))))),f335(f293(x44411,x44412,x44414),x44413)) % 186.01/186.02 [4528]E(f335(f335(f117(f934(x45281,a922)),f335(f335(f117(f934(x45281,a922)),f335(f335(f108(f934(x45281,a922)),x45282),x45283)),f335(f335(f108(f934(x45281,a922)),x45283),x45284))),f335(f335(f108(f934(x45281,a922)),x45284),x45282)),f335(f335(f108(f934(x45281,a922)),f335(f335(f108(f934(x45281,a922)),f335(f335(f117(f934(x45281,a922)),x45282),x45283)),f335(f335(f117(f934(x45281,a922)),x45283),x45284))),f335(f335(f117(f934(x45281,a922)),x45284),x45282))) % 186.01/186.02 [4591]E(f335(f149(f928(x45911),f928(x45911),f141(x45911),f120(x45911)),f335(f335(f161(x45912,f928(x45911)),f335(f335(f7(x45912,f928(x45911),f928(x45911)),f335(f335(f8(x45911,f934(f928(x45911),f928(x45911)),x45912),f158(x45911)),x45913)),f120(x45911))),x45914)),f335(f335(f161(x45912,x45911),x45913),x45914)) % 186.01/186.02 [4601]E(f335(f335(f92(a1,x46011),f335(f110(a1),f335(f335(f86(a1),x46012),a104))),f335(f335(f18(a1,x46011,x46011),f335(f335(f7(a1,x46011,f934(x46011,x46011)),f335(f335(f8(a922,f934(x46011,f934(x46011,x46011)),a1),f103(x46011)),a200)),x46013)),f335(f335(f8(a927,x46011,a1),x46014),a111))),f192(x46011,x46013,x46014,f335(f110(a927),x46012))) % 186.01/186.02 [4632]E(f335(f270(x46321),f335(f335(f8(f934(x46322,a922),a922,x46321),f93(x46322)),f335(f335(f8(f934(x46322,a922),f934(x46322,a922),x46321),f335(f18(x46322,a922,a922),f335(f335(f8(a922,f934(a922,a922),x46322),a333),f335(f335(f7(x46322,f934(x46322,a922),a922),f337(x46322)),x46323)))),f335(f7(x46322,x46321,a922),x46324)))),f335(f293(x46322,x46321,f335(f270(f933(x46322,x46321)),f335(f265(x46322,x46321,a922),x46324))),x46323)) % 186.01/186.02 [4800]~P1(f335(f335(f195(f934(x48001,f934(x48002,a922))),x48003),x48004)) % 186.01/186.02 [4088]E(f335(f335(f171(x40881),f335(f335(f141(x40881),x40882),x40883)),f335(f335(f86(a927),f335(f196(f928(x40881)),x40882)),x40884)),f335(f335(f171(x40881),x40883),x40884)) % 186.01/186.02 [4093]E(f335(f335(f145(x40931),x40932),f335(f335(f182(x40931),f335(f335(f86(a927),x40933),x40932)),x40934)),f335(f335(f182(x40931),x40933),f335(f335(f145(x40931),x40932),x40934))) % 186.01/186.02 [4194]E(f335(f335(f117(f934(x41941,a922)),f335(f292(x41942,x41941),x41943)),f335(f292(x41942,x41941),x41944)),f335(f292(x41942,x41941),f335(f335(f117(f934(f933(x41942,x41941),a922)),x41943),x41944))) % 186.01/186.02 [4195]E(f335(f335(f117(f934(x41951,a922)),f335(f272(x41951,x41952),x41953)),f335(f272(x41951,x41952),x41954)),f335(f272(x41951,x41952),f335(f335(f117(f934(f933(x41951,x41952),a922)),x41953),x41954))) % 186.01/186.02 [4200]E(f335(f335(f23(f934(x42001,a922)),f335(f335(f108(f934(x42001,a922)),x42002),x42003)),x42004),f335(f335(f108(f934(x42001,a922)),x42002),f335(f335(f23(f934(x42001,a922)),x42003),x42004))) % 186.01/186.02 [4201]E(f335(f335(f108(f934(x42011,a922)),f335(f335(f108(f934(x42011,a922)),x42012),x42013)),x42014),f335(f335(f108(f934(x42011,a922)),x42012),f335(f335(f108(f934(x42011,a922)),x42013),x42014))) % 186.01/186.02 [4202]E(f335(f335(f117(f934(x42021,a922)),f335(f335(f117(f934(x42021,a922)),x42022),x42023)),x42024),f335(f335(f117(f934(x42021,a922)),x42022),f335(f335(f117(f934(x42021,a922)),x42023),x42024))) % 186.01/186.02 [4240]E(f335(f335(f108(f934(f933(x42401,x42402),a922)),f335(f294(x42402,x42401),x42403)),f335(f294(x42402,x42401),x42404)),f335(f294(x42402,x42401),f335(f335(f108(f934(f933(x42402,x42401),a922)),x42403),x42404))) % 186.01/186.02 [4241]E(f335(f335(f117(f934(f933(x42411,x42412),a922)),f335(f294(x42412,x42411),x42413)),f335(f294(x42412,x42411),x42414)),f335(f294(x42412,x42411),f335(f335(f117(f934(f933(x42412,x42411),a922)),x42413),x42414))) % 186.01/186.02 [4254]E(f335(f335(f108(f934(x42541,f934(x42542,a922))),f251(x42542,x42541,x42543)),f251(x42542,x42541,x42544)),f251(x42542,x42541,f335(f335(f108(f934(x42542,f934(x42541,a922))),x42543),x42544))) % 186.01/186.02 [4255]E(f335(f335(f117(f934(x42551,f934(x42552,a922))),f251(x42552,x42551,x42553)),f251(x42552,x42551,x42554)),f251(x42552,x42551,f335(f335(f117(f934(x42552,f934(x42551,a922))),x42553),x42554))) % 186.01/186.02 [4309]E(f335(f335(f117(f934(x43091,a922)),f335(f335(f23(f934(x43091,a922)),x43092),x43093)),f335(f335(f23(f934(x43091,a922)),x43094),x43093)),f335(f335(f23(f934(x43091,a922)),f335(f335(f117(f934(x43091,a922)),x43092),x43094)),x43093)) % 186.01/186.02 [4310]E(f335(f335(f23(f934(x43101,a922)),f335(f335(f108(f934(x43101,a922)),x43102),x43103)),f335(f335(f108(f934(x43101,a922)),x43104),x43103)),f335(f335(f108(f934(x43101,a922)),f335(f335(f23(f934(x43101,a922)),x43102),x43104)),x43103)) % 186.01/186.02 [4311]E(f335(f335(f117(f934(x43111,a922)),f335(f335(f108(f934(x43111,a922)),x43112),x43113)),f335(f335(f108(f934(x43111,a922)),x43114),x43113)),f335(f335(f108(f934(x43111,a922)),f335(f335(f117(f934(x43111,a922)),x43112),x43114)),x43113)) % 186.01/186.02 [4312]E(f335(f335(f108(f934(x43121,a922)),f335(f335(f117(f934(x43121,a922)),x43122),x43123)),f335(f335(f117(f934(x43121,a922)),x43124),x43123)),f335(f335(f117(f934(x43121,a922)),f335(f335(f108(f934(x43121,a922)),x43122),x43124)),x43123)) % 186.01/186.02 [4313]E(f335(f335(f23(f934(x43131,a922)),f335(f335(f108(f934(x43131,a922)),x43132),x43133)),f335(f335(f108(f934(x43131,a922)),x43134),x43133)),f335(f335(f23(f934(x43131,a922)),f335(f335(f108(f934(x43131,a922)),x43132),x43133)),x43134)) % 186.01/186.02 [4325]E(f335(f335(f23(f934(x43251,a922)),f335(f335(f23(f934(x43251,a922)),x43252),f335(f335(f317(x43251),x43253),f195(f934(x43251,a922))))),x43254),f335(f335(f23(f934(x43251,a922)),x43252),f335(f335(f317(x43251),x43253),x43254))) % 186.01/186.02 [4378]E(f335(f335(f117(f934(x43781,a922)),f335(f335(f317(x43781),x43782),f335(f335(f317(x43781),x43783),f195(f934(x43781,a922))))),f335(f289(x43781),x43784)),f335(f289(x43781),f335(f335(f317(f933(x43781,x43781)),f335(f335(f260(x43781,x43781),x43782),x43783)),x43784))) % 186.01/186.02 [4405]E(f335(f335(f45(a927,f934(x44051,a922)),f335(f309(a927),x44052)),f335(f335(f8(a927,f934(x44051,a922),a927),x44053),f335(f335(f7(a927,a927,a927),f86(a927)),x44054))),f335(f335(f45(a927,f934(x44051,a922)),f311(a927,x44054,f335(f335(f86(a927),x44052),x44054))),x44053)) % 186.01/186.02 [4406]E(f181(x44061,f335(f293(x44061,x44061,x44062),f335(f335(f317(x44061),x44063),f195(f934(x44061,a922)))),f335(f293(f928(x44061),f928(x44061),f165(x44061,x44062)),f335(f335(f317(f928(x44061)),x44064),f195(f934(f928(x44061),a922))))),f335(f293(f928(x44061),f928(x44061),f165(x44061,x44062)),f335(f335(f317(f928(x44061)),f335(f335(f158(x44061),x44063),x44064)),f195(f934(f928(x44061),a922))))) % 186.01/186.02 [4470]E(f335(f270(x44701),f335(f335(f7(x44701,f934(x44702,a922),a922),f335(f335(f8(x44702,f934(f934(x44702,a922),a922),x44701),f337(x44702)),x44703)),x44704)),f335(f319(x44701,x44702,x44703),x44704)) % 186.01/186.02 [4560]E(f335(f270(x45601),f335(f335(f7(x45601,f934(f933(x45602,x45601),a922),a922),f335(f335(f8(f933(x45602,x45601),f934(f934(f933(x45602,x45601),a922),a922),x45601),f337(f933(x45602,x45601))),f335(f260(x45602,x45601),x45603))),x45604)),f335(f293(x45602,x45601,x45604),f335(f335(f317(x45602),x45603),f195(f934(x45602,a922))))) % 186.01/186.02 [4574]E(f335(f335(f161(f933(x45741,a927),x45741),f259(x45741,a927)),f335(f143(f933(x45741,a927),f335(f335(f8(a927,a922,f933(x45741,a927)),x45742),f335(f335(f8(a927,a927,f933(x45741,a927)),a119),f264(x45741,a927)))),f335(f335(f188(x45741,a927),x45743),x45744))),f335(f335(f161(f933(x45741,a927),x45741),f259(x45741,a927)),f335(f143(f933(x45741,a927),f335(f335(f8(a927,a922,f933(x45741,a927)),x45742),f264(x45741,a927))),f335(f335(f188(x45741,a927),x45743),f335(f335(f161(a927,a927),a119),x45744))))) % 186.01/186.02 [4583]P1(f335(f335(f243(f934(f934(x45831,a922),a922)),f335(f335(f45(x45832,f934(f934(x45831,a922),a922)),x45833),f335(f335(f8(f934(x45831,a922),f934(f934(x45831,a922),a922),x45832),f316(x45831)),x45834))),f335(f316(x45831),f335(f335(f45(x45832,f934(x45831,a922)),x45833),x45834)))) % 186.01/186.02 [4624]E(f335(f335(f92(a1,x46241),f335(f110(a1),f335(f335(f86(a1),x46242),a104))),f335(f335(f18(a1,x46241,x46241),f335(f335(f7(a1,x46241,f934(x46241,x46241)),f335(f335(f8(a922,f934(x46241,f934(x46241,x46241)),a1),f103(x46241)),a200)),x46243)),f335(f335(f18(a1,x46241,x46241),f335(f335(f8(a927,f934(x46241,x46241),a1),x46244),a111)),f335(f335(f8(a927,x46241,a1),f191(x46241,x46243,x46244)),a111)))),f335(f191(x46241,x46243,x46244),f335(f110(a927),x46242))) % 186.01/186.02 [4648]E(f335(f270(f933(x46481,x46482)),f335(f265(x46481,x46482,a922),f335(f335(f7(x46481,f934(x46482,a922),f934(x46482,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46482,a922),f934(x46482,a922)),x46481),f8(a922,a922,x46482)),f335(f335(f8(a922,f934(a922,a922),x46481),a333),f335(f335(f7(x46481,f934(x46481,a922),a922),f337(x46481)),x46483)))),f335(f335(f7(x46482,f934(x46482,a922),a922),f337(x46482)),x46484)))),f238(x46481,x46482,x46483,x46484)) % 186.01/186.02 [4686]E(f335(f335(f45(x46861,f934(f933(x46861,x46862),a922)),x46863),f335(f335(f18(x46861,f934(x46862,f934(f933(x46861,x46862),a922)),f934(f933(x46861,x46862),a922)),f335(f335(f8(f934(x46862,a922),f934(f934(x46862,f934(f933(x46861,x46862),a922)),f934(f933(x46861,x46862),a922)),x46861),f45(x46862,f934(f933(x46861,x46862),a922))),x46864)),f335(f335(f7(x46861,f934(f933(x46861,x46862),a922),f934(x46862,f934(f933(x46861,x46862),a922))),f335(f335(f8(f934(x46862,f934(f934(f933(x46861,x46862),a922),f934(f933(x46861,x46862),a922))),f934(f934(f933(x46861,x46862),a922),f934(x46862,f934(f933(x46861,x46862),a922))),x46861),f7(x46862,f934(f933(x46861,x46862),a922),f934(f933(x46861,x46862),a922))),f335(f335(f8(f934(x46862,f933(x46861,x46862)),f934(x46862,f934(f934(f933(x46861,x46862),a922),f934(f933(x46861,x46862),a922))),x46861),f335(f8(f933(x46861,x46862),f934(f934(f933(x46861,x46862),a922),f934(f933(x46861,x46862),a922)),x46862),f317(f933(x46861,x46862)))),f260(x46861,x46862)))),f195(f934(f933(x46861,x46862),a922))))),f335(f335(f262(x46861,x46862),x46863),x46864)) % 186.01/186.02 [4249]E(f335(f335(f141(x42491),f335(f335(f182(x42491),x42492),x42493)),f335(f335(f182(x42491),f335(f335(f23(a927),x42492),f335(f196(f928(x42491)),x42493))),x42494)),f335(f335(f182(x42491),x42492),f335(f335(f141(x42491),x42493),x42494))) % 186.01/186.02 [4250]E(f335(f335(f141(x42501),f335(f335(f145(x42501),x42502),x42503)),f335(f335(f145(x42501),f335(f335(f23(a927),x42502),f335(f196(f928(x42501)),x42503))),x42504)),f335(f335(f145(x42501),x42502),f335(f335(f141(x42501),x42503),x42504))) % 186.01/186.02 [4299]E(f335(f335(f86(a927),f335(f335(f87(a927),x42991),x42992)),f335(f335(f86(a927),f335(f335(f87(a927),x42993),x42992)),x42994)),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f86(a927),x42991),x42993)),x42992)),x42994)) % 186.01/186.02 [4446]E(f96(x44461,f335(f335(f7(x44461,x44462,a922),f335(f335(f8(x44462,f934(x44462,a922),x44461),a332),x44463)),x44464)),f335(f97(x44461,x44462,f250(f934(x44461,a922)),x44463),x44464)) % 186.01/186.02 [4494]P1(f335(f335(f243(f934(x44941,a922)),f335(f335(f23(f934(x44941,a922)),f335(f292(x44942,x44941),x44943)),f335(f292(x44942,x44941),x44944))),f335(f292(x44942,x44941),f335(f335(f23(f934(f933(x44942,x44941),a922)),x44943),x44944)))) % 186.01/186.02 [4495]P1(f335(f335(f243(f934(x44951,a922)),f335(f335(f23(f934(x44951,a922)),f335(f272(x44951,x44952),x44953)),f335(f272(x44951,x44952),x44954))),f335(f272(x44951,x44952),f335(f335(f23(f934(f933(x44951,x44952),a922)),x44953),x44954)))) % 186.01/186.02 [4603]E(f335(f335(f86(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x46031),x46032)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x46033),x46034)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),f335(f335(f86(a927),x46031),x46033)),f335(f335(f86(a927),x46032),x46034))),f195(f934(f933(a927,a927),a922)))))) % 186.01/186.02 [4643]E(f335(f335(f87(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x46431),x46432)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x46433),x46434)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),f335(f335(f86(a927),f335(f335(f87(a927),x46431),x46433)),f335(f335(f87(a927),x46432),x46434))),f335(f335(f86(a927),f335(f335(f87(a927),x46431),x46434)),f335(f335(f87(a927),x46432),x46433)))),f195(f934(f933(a927,a927),a922)))))) % 186.01/186.02 [4664]E(f335(f270(x46641),f335(f335(f8(f934(x46642,a922),a922,x46641),f94(x46642)),f335(f335(f8(f934(x46642,a922),f934(x46642,a922),x46641),f335(f18(x46642,a922,a922),f335(f335(f8(a922,f934(a922,a922),x46642),a338),f335(f335(f7(x46642,f934(x46642,a922),a922),f337(x46642)),x46643)))),f335(f335(f7(x46641,f934(x46642,f934(x46641,a922)),f934(x46642,a922)),f335(f335(f8(f934(f934(x46641,a922),a922),f934(f934(x46642,f934(x46641,a922)),f934(x46642,a922)),x46641),f8(f934(x46641,a922),a922,x46642)),f337(x46641))),x46644)))),f335(f335(f46(x46642,f934(x46641,a922)),x46643),x46644)) % 186.01/186.02 [4698]E(f335(f335(f297(x46981,x46981,x46981),f335(f335(f317(f933(x46981,x46981)),f335(f335(f260(x46981,x46981),x46982),x46983)),x46984)),f315(x46981,f335(f335(f317(f933(x46981,x46981)),f335(f335(f260(x46981,x46981),x46982),x46983)),x46984))),f335(f335(f117(f934(f933(x46981,x46981),a922)),f335(f335(f297(x46981,x46981,x46981),x46984),f315(x46981,x46984))),f335(f270(f933(x46981,x46981)),f335(f265(x46981,x46981,a922),f335(f335(f7(x46981,f934(x46981,a922),f934(x46981,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46981,a922),f934(x46981,a922)),x46981),f8(a922,a922,x46981)),f335(f335(f8(a922,f934(a922,a922),x46981),a333),f335(f335(f7(x46981,f934(f933(x46981,x46981),a922),a922),f335(f335(f8(f933(x46981,x46981),f934(f934(f933(x46981,x46981),a922),a922),x46981),f337(f933(x46981,x46981))),f335(f335(f7(x46981,x46981,f933(x46981,x46981)),f260(x46981,x46981)),x46982))),f315(x46981,x46984))))),f335(f335(f7(x46981,f934(f933(x46981,x46981),a922),a922),f335(f335(f8(f933(x46981,x46981),f934(f934(f933(x46981,x46981),a922),a922),x46981),f337(f933(x46981,x46981))),f335(f260(x46981,x46981),x46983))),f315(x46981,x46984))))))) % 186.01/186.02 [4496]E(f335(f143(x44961,f335(f335(f18(x44961,a922,a922),f335(f335(f8(a922,f934(a922,a922),x44961),a333),x44962)),x44963)),x44964),f335(f143(x44961,x44963),f335(f143(x44961,x44962),x44964))) % 186.01/186.02 [4597]E(f335(f335(f141(x45971),f335(f335(f335(f103(f928(x45971)),f335(f335(f337(a927),f2(a927)),x45972)),f335(f335(f158(x45971),x45973),f120(x45971))),f120(x45971))),f183(x45971,x45974,f335(f270(a927),f335(f335(f7(a927,f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),a927),f337(a927)),a119)),x45972)))),f183(x45971,f335(f335(f158(x45971),x45973),x45974),x45972)) % 186.01/186.02 [4694]E(f335(f270(f933(x46941,x46942)),f335(f335(f8(f934(a927,a922),a922,f933(x46941,x46942)),f93(a927)),f335(f335(f7(f933(x46941,x46942),f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),f933(x46941,x46942)),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),f933(x46941,x46942)),f335(f8(a922,f934(a922,a922),a927),a333)),f335(f335(f7(f933(x46941,x46942),f934(a927,f933(x46941,x46942)),f934(a927,a922)),f335(f335(f8(f934(f933(x46941,x46942),a922),f934(f934(a927,f933(x46941,x46942)),f934(a927,a922)),f933(x46941,x46942)),f8(f933(x46941,x46942),a922,a927)),a332)),f335(f335(f18(a927,x46942,f933(x46941,x46942)),f335(f335(f8(x46941,f934(x46942,f933(x46941,x46942)),a927),f260(x46941,x46942)),f335(f171(x46941),x46943))),f335(f171(x46942),x46944)))))),f335(f335(f7(a927,a927,a922),f244(a927)),f335(f335(f241(a927),f335(f196(f928(x46941)),x46943)),f335(f196(f928(x46942)),x46944)))))),f335(f179(f933(x46941,x46942)),f335(f335(f188(x46941,x46942),x46943),x46944))) % 186.01/186.02 [4616]E(f335(f270(f933(x46161,x46162)),f335(f265(x46161,x46162,a922),f335(f335(f7(x46161,f934(x46162,a922),f934(x46162,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46162,a922),f934(x46162,a922)),x46161),f8(a922,a922,x46162)),f335(f335(f8(a922,f934(a922,a922),x46161),a333),x46163))),x46164))),f335(f335(f262(x46161,x46162),f335(f270(x46161),x46163)),f335(f16(f934(x46162,a922),x46161),f335(f270(x46162),x46164)))) % 186.01/186.02 [4619]E(f335(f270(f933(x46191,x46192)),f335(f265(x46191,x46192,a922),f335(f335(f18(x46191,f934(x46192,a922),f934(x46192,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x46192,a922),f934(x46192,a922)),x46191),f8(a922,a922,x46192)),f335(f335(f8(a922,f934(a922,a922),x46191),a333),x46193))),x46194))),f335(f335(f262(x46191,x46192),f335(f270(x46191),x46193)),f335(f335(f8(f934(x46192,a922),f934(x46192,a922),x46191),f270(x46192)),x46194))) % 186.01/186.02 [4631]E(f335(f270(x46311),f335(f335(f8(f934(x46312,a922),a922,x46311),f94(x46312)),f335(f335(f8(f934(x46312,a922),f934(x46312,a922),x46311),f335(f18(x46312,a922,a922),f335(f335(f8(a922,f934(a922,a922),x46312),a338),f335(f335(f7(x46312,f934(x46312,a922),a922),f337(x46312)),x46313)))),x46314))),f335(f335(f46(x46312,f934(x46311,a922)),x46313),f335(f335(f8(f934(x46311,a922),f934(x46311,a922),x46312),f270(x46311)),f335(f7(x46311,x46312,a922),x46314)))) % 186.01/186.02 [4678]E(f335(f335(f161(f933(x46781,a927),x46781),f259(x46781,a927)),f335(f143(f933(x46781,a927),f335(f335(f7(f933(x46781,a927),f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),f933(x46781,a927)),f337(a927)),f264(x46781,a927))),x46782)),f335(f335(f188(x46781,a927),x46783),f146(a927,f335(f310(a927,x46784),f335(f335(f86(a927),x46784),f335(f196(f928(x46781)),x46783))))))),f335(f335(f161(f933(x46781,a927),x46781),f259(x46781,a927)),f335(f143(f933(x46781,a927),f335(f335(f7(f933(x46781,a927),f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),f933(x46781,a927)),f337(a927)),f335(f335(f7(f933(x46781,a927),a927,a927),f335(f335(f8(a927,f934(a927,a927),f933(x46781,a927)),f86(a927)),f264(x46781,a927))),x46784))),x46782)),f335(f335(f188(x46781,a927),x46783),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(x46781)),x46783))))))) % 186.01/186.02 [4679]E(f335(a119,f335(f335(f242(a927),f335(f196(f928(x46791)),x46792)),f335(f149(a927,f928(x46793),f335(f7(f928(x46793),a927,a927),f335(f335(f8(a927,f934(a927,a927),f928(x46793)),f242(a927)),f335(f335(f7(f928(x46793),a927,a927),f335(f335(f8(a927,f934(a927,a927),f928(x46793)),f23(a927)),f196(f928(x46793)))),f335(a119,f2(a927))))),f2(a927)),f335(f175(f928(x46793)),f335(f143(f928(x46793),f335(f335(f8(a922,a922,f928(x46793)),a330),f335(f335(f7(f928(x46793),f928(x46793),a922),a332),f120(x46793)))),x46794))))),f335(f335(f242(a927),f335(a119,f335(f196(f928(x46791)),x46792))),f335(f149(a927,f928(x46793),f335(f7(f928(x46793),a927,a927),f335(f335(f8(a927,f934(a927,a927),f928(x46793)),f242(a927)),f196(f928(x46793)))),f2(a927)),f335(f175(f928(x46793)),x46794)))) % 186.01/186.02 [4630]E(f335(f335(f141(x46301),f183(x46301,x46302,x46303)),f183(x46301,x46304,f335(f270(a927),f335(f335(f7(a927,f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),a927),f337(a927)),f335(f335(f7(a927,a927,a927),f86(a927)),f335(f196(f928(x46301)),x46302)))),x46303)))),f183(x46301,f335(f335(f141(x46301),x46302),x46304),x46303)) % 186.01/186.02 [4680]E(f43(f934(x46801,a922),f335(f270(f934(x46801,a922)),f335(f335(f8(f934(x46802,a922),a922,f934(x46801,a922)),f93(x46802)),f335(f335(f8(f934(x46802,a922),f934(x46802,a922),f934(x46801,a922)),f335(f18(x46802,a922,a922),f335(f335(f8(a922,f934(a922,a922),x46802),a333),f335(f335(f7(x46802,f934(x46802,a922),a922),f337(x46802)),x46803)))),f335(f335(f7(f934(x46801,a922),f934(x46802,f934(x46801,a922)),f934(x46802,a922)),f335(f335(f8(f934(f934(x46801,a922),a922),f934(f934(x46802,f934(x46801,a922)),f934(x46802,a922)),f934(x46801,a922)),f8(f934(x46801,a922),a922,x46802)),a332)),x46804))))),f335(f335(f45(x46802,f934(x46801,a922)),x46803),x46804)) % 186.01/186.02 [4681]E(f44(f934(x46811,a922),f335(f270(f934(x46811,a922)),f335(f335(f8(f934(x46812,a922),a922,f934(x46811,a922)),f93(x46812)),f335(f335(f8(f934(x46812,a922),f934(x46812,a922),f934(x46811,a922)),f335(f18(x46812,a922,a922),f335(f335(f8(a922,f934(a922,a922),x46812),a333),f335(f335(f7(x46812,f934(x46812,a922),a922),f337(x46812)),x46813)))),f335(f335(f7(f934(x46811,a922),f934(x46812,f934(x46811,a922)),f934(x46812,a922)),f335(f335(f8(f934(f934(x46811,a922),a922),f934(f934(x46812,f934(x46811,a922)),f934(x46812,a922)),f934(x46811,a922)),f8(f934(x46811,a922),a922,x46812)),a332)),x46814))))),f335(f335(f46(x46812,f934(x46811,a922)),x46813),x46814)) % 186.01/186.02 [4688]E(f335(f335(f158(f928(x46881)),f335(f335(f158(x46881),x46882),f335(f149(f928(x46881),f928(x46881),f141(x46881),f120(x46881)),f335(f335(f161(f928(x46881),f928(x46881)),f163(f928(x46881),x46881,f120(x46881),f335(f335(f8(f928(x46881),f934(f928(x46881),f928(x46881)),x46881),f16(f928(x46881),f928(x46881))),f335(f335(f7(x46881,f928(x46881),f928(x46881)),f158(x46881)),f120(x46881))))),x46883)))),f186(x46881,f335(f335(f158(f928(x46881)),x46884),f335(f149(f928(f928(x46881)),f928(f928(x46881)),f141(f928(x46881)),f120(f928(x46881))),f335(f335(f161(f928(x46881),f928(f928(x46881))),f163(f928(f928(x46881)),x46881,f120(f928(x46881)),f335(f16(f934(f928(x46881),f928(f928(x46881))),x46881),f335(f335(f7(f928(x46881),f928(f928(x46881)),f928(f928(x46881))),f158(f928(x46881))),f120(f928(x46881)))))),x46883))))),f186(x46881,f335(f335(f158(f928(x46881)),f335(f335(f158(x46881),x46882),x46884)),x46883))) % 186.01/186.02 [4695]E(f335(f270(f933(x46951,x46951)),f335(f265(x46951,x46951,a922),f335(f335(f7(x46951,f934(f933(x46952,x46952),a922),f934(x46951,a922)),f335(f335(f8(f934(x46951,f934(f934(f933(x46952,x46952),a922),a922)),f934(f934(f933(x46952,x46952),a922),f934(x46951,a922)),x46951),f7(x46951,f934(f933(x46952,x46952),a922),a922)),f335(f335(f8(f934(x46951,f933(x46952,x46952)),f934(x46951,f934(f934(f933(x46952,x46952),a922),a922)),x46951),f335(f8(f933(x46952,x46952),f934(f934(f933(x46952,x46952),a922),a922),x46951),f337(f933(x46952,x46952)))),f335(f335(f7(x46951,f934(x46951,x46952),f934(x46951,f933(x46952,x46952))),f335(f335(f8(f934(x46952,f933(x46952,x46952)),f934(f934(x46951,x46952),f934(x46951,f933(x46952,x46952))),x46951),f8(x46952,f933(x46952,x46952),x46951)),f335(f335(f8(x46952,f934(x46952,f933(x46952,x46952)),x46951),f260(x46952,x46952)),x46953))),x46953)))),x46954))),f335(f335(f296(x46952,x46951),x46954),x46953)) % 186.01/186.02 [4749]~E(f32(x47491,x47492),f29(x47493,x47494,x47495)) % 186.01/186.02 [4750]~E(f32(x47501,x47502),f28(x47503,x47504,x47505)) % 186.01/186.02 [4751]~E(f31(x47511,x47512),f29(x47513,x47514,x47515)) % 186.01/186.02 [4752]~E(f31(x47521,x47522),f28(x47523,x47524,x47525)) % 186.01/186.02 [4753]~E(f27(x47531,x47532),f29(x47533,x47534,x47535)) % 186.01/186.02 [4754]~E(f27(x47541,x47542),f28(x47543,x47544,x47545)) % 186.01/186.02 [4755]~E(f29(x47551,x47552,x47553),f32(x47554,x47555)) % 186.01/186.02 [4756]~E(f29(x47561,x47562,x47563),f31(x47564,x47565)) % 186.01/186.02 [4757]~E(f29(x47571,x47572,x47573),f27(x47574,x47575)) % 186.01/186.02 [4758]~E(f28(x47581,x47582,x47583),f32(x47584,x47585)) % 186.01/186.02 [4759]~E(f28(x47591,x47592,x47593),f31(x47594,x47595)) % 186.01/186.02 [4760]~E(f28(x47601,x47602,x47603),f27(x47604,x47605)) % 186.01/186.02 [3824]E(f335(f335(f161(x38241,x38242),x38243),f176(x38241,x38244,x38245)),f176(x38242,x38244,f335(x38243,x38245))) % 186.01/186.02 [4038]E(f100(x40381,x40382,f98(x40381,x40383,x40384,x40385)),f2(a927)) % 186.01/186.02 [4162]E(f137(x41621,x41622,x41623,f133(x41621,x41624,x41625)),f133(x41622,f335(x41623,x41624),f137(x41621,x41622,x41623,x41625))) % 186.01/186.02 [4395]E(f335(f80(x43951,x43952,x43953,x43954,x43955),x43954),x43955) % 186.01/186.02 [4447]E(f261(x44471,x44472,x44473,f251(x44472,x44471,x44474),f251(x44473,x44472,x44475)),f251(x44473,x44471,f261(x44473,x44472,x44471,x44475,x44474))) % 186.01/186.02 [4017]E(f335(f335(f265(x40171,x40172,x40173),x40174),x40175),f335(f335(x40174,f335(f259(x40171,x40172),x40175)),f335(f264(x40171,x40172),x40175))) % 186.01/186.02 [4053]E(f335(f335(f335(f71(x40531,x40532,x40533),x40534),x40535),f195(f934(x40532,a922))),x40535) % 186.01/186.02 [4333]E(f335(f78(f928(x43331),f928(x43332),f928(x43333),f335(f161(x43331,x43332),x43334)),f335(f161(x43333,x43331),x43335)),f335(f161(x43333,x43332),f335(f78(x43331,x43332,x43333,x43334),x43335))) % 186.01/186.02 [4409]E(f91(x44091,f72(x44092,x44091,x44093,x44094,x44095)),f335(f335(f70(x44092,x44091,x44093),x44094),x44095)) % 186.01/186.02 [4443]E(f335(f335(f86(a927),f335(f335(f86(a927),f335(x44431,f335(f259(x44432,x44433),x44434))),f335(x44435,f335(f264(x44432,x44433),x44434)))),f335(a119,f2(a927))),f269(x44432,x44433,x44431,x44435,x44434)) % 186.01/186.02 [3953]E(f335(f335(f182(x39531),x39532),f335(f335(f161(x39533,x39531),x39534),x39535)),f335(f335(f161(x39533,x39531),x39534),f335(f335(f182(x39533),x39532),x39535))) % 186.01/186.02 [3954]E(f335(f335(f145(x39541),x39542),f335(f335(f161(x39543,x39541),x39544),x39545)),f335(f335(f161(x39543,x39541),x39544),f335(f335(f145(x39543),x39542),x39545))) % 186.01/186.02 [3986]E(f335(f335(f161(x39861,x39862),x39863),f335(f335(f158(x39861),x39864),x39865)),f335(f335(f158(x39862),f335(x39863,x39864)),f335(f335(f161(x39861,x39862),x39863),x39865))) % 186.01/186.02 [4049]E(f335(f318(x40491,x40492,x40493),f335(f335(f317(x40491),x40494),x40495)),f335(f335(f317(x40492),f335(x40493,x40494)),f335(f318(x40491,x40492,x40493),x40495))) % 186.01/186.02 [4077]E(f180(x40771,f335(f335(f158(x40771),x40772),x40773),f335(f335(f158(x40771),x40774),x40775)),f335(f335(f158(x40771),x40772),f335(f335(f158(x40771),x40774),f180(x40771,x40773,x40775)))) % 186.01/186.02 [4114]E(f335(f335(f188(x41141,x41142),f335(f335(f182(x41141),x41143),x41144)),f335(f335(f182(x41142),x41143),x41145)),f335(f335(f182(f933(x41141,x41142)),x41143),f335(f335(f188(x41141,x41142),x41144),x41145))) % 186.01/186.02 [4115]E(f335(f335(f188(x41151,x41152),f335(f335(f145(x41151),x41153),x41154)),f335(f335(f145(x41152),x41153),x41155)),f335(f335(f145(f933(x41151,x41152)),x41153),f335(f335(f188(x41151,x41152),x41154),x41155))) % 186.01/186.02 [4125]E(f335(f335(f166(x41251,f335(f335(f158(x41251),x41252),x41253)),f335(a119,x41254)),x41255),f335(f335(f158(x41251),x41252),f335(f335(f166(x41251,x41253),x41254),x41255))) % 186.01/186.02 [4128]E(f335(f335(f141(x41281),f335(f335(f161(x41282,x41281),x41283),x41284)),f335(f335(f161(x41282,x41281),x41283),x41285)),f335(f335(f161(x41282,x41281),x41283),f335(f335(f141(x41282),x41284),x41285))) % 186.01/186.02 [4132]E(f335(f335(x41321,x41322),f335(f335(f253(x41323,x41324,x41321),x41322),x41325)),f335(f335(f253(x41323,x41324,x41321),x41322),f335(a119,x41325))) % 186.01/186.02 [4166]E(f170(x41661,x41662,x41663,f335(f335(f158(x41661),x41664),x41665)),f335(f335(f141(x41662),f335(x41663,x41664)),f170(x41661,x41662,x41663,x41665))) % 186.01/186.02 [4178]E(f335(f335(f297(x41781,x41782,x41783),f335(f294(x41782,x41781),x41784)),f335(f294(x41783,x41782),x41785)),f335(f294(x41783,x41781),f335(f335(f297(x41783,x41782,x41781),x41785),x41784))) % 186.01/186.02 [4210]E(f335(f335(f335(f190(f928(x42101),f928(x42101)),x42102),f174(x42101)),f335(f335(f161(x42103,x42101),x42104),x42105)),f335(f335(f161(x42103,x42101),x42104),f335(f335(f335(f190(f928(x42103),f928(x42103)),x42102),f174(x42103)),x42105))) % 186.01/186.02 [4211]E(f335(f335(f267(x42111,x42112,x42111,x42113),f335(f260(x42112,x42111),x42114)),x42115),f335(x42115,x42114)) % 186.01/186.02 [4235]E(f162(x42351,x42352,f335(f335(f161(x42353,x42351),x42354),x42355)),f162(x42353,f335(f78(x42351,a927,x42353,x42352),x42354),x42355)) % 186.01/186.02 [4298]E(f184(f933(x42981,x42982),f335(f78(x42982,a922,f933(x42981,x42982),x42983),f264(x42981,x42982)),f335(f335(f188(x42981,x42982),x42984),x42985)),f335(f335(f188(x42981,x42982),x42984),f184(x42982,x42983,x42985))) % 186.01/186.02 [4303]E(f335(f318(x43031,x43032,f335(f335(f8(x43033,x43032,x43031),x43034),x43035)),f250(f934(x43031,a922))),f335(f318(x43033,x43032,x43034),f335(f318(x43031,x43033,x43035),f250(f934(x43031,a922))))) % 186.01/186.02 [4316]E(f184(f933(x43161,x43162),f335(f78(x43161,a922,f933(x43161,x43162),x43163),f259(x43161,x43162)),f335(f335(f188(x43161,x43162),x43164),x43165)),f335(f335(f188(x43161,x43162),f184(x43161,x43163,x43164)),x43165)) % 186.01/186.02 [4337]E(f335(f335(f117(f934(x43371,a922)),f335(f319(x43371,x43372,x43373),f335(f335(f317(x43372),x43374),f195(f934(x43372,a922))))),f335(f319(x43371,x43372,x43373),x43375)),f335(f319(x43371,x43372,x43373),f335(f335(f317(x43372),x43374),x43375))) % 186.01/186.02 [4394]E(f335(f335(f141(f933(x43941,x43942)),f335(f335(f161(x43942,f933(x43941,x43942)),f335(f260(x43941,x43942),x43943)),x43944)),f65(x43941,x43942,x43945,x43944)),f65(x43941,x43942,f335(f335(f158(x43941),x43943),x43945),x43944)) % 186.01/186.02 [4396]E(f335(f335(f161(x43961,x43962),x43963),f184(x43961,f335(f78(x43962,a922,x43961,x43964),x43963),x43965)),f184(x43962,x43964,f335(f335(f161(x43961,x43962),x43963),x43965))) % 186.01/186.02 [4401]E(f335(f149(x44011,x44012,f335(f7(x44012,x44011,x44011),f335(f7(x44011,x44012,x44011),x44013)),x44014),f335(f175(x44012),f335(f175(x44012),x44015))),f335(f149(x44011,x44012,x44013,x44014),x44015)) % 186.01/186.02 [4504]P1(f335(f335(f243(f934(x45041,a922)),f335(f318(x45042,x45041,x45043),f335(f335(f108(f934(x45042,a922)),x45044),x45045))),f335(f335(f108(f934(x45041,a922)),f335(f318(x45042,x45041,x45043),x45044)),f335(f318(x45042,x45041,x45043),x45045)))) % 186.01/186.02 [4505]P1(f335(f335(f243(f934(x45051,a922)),f335(f293(x45052,x45051,x45053),f335(f335(f108(f934(x45052,a922)),x45054),x45055))),f335(f335(f108(f934(x45051,a922)),f335(f293(x45052,x45051,x45053),x45054)),f335(f293(x45052,x45051,x45053),x45055)))) % 186.01/186.02 [4604]E(f335(f264(x46041,x46042),f335(f266(x46043,x46041,x46042,x46042,x46044,f25(x46042)),x46045)),f335(f264(x46043,x46042),x46045)) % 186.01/186.02 [4605]E(f335(f259(x46051,x46052),f335(f266(x46051,x46051,x46053,x46052,f25(x46051),x46054),x46055)),f335(f259(x46051,x46053),x46055)) % 186.01/186.02 [4670]P25(x46701,x46702,f335(f335(f317(f926(x46701)),f98(x46701,f335(f335(f7(x46701,f934(a923,a923),f934(a923,a922)),f335(f335(f8(f934(a923,a922),f934(f934(a923,a923),f934(a923,a922)),x46701),f8(a923,a922,a923)),x46703)),f335(f335(f18(a923,a927,a923),f335(f335(f7(a923,a925,f934(a927,a923)),a203),x46704)),x46705)),f27(x46704,x46705),x46703)),f195(f934(f926(x46701),a922)))) % 186.01/186.02 [3791]E(f335(f335(f335(f335(f213(x37911),x37912),x37913),x37914),x37915),f199(x37911,x37912)) % 186.01/186.02 [3792]E(f335(f335(f335(f335(f217(x37921),x37922),x37923),x37924),x37925),f208(x37921,x37922)) % 186.01/186.02 [4167]E(f335(f335(f45(x41671,f934(x41672,a922)),f335(f335(f317(x41671),x41673),x41674)),x41675),f335(f335(f117(f934(x41672,a922)),f335(x41675,x41673)),f335(f335(f45(x41671,f934(x41672,a922)),x41674),x41675))) % 186.01/186.02 [4168]E(f335(f335(f46(x41681,f934(x41682,a922)),f335(f335(f317(x41681),x41683),x41684)),x41685),f335(f335(f108(f934(x41682,a922)),f335(x41685,x41683)),f335(f335(f46(x41681,f934(x41682,a922)),x41684),x41685))) % 186.01/186.02 [4218]E(f335(f125(x42181,x42182,f335(x42183,x42184)),f335(f335(f7(x42181,a106,f929(x42182)),x42185),x42184)),f335(f206(x42181,x42182,x42183,x42185),x42184)) % 186.01/186.02 [4229]E(f335(f335(f117(f934(x42291,a922)),f335(f318(x42292,x42291,x42293),x42294)),f335(f318(x42292,x42291,x42293),x42295)),f335(f318(x42292,x42291,x42293),f335(f335(f117(f934(x42292,a922)),x42294),x42295))) % 186.01/186.02 [4230]E(f335(f335(f23(f934(x42301,a922)),f335(f319(x42301,x42302,x42303),x42304)),f335(f319(x42301,x42302,x42303),x42305)),f335(f319(x42301,x42302,x42303),f335(f335(f23(f934(x42302,a922)),x42304),x42305))) % 186.01/186.02 [4231]E(f335(f335(f108(f934(x42311,a922)),f335(f319(x42311,x42312,x42313),x42314)),f335(f319(x42311,x42312,x42313),x42315)),f335(f319(x42311,x42312,x42313),f335(f335(f108(f934(x42312,a922)),x42314),x42315))) % 186.01/186.02 [4232]E(f335(f335(f117(f934(x42321,a922)),f335(f319(x42321,x42322,x42323),x42324)),f335(f319(x42321,x42322,x42323),x42325)),f335(f319(x42321,x42322,x42323),f335(f335(f117(f934(x42322,a922)),x42324),x42325))) % 186.01/186.02 [4233]E(f335(f335(f117(f934(x42331,a922)),f335(f293(x42332,x42331,x42333),x42334)),f335(f293(x42332,x42331,x42333),x42335)),f335(f293(x42332,x42331,x42333),f335(f335(f117(f934(x42332,a922)),x42334),x42335))) % 186.01/186.02 [4294]E(f335(f335(f166(x42941,f335(f335(f141(x42941),x42942),f335(f335(f158(x42941),x42943),x42944))),f335(f196(f928(x42941)),x42942)),x42945),f335(f335(f141(x42941),x42942),f335(f335(f158(x42941),x42945),x42944))) % 186.01/186.02 [4301]E(f335(f335(f46(x43011,f934(x43012,a922)),x43013),f335(f335(f8(f934(x43012,a922),f934(x43012,a922),x43011),f335(f317(x43012),x43014)),x43015)),f335(f335(f317(x43012),x43014),f335(f335(f46(x43011,f934(x43012,a922)),x43013),x43015))) % 186.01/186.02 [4456]E(f335(f335(f161(x44561,x44562),x44563),f335(f143(x44561,f335(f78(x44562,a922,x44561,x44564),x44563)),x44565)),f335(f143(x44562,x44564),f335(f335(f161(x44561,x44562),x44563),x44565))) % 186.01/186.02 [4462]E(f335(f196(f928(x44621)),f335(f143(x44621,x44622),f335(f335(f161(x44623,x44621),x44624),x44625))),f335(f196(f928(x44623)),f335(f143(x44623,f335(f78(x44621,a922,x44623,x44622),x44624)),x44625))) % 186.01/186.02 [4671]E(f335(f163(f928(f933(x46711,x46712)),x46712,f120(f933(x46711,x46712)),f335(f335(f7(x46712,f934(f928(x46712),f928(f933(x46711,x46712))),f934(f928(x46712),f928(f933(x46711,x46712)))),f335(f335(f8(f934(f928(f933(x46711,x46712)),f928(f933(x46711,x46712))),f934(f934(f928(x46712),f928(f933(x46711,x46712))),f934(f928(x46712),f928(f933(x46711,x46712)))),x46712),f8(f928(f933(x46711,x46712)),f928(f933(x46711,x46712)),f928(x46712))),f335(f335(f8(f933(x46711,x46712),f934(f928(f933(x46711,x46712)),f928(f933(x46711,x46712))),x46712),f158(f933(x46711,x46712))),f335(f260(x46711,x46712),x46713)))),f335(f188(x46711,x46712),x46714))),x46715),f335(f335(f188(x46711,x46712),f335(f335(f158(x46711),x46713),x46714)),x46715)) % 186.01/186.02 [4159]E(f335(f335(f166(x41591,f335(f335(f166(x41591,x41592),x41593),x41594)),x41593),x41595),f335(f335(f166(x41591,x41592),x41593),x41595)) % 186.01/186.02 [4212]E(f335(f292(x42121,x42122),f335(f335(f317(f933(x42121,x42122)),f335(f335(f260(x42121,x42122),x42123),x42124)),x42125)),f335(f335(f317(x42122),x42124),f335(f292(x42121,x42122),x42125))) % 186.01/186.02 [4213]E(f335(f272(x42131,x42132),f335(f335(f317(f933(x42131,x42132)),f335(f335(f260(x42131,x42132),x42133),x42134)),x42135)),f335(f335(f317(x42131),x42133),f335(f272(x42131,x42132),x42135))) % 186.01/186.02 [4259]E(f129(x42591,x42592,f335(x42593,x42594),f335(f335(f7(x42591,a106,f929(f931(x42592))),x42595),x42594)),f335(f202(x42591,x42592,x42593,x42595),x42594)) % 186.01/186.02 [4287]E(f335(f335(f23(f934(f933(x42871,x42872),a922)),f335(f335(f262(x42871,x42872),x42873),x42874)),f335(f335(f262(x42871,x42872),x42875),x42874)),f335(f335(f262(x42871,x42872),f335(f335(f23(f934(x42871,a922)),x42873),x42875)),x42874)) % 186.01/186.02 [4288]E(f335(f335(f108(f934(f933(x42881,x42882),a922)),f335(f335(f262(x42881,x42882),x42883),x42884)),f335(f335(f262(x42881,x42882),x42885),x42884)),f335(f335(f262(x42881,x42882),f335(f335(f108(f934(x42881,a922)),x42883),x42885)),x42884)) % 186.01/186.02 [4289]E(f335(f335(f117(f934(f933(x42891,x42892),a922)),f335(f335(f262(x42891,x42892),x42893),x42894)),f335(f335(f262(x42891,x42892),x42895),x42894)),f335(f335(f262(x42891,x42892),f335(f335(f117(f934(x42891,a922)),x42893),x42895)),x42894)) % 186.01/186.02 [4348]E(f335(f335(f117(f934(x43481,a922)),f335(f335(f45(x43482,f934(x43481,a922)),x43483),x43484)),f335(f335(f45(x43482,f934(x43481,a922)),x43485),x43484)),f335(f335(f45(x43482,f934(x43481,a922)),f335(f335(f117(f934(x43482,a922)),x43483),x43485)),x43484)) % 186.01/186.02 [4349]E(f335(f335(f108(f934(x43491,a922)),f335(f335(f46(x43492,f934(x43491,a922)),x43493),x43494)),f335(f335(f46(x43492,f934(x43491,a922)),x43495),x43494)),f335(f335(f46(x43492,f934(x43491,a922)),f335(f335(f117(f934(x43492,a922)),x43493),x43495)),x43494)) % 186.01/186.02 [4363]E(f335(f335(f45(x43631,f934(x43632,a922)),x43633),f335(f335(f8(f934(x43632,a922),f934(x43632,a922),x43631),f335(f23(f934(x43632,a922)),x43634)),x43635)),f335(f335(f23(f934(x43632,a922)),x43634),f335(f335(f46(x43631,f934(x43632,a922)),x43633),x43635))) % 186.01/186.02 [4364]E(f335(f335(f45(x43641,f934(x43642,a922)),x43643),f335(f335(f8(f934(x43642,a922),f934(x43642,a922),x43641),f335(f108(f934(x43642,a922)),x43644)),x43645)),f335(f335(f108(f934(x43642,a922)),x43644),f335(f335(f45(x43641,f934(x43642,a922)),x43643),x43645))) % 186.01/186.02 [4365]E(f335(f335(f46(x43651,f934(x43652,a922)),x43653),f335(f335(f8(f934(x43652,a922),f934(x43652,a922),x43651),f335(f117(f934(x43652,a922)),x43654)),x43655)),f335(f335(f117(f934(x43652,a922)),x43654),f335(f335(f46(x43651,f934(x43652,a922)),x43653),x43655))) % 186.01/186.02 [4421]E(f192(f928(x44211),f335(f335(f158(x44211),x44212),x44213),f335(f335(f8(f928(x44211),f928(x44211),a927),f335(f158(x44211),x44214)),f335(f335(f7(a927,x44211,f928(x44211)),f166(x44211,x44213)),x44212)),x44215),f335(f335(f166(x44211,f335(f335(f158(x44211),x44214),x44213)),x44215),x44212)) % 186.01/186.02 [4425]E(f335(f335(f45(x44251,f934(f933(x44252,x44253),a922)),x44254),f335(f335(f8(f934(f933(x44253,x44252),a922),f934(f933(x44252,x44253),a922),x44251),f294(x44253,x44252)),x44255)),f335(f294(x44253,x44252),f335(f335(f45(x44251,f934(f933(x44253,x44252),a922)),x44254),x44255))) % 186.01/186.02 [4426]E(f335(f335(f46(x44261,f934(f933(x44262,x44263),a922)),x44264),f335(f335(f8(f934(f933(x44263,x44262),a922),f934(f933(x44262,x44263),a922),x44261),f294(x44263,x44262)),x44265)),f335(f294(x44263,x44262),f335(f335(f46(x44261,f934(f933(x44263,x44262),a922)),x44264),x44265))) % 186.01/186.02 [4527]P1(f335(f335(f243(f934(x45271,a922)),f335(f335(f23(f934(x45271,a922)),f335(f318(x45272,x45271,x45273),x45274)),f335(f318(x45272,x45271,x45273),x45275))),f335(f318(x45272,x45271,x45273),f335(f335(f23(f934(x45272,a922)),x45274),x45275)))) % 186.01/186.02 [4674]E(f335(f163(f928(f933(x46741,x46742)),x46741,f120(f933(x46741,x46742)),f335(f335(f7(x46741,f934(f928(x46741),f928(f933(x46741,x46742))),f934(f928(x46741),f928(f933(x46741,x46742)))),f335(f335(f8(f934(f928(f933(x46741,x46742)),f928(f933(x46741,x46742))),f934(f934(f928(x46741),f928(f933(x46741,x46742))),f934(f928(x46741),f928(f933(x46741,x46742)))),x46741),f8(f928(f933(x46741,x46742)),f928(f933(x46741,x46742)),f928(x46741))),f335(f335(f8(f933(x46741,x46742),f934(f928(f933(x46741,x46742)),f928(f933(x46741,x46742))),x46741),f158(f933(x46741,x46742))),f335(f335(f7(x46741,x46742,f933(x46741,x46742)),f260(x46741,x46742)),x46743)))),f335(f335(f7(f928(x46741),f928(x46742),f928(f933(x46741,x46742))),f188(x46741,x46742)),x46744))),x46745),f335(f335(f188(x46741,x46742),x46745),f335(f335(f158(x46742),x46743),x46744))) % 186.01/186.02 [4390]E(f335(f335(f117(f934(x43901,a922)),f335(f293(x43902,x43901,x43903),x43904)),f335(f293(x43902,x43901,x43905),x43904)),f335(f293(x43902,x43901,f335(f335(f117(f934(f933(x43902,x43901),a922)),x43903),x43905)),x43904)) % 186.01/186.02 [4427]E(f335(f335(f141(f933(x44271,x44272)),f335(f335(f188(x44271,x44272),x44273),f335(f335(f182(x44272),f335(f196(f928(x44271)),x44273)),x44274))),f335(f335(f188(x44271,x44272),x44275),f335(f335(f145(x44272),f335(f196(f928(x44271)),x44273)),x44274))),f335(f335(f188(x44271,x44272),f335(f335(f141(x44271),x44273),x44275)),x44274)) % 186.01/186.02 [4530]E(f335(f335(f262(x45301,x45302),x45303),f335(f335(f18(x45301,f934(x45302,a922),f934(x45302,a922)),f335(f335(f8(f934(x45302,a922),f934(f934(x45302,a922),f934(x45302,a922)),x45301),f23(f934(x45302,a922))),x45304)),x45305)),f335(f335(f23(f934(f933(x45301,x45302),a922)),f335(f335(f262(x45301,x45302),x45303),x45304)),f335(f335(f262(x45301,x45302),x45303),x45305))) % 186.01/186.02 [4531]E(f335(f335(f262(x45311,x45312),x45313),f335(f335(f18(x45311,f934(x45312,a922),f934(x45312,a922)),f335(f335(f8(f934(x45312,a922),f934(f934(x45312,a922),f934(x45312,a922)),x45311),f108(f934(x45312,a922))),x45314)),x45315)),f335(f335(f108(f934(f933(x45311,x45312),a922)),f335(f335(f262(x45311,x45312),x45313),x45314)),f335(f335(f262(x45311,x45312),x45313),x45315))) % 186.01/186.02 [4532]E(f335(f335(f262(x45321,x45322),x45323),f335(f335(f18(x45321,f934(x45322,a922),f934(x45322,a922)),f335(f335(f8(f934(x45322,a922),f934(f934(x45322,a922),f934(x45322,a922)),x45321),f117(f934(x45322,a922))),x45324)),x45325)),f335(f335(f117(f934(f933(x45321,x45322),a922)),f335(f335(f262(x45321,x45322),x45323),x45324)),f335(f335(f262(x45321,x45322),x45323),x45325))) % 186.01/186.02 [4536]E(f335(f335(f45(x45361,f934(x45362,a922)),x45363),f335(f335(f7(x45361,f934(x45362,a922),f934(x45362,a922)),f335(f335(f8(f934(x45362,a922),f934(f934(x45362,a922),f934(x45362,a922)),x45361),f23(f934(x45362,a922))),x45364)),x45365)),f335(f335(f23(f934(x45362,a922)),f335(f335(f45(x45361,f934(x45362,a922)),x45363),x45364)),x45365)) % 186.01/186.02 [4537]E(f335(f335(f45(x45371,f934(x45372,a922)),x45373),f335(f335(f7(x45371,f934(x45372,a922),f934(x45372,a922)),f335(f335(f8(f934(x45372,a922),f934(f934(x45372,a922),f934(x45372,a922)),x45371),f108(f934(x45372,a922))),x45374)),x45375)),f335(f335(f108(f934(x45372,a922)),f335(f335(f45(x45371,f934(x45372,a922)),x45373),x45374)),x45375)) % 186.01/186.02 [4538]E(f335(f335(f46(x45381,f934(x45382,a922)),x45383),f335(f335(f7(x45381,f934(x45382,a922),f934(x45382,a922)),f335(f335(f8(f934(x45382,a922),f934(f934(x45382,a922),f934(x45382,a922)),x45381),f117(f934(x45382,a922))),x45384)),x45385)),f335(f335(f117(f934(x45382,a922)),f335(f335(f46(x45381,f934(x45382,a922)),x45383),x45384)),x45385)) % 186.01/186.02 [4542]E(f335(f335(f45(x45421,f934(x45422,a922)),x45423),f335(f335(f18(x45421,f934(x45422,a922),f934(x45422,a922)),f335(f335(f8(f934(x45422,a922),f934(f934(x45422,a922),f934(x45422,a922)),x45421),f117(f934(x45422,a922))),x45424)),x45425)),f335(f335(f117(f934(x45422,a922)),f335(f335(f45(x45421,f934(x45422,a922)),x45423),x45424)),f335(f335(f45(x45421,f934(x45422,a922)),x45423),x45425))) % 186.01/186.02 [4543]E(f335(f335(f46(x45431,f934(x45432,a922)),x45433),f335(f335(f18(x45431,f934(x45432,a922),f934(x45432,a922)),f335(f335(f8(f934(x45432,a922),f934(f934(x45432,a922),f934(x45432,a922)),x45431),f108(f934(x45432,a922))),x45434)),x45435)),f335(f335(f108(f934(x45432,a922)),f335(f335(f46(x45431,f934(x45432,a922)),x45433),x45434)),f335(f335(f46(x45431,f934(x45432,a922)),x45433),x45435))) % 186.01/186.02 [4556]E(f335(f335(f45(x45561,f934(x45562,a922)),x45563),f335(f335(f18(x45561,f934(x45562,a922),f934(x45562,a922)),f335(f335(f8(f934(x45562,a922),f934(f934(x45562,a922),f934(x45562,a922)),x45561),f117(f934(x45562,a922))),x45564)),x45565)),f335(f335(f117(f934(x45562,a922)),f43(f934(x45562,a922),f335(f318(x45561,f934(x45562,a922),x45564),x45563))),f43(f934(x45562,a922),f335(f318(x45561,f934(x45562,a922),x45565),x45563)))) % 186.01/186.02 [4557]E(f335(f335(f46(x45571,f934(x45572,a922)),x45573),f335(f335(f18(x45571,f934(x45572,a922),f934(x45572,a922)),f335(f335(f8(f934(x45572,a922),f934(f934(x45572,a922),f934(x45572,a922)),x45571),f108(f934(x45572,a922))),x45574)),x45575)),f335(f335(f108(f934(x45572,a922)),f44(f934(x45572,a922),f335(f318(x45571,f934(x45572,a922),x45574),x45573))),f44(f934(x45572,a922),f335(f318(x45571,f934(x45572,a922),x45575),x45573)))) % 186.01/186.02 [4593]E(f335(f335(f145(x45931),f335(f196(f928(x45931)),f184(x45931,x45932,f335(f335(f161(x45933,x45931),x45934),x45935)))),f335(f335(f161(x45933,x45931),x45934),x45935)),f335(f335(f161(x45933,x45931),x45934),f335(f335(f145(x45933),f335(f196(f928(x45933)),f184(x45933,f335(f78(x45931,a922,x45933,x45932),x45934),x45935))),x45935))) % 186.01/186.02 [4469]E(f335(f335(f141(f933(x44691,x44692)),f335(f335(f188(x44691,x44692),f335(f335(f182(x44691),f335(f196(f928(x44692)),x44693)),x44694)),x44693)),f335(f335(f188(x44691,x44692),f335(f335(f145(x44691),f335(f196(f928(x44692)),x44693)),x44694)),x44695)),f335(f335(f188(x44691,x44692),x44694),f335(f335(f141(x44692),x44693),x44695))) % 186.01/186.02 [4584]E(f91(x45841,f335(f335(f18(x45841,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45841),a333),f335(f335(f7(x45841,f934(x45841,a922),a922),f337(x45841)),x45842))),f335(f335(f7(x45841,x45843,a922),f335(f335(f8(x45843,f934(x45843,a922),x45841),a332),x45844)),x45845))),f335(f83(x45841,x45843,x45842,x45844),x45845)) % 186.01/186.02 [4585]E(f96(x45851,f335(f335(f18(x45851,a922,a922),f335(f335(f8(a922,f934(a922,a922),x45851),a333),f335(f335(f7(x45851,f934(x45851,a922),a922),f337(x45851)),x45852))),f335(f335(f7(x45851,x45853,a922),f335(f335(f8(x45853,f934(x45853,a922),x45851),a332),x45854)),x45855))),f335(f97(x45851,x45853,x45852,x45854),x45855)) % 186.01/186.02 [4633]E(f335(f335(f92(a1,x46331),f335(f110(a1),f335(f335(f86(a1),x46332),a104))),f335(f335(f18(a1,x46331,x46331),f335(f335(f7(a1,x46331,f934(x46331,x46331)),f335(f335(f8(a922,f934(x46331,f934(x46331,x46331)),a1),f103(x46331)),a200)),f192(x46331,x46333,x46334,x46335))),f335(f335(f8(a927,x46331,a1),x46334),f335(f335(f7(a1,a927,a927),f335(f335(f8(a927,f934(a927,a927),a1),f86(a927)),a111)),x46335)))),f192(x46331,x46333,x46334,f335(f335(f86(a927),f335(f110(a927),x46332)),x46335))) % 186.01/186.02 [4668]E(f335(f335(f92(a1,x46681),f335(f110(a1),f335(f335(f86(a1),x46682),a104))),f335(f335(f18(a1,x46681,x46681),f335(f335(f7(a1,x46681,f934(x46681,x46681)),f335(f335(f8(a922,f934(x46681,f934(x46681,x46681)),a1),f103(x46681)),a200)),f335(f191(x46681,x46683,x46684),x46685))),f335(f335(f18(a1,x46681,x46681),f335(f335(f8(a927,f934(x46681,x46681),a1),x46684),f335(f335(f7(a1,a927,a927),f335(f335(f8(a927,f934(a927,a927),a1),f86(a927)),a111)),x46685))),f335(f335(f8(a927,x46681,a1),f191(x46681,x46683,x46684)),f335(f335(f7(a1,a927,a927),f335(f335(f8(a927,f934(a927,a927),a1),f86(a927)),a111)),x46685))))),f335(f191(x46681,x46683,x46684),f335(f335(f86(a927),f335(f110(a927),x46682)),x46685))) % 186.01/186.02 [4703]E(f335(f270(f933(x47031,x47032)),f335(f265(x47031,x47032,a922),f335(f335(f8(f934(x47032,f934(x47033,a922)),f934(x47032,a922),x47031),f335(f8(f934(x47033,a922),a922,x47032),f93(x47033))),f335(f335(f7(x47031,f934(x47032,f934(x47033,a922)),f934(x47032,f934(x47033,a922))),f335(f335(f8(f934(f934(x47033,a922),f934(x47033,a922)),f934(f934(x47032,f934(x47033,a922)),f934(x47032,f934(x47033,a922))),x47031),f8(f934(x47033,a922),f934(x47033,a922),x47032)),f335(f335(f8(f934(x47033,f934(a922,a922)),f934(f934(x47033,a922),f934(x47033,a922)),x47031),f18(x47033,a922,a922)),f335(f335(f8(f934(x47033,a922),f934(x47033,f934(a922,a922)),x47031),f335(f8(a922,f934(a922,a922),x47033),a333)),f335(f335(f7(x47031,f934(f933(x47031,x47033),a922),f934(x47033,a922)),f335(f335(f8(f934(x47033,f934(f934(f933(x47031,x47033),a922),a922)),f934(f934(f933(x47031,x47033),a922),f934(x47033,a922)),x47031),f7(x47033,f934(f933(x47031,x47033),a922),a922)),f335(f335(f8(f934(x47033,f933(x47031,x47033)),f934(x47033,f934(f934(f933(x47031,x47033),a922),a922)),x47031),f335(f8(f933(x47031,x47033),f934(f934(f933(x47031,x47033),a922),a922),x47033),f337(f933(x47031,x47033)))),f260(x47031,x47033)))),x47034))))),f335(f335(f7(x47032,f934(f933(x47033,x47032),a922),f934(x47033,a922)),f335(f335(f8(f934(x47033,f934(f934(f933(x47033,x47032),a922),a922)),f934(f934(f933(x47033,x47032),a922),f934(x47033,a922)),x47032),f7(x47033,f934(f933(x47033,x47032),a922),a922)),f335(f335(f8(f934(x47033,f933(x47033,x47032)),f934(x47033,f934(f934(f933(x47033,x47032),a922),a922)),x47032),f335(f8(f933(x47033,x47032),f934(f934(f933(x47033,x47032),a922),a922),x47033),f337(f933(x47033,x47032)))),f335(f7(x47033,x47032,f933(x47033,x47032)),f260(x47033,x47032))))),x47035))))),f335(f335(f297(x47031,x47033,x47032),x47034),x47035)) % 186.01/186.02 [4779]~E(f28(x47791,x47792,x47793),f29(x47794,x47795,x47796)) % 186.01/186.02 [4317]E(f233(x43171,x43172,x43173,x43174,f229(x43171,x43172,x43175,x43176)),f335(f335(x43174,x43175),x43176)) % 186.01/186.02 [4318]E(f234(x43181,x43182,x43183,x43184,f229(x43181,x43182,x43185,x43186)),f335(f335(x43184,x43185),x43186)) % 186.01/186.02 [4445]E(f134(x44451,x44452,x44453,x44454,f133(x44452,x44455,x44456)),f335(f335(f335(x44454,x44455),x44456),f134(x44451,x44452,x44453,x44454,x44456))) % 186.01/186.02 [4464]E(f80(x44641,x44642,f80(x44641,x44642,x44643,x44644,x44645),x44644,x44646),f80(x44641,x44642,x44643,x44644,x44646)) % 186.01/186.02 [4572]E(f335(f78(f933(x45721,x45722),x45722,f933(x45723,x45724),f264(x45721,x45722)),f266(x45723,x45721,x45724,x45722,x45725,x45726)),f335(f78(x45724,x45722,f933(x45723,x45724),x45726),f264(x45723,x45724))) % 186.01/186.02 [4573]E(f335(f78(f933(x45731,x45732),x45731,f933(x45733,x45734),f259(x45731,x45732)),f266(x45733,x45731,x45734,x45732,x45735,x45736)),f335(f78(x45733,x45731,f933(x45733,x45734),x45735),f259(x45733,x45734))) % 186.01/186.02 [4135]E(f101(x41351,x41352,x41353,f98(x41351,x41354,x41355,x41356)),f335(f335(f335(x41353,x41354),x41355),x41356)) % 186.01/186.02 [4136]E(f102(x41361,x41362,x41363,f98(x41361,x41364,x41365,x41366)),f335(f335(f335(x41363,x41364),x41365),x41366)) % 186.01/186.02 [4188]E(f335(f335(f78(x41881,x41882,x41883,x41884),x41885),x41886),f335(x41884,f335(x41885,x41886))) % 186.01/186.02 [4327]E(f232(x43271,f933(x43272,f929(x43272)),x43273,f335(f265(x43272,f929(x43272),x43271),x43274),f335(f142(x43272),f133(x43272,x43275,x43276))),f335(f335(x43274,x43275),x43276)) % 186.01/186.02 [4377]E(f235(x43771,x43772,x43773,x43774,f229(x43771,x43772,x43775,x43776)),f335(f335(f86(a927),f335(f335(f86(a927),f335(x43773,x43775)),f335(x43774,x43776))),f335(a119,f2(a927)))) % 186.01/186.02 [3984]E(f335(f335(f265(x39841,x39842,x39843),x39844),f335(f335(f260(x39841,x39842),x39845),x39846)),f335(f335(x39844,x39845),x39846)) % 186.01/186.02 [4046]E(f335(f335(f335(f8(x40461,x40462,x40463),x40464),x40465),x40466),f335(x40464,f335(x40465,x40466))) % 186.01/186.02 [4047]E(f335(f335(f335(f7(x40471,x40472,x40473),x40474),x40475),x40476),f335(f335(x40474,x40476),x40475)) % 186.01/186.02 [4063]E(f335(f335(f335(f18(x40631,x40632,x40633),x40634),x40635),x40636),f335(f335(x40634,x40636),f335(x40635,x40636))) % 186.01/186.02 [4086]E(f335(f163(x40861,x40862,x40863,x40864),f335(f335(f158(x40862),x40865),x40866)),f335(f335(x40864,x40865),x40866)) % 186.01/186.02 [4124]E(f176(f933(x41241,x41242),f335(f335(f241(a927),x41243),x41244),f335(f335(f260(x41241,x41242),x41245),x41246)),f335(f335(f188(x41241,x41242),f176(x41241,x41243,x41245)),f176(x41242,x41244,x41246))) % 186.01/186.02 [4192]E(f335(f335(f158(f933(x41921,x41922)),f335(f335(f260(x41921,x41922),x41923),x41924)),f335(f335(f188(x41921,x41922),x41925),x41926)),f335(f335(f188(x41921,x41922),f335(f335(f158(x41921),x41923),x41925)),f335(f335(f158(x41922),x41924),x41926))) % 186.01/186.02 [4193]E(f335(f335(f161(x41931,x41932),x41933),f335(f335(f166(x41931,x41934),x41935),x41936)),f335(f335(f166(x41932,f335(f335(f161(x41931,x41932),x41933),x41934)),x41935),f335(x41933,x41936))) % 186.01/186.02 [4217]E(f335(f335(f263(x42171,x42172,x42173,x42174),x42175),x42176),f335(x42174,f335(f335(f260(x42171,x42172),x42175),x42176))) % 186.01/186.02 [4234]E(f335(f149(x42341,x42342,x42343,x42344),f335(f335(f158(x42342),x42345),x42346)),f335(f149(x42341,x42342,x42343,f335(f335(x42343,x42344),x42345)),x42346)) % 186.01/186.02 [4260]E(f268(x42601,x42602,x42603,x42604,f335(f335(f260(x42601,x42602),x42605),x42606)),f335(f335(x42604,x42605),x42606)) % 186.01/186.02 [4341]E(f335(f335(f45(x43411,f934(x43412,a922)),x43413),f335(f78(x43414,f934(x43412,a922),x43411,x43415),x43416)),f335(f335(f45(x43414,f934(x43412,a922)),f335(f318(x43411,x43414,x43416),x43413)),x43415)) % 186.01/186.02 [4393]E(f335(f335(f161(x43931,x43932),x43933),f335(f335(f161(x43934,x43931),x43935),x43936)),f335(f335(f161(x43934,x43932),f335(f78(x43931,x43932,x43934,x43933),x43935)),x43936)) % 186.01/186.02 [4399]E(f335(f318(x43991,x43992,f335(f78(x43993,x43992,x43991,x43994),x43995)),x43996),f335(f318(x43993,x43992,x43994),f335(f318(x43991,x43993,x43995),x43996))) % 186.01/186.02 [4400]E(f335(f319(x44001,x44002,f335(f78(x44003,x44002,x44001,x44004),x44005)),x44006),f335(f319(x44001,x44003,x44005),f335(f319(x44003,x44002,x44004),x44006))) % 186.01/186.02 [4428]E(f335(f149(x44281,x44282,x44283,f335(f149(x44281,x44282,x44283,x44284),x44285)),x44286),f335(f149(x44281,x44282,x44283,x44284),f335(f335(f141(x44282),x44285),x44286))) % 186.01/186.02 [4562]E(f335(f266(x45621,x45621,x45622,x45623,f25(x45621),x45624),f335(f335(f260(x45621,x45622),x45625),x45626)),f335(f335(f260(x45621,x45623),x45625),f335(x45624,x45626))) % 186.01/186.02 [4563]E(f335(f266(x45631,x45632,x45633,x45633,x45634,f25(x45633)),f335(f335(f260(x45631,x45633),x45635),x45636)),f335(f335(f260(x45632,x45633),f335(x45634,x45635)),x45636)) % 186.01/186.02 [4651]E(f335(f335(f161(f933(x46511,x46512),f933(x46511,x46513)),f335(f265(x46511,x46512,f933(x46511,x46513)),f335(f335(f7(x46511,f934(x46512,x46513),f934(x46512,f933(x46511,x46513))),f335(f335(f8(f934(x46513,f933(x46511,x46513)),f934(f934(x46512,x46513),f934(x46512,f933(x46511,x46513))),x46511),f8(x46513,f933(x46511,x46513),x46512)),f260(x46511,x46513))),x46514))),f335(f335(f188(x46511,x46512),x46515),x46516)),f335(f335(f188(x46511,x46513),x46515),f335(f335(f161(x46512,x46513),x46514),x46516))) % 186.01/186.02 [4244]E(f335(f335(f78(x42441,x42442,x42443,f335(f16(x42442,x42441),x42444)),x42445),x42446),x42444) % 186.01/186.02 [4276]E(f335(f318(x42761,x42762,x42763),f335(f318(x42764,x42761,x42765),x42766)),f335(f318(x42764,x42762,f335(f335(f8(x42761,x42762,x42764),x42763),x42765)),x42766)) % 186.01/186.02 [4282]E(f335(f335(f45(x42821,f934(x42822,a922)),f335(f318(x42823,x42821,x42824),x42825)),x42826),f335(f335(f45(x42823,f934(x42822,a922)),x42825),f335(f335(f8(x42821,f934(x42822,a922),x42823),x42826),x42824))) % 186.01/186.02 [4283]E(f335(f335(f46(x42831,f934(x42832,a922)),f335(f318(x42833,x42831,x42834),x42835)),x42836),f335(f335(f46(x42833,f934(x42832,a922)),x42835),f335(f335(f8(x42831,f934(x42832,a922),x42833),x42836),x42834))) % 186.01/186.02 [4284]E(f335(f335(f45(x42841,f934(x42842,a922)),x42843),f335(f335(f8(x42844,f934(x42842,a922),x42841),x42845),x42846)),f335(f335(f45(x42844,f934(x42842,a922)),f335(f318(x42841,x42844,x42846),x42843)),x42845)) % 186.01/186.02 [4285]E(f335(f335(f46(x42851,f934(x42852,a922)),x42853),f335(f335(f8(x42854,f934(x42852,a922),x42851),x42855),x42856)),f335(f335(f46(x42854,f934(x42852,a922)),f335(f318(x42851,x42854,x42856),x42853)),x42855)) % 186.01/186.02 [4343]E(f335(f335(f45(x43431,f934(x43432,a922)),x43433),f335(f335(f8(f934(x43434,a922),f934(x43432,a922),x43431),f318(x43434,x43432,x43435)),x43436)),f335(f318(x43434,x43432,x43435),f335(f335(f45(x43431,f934(x43434,a922)),x43433),x43436))) % 186.01/186.02 [4344]E(f335(f335(f45(x43441,f934(x43442,a922)),x43443),f335(f335(f8(f934(x43444,a922),f934(x43442,a922),x43441),f319(x43442,x43444,x43445)),x43446)),f335(f319(x43442,x43444,x43445),f335(f335(f45(x43441,f934(x43444,a922)),x43443),x43446))) % 186.01/186.02 [4345]E(f335(f335(f46(x43451,f934(x43452,a922)),x43453),f335(f335(f8(f934(x43454,a922),f934(x43452,a922),x43451),f319(x43452,x43454,x43455)),x43456)),f335(f319(x43452,x43454,x43455),f335(f335(f46(x43451,f934(x43454,a922)),x43453),x43456))) % 186.01/186.02 [4346]E(f335(f335(f45(x43461,f934(x43462,a922)),x43463),f335(f335(f8(f934(x43464,a922),f934(x43462,a922),x43461),f293(x43464,x43462,x43465)),x43466)),f335(f293(x43464,x43462,x43465),f335(f335(f45(x43461,f934(x43464,a922)),x43463),x43466))) % 186.01/186.02 [4433]E(f335(f149(x44331,x44332,f335(f7(x44332,x44331,x44331),x44333),x44334),f335(f175(x44332),f335(f335(f158(x44332),x44335),x44336))),f335(f335(x44333,x44335),f335(f149(x44331,x44332,f335(f7(x44332,x44331,x44331),x44333),x44334),f335(f175(x44332),x44336)))) % 186.01/186.02 [4491]E(f335(f335(f18(f933(x44911,x44912),x44912,x44913),f335(f335(f8(x44914,f934(x44912,x44913),f933(x44911,x44912)),x44915),f335(f335(f8(x44911,x44914,f933(x44911,x44912)),x44916),f259(x44911,x44912)))),f264(x44911,x44912)),f335(f265(x44911,x44912,x44913),f335(f335(f8(x44914,f934(x44912,x44913),x44911),x44915),x44916))) % 186.01/186.02 [4498]E(f335(f149(x44981,x44982,f335(f7(x44982,x44981,x44981),x44983),f335(f149(x44981,x44982,f335(f7(x44982,x44981,x44981),x44983),x44984),f335(f175(x44982),x44985))),f335(f175(x44982),x44986)),f335(f149(x44981,x44982,f335(f7(x44982,x44981,x44981),x44983),x44984),f335(f175(x44982),f335(f335(f141(x44982),x44986),x44985)))) % 186.01/186.02 [4500]E(f335(f335(f161(f933(x45001,x45002),f933(x45003,x45002)),f335(f265(x45001,x45002,f933(x45003,x45002)),f335(f335(f8(x45003,f934(x45002,f933(x45003,x45002)),x45001),f260(x45003,x45002)),x45004))),f335(f335(f188(x45001,x45002),x45005),x45006)),f335(f335(f188(x45003,x45002),f335(f335(f161(x45001,x45003),x45004),x45005)),x45006)) % 186.01/186.02 [4545]P1(f335(f335(f243(f934(x45451,a922)),f335(f293(x45452,x45451,x45453),f335(f335(f46(x45454,f934(x45452,a922)),x45455),x45456))),f335(f335(f46(x45454,f934(x45451,a922)),x45455),f335(f335(f8(f934(x45452,a922),f934(x45451,a922),x45454),f293(x45452,x45451,x45453)),x45456)))) % 186.01/186.02 [4356]E(f335(f335(f188(x43561,x43562),f335(f335(f166(x43561,x43563),x43564),f335(f259(x43561,x43562),x43565))),f335(f335(f166(x43562,x43566),x43564),f335(f264(x43561,x43562),x43565))),f335(f335(f166(f933(x43561,x43562),f335(f335(f188(x43561,x43562),x43563),x43566)),x43564),x43565)) % 186.01/186.02 [4416]E(f335(f335(f117(f934(f933(x44161,x44162),a922)),f335(f335(f297(x44161,x44163,x44162),x44164),x44165)),f335(f335(f297(x44161,x44163,x44162),x44164),x44166)),f335(f335(f297(x44161,x44163,x44162),x44164),f335(f335(f117(f934(f933(x44163,x44162),a922)),x44165),x44166))) % 186.01/186.02 [4510]E(f335(f335(f317(f933(x45101,x45102)),f335(f335(f260(x45101,x45102),x45103),x45104)),f335(f335(f117(f934(f933(x45101,x45102),a922)),f335(f335(f262(x45101,x45102),x45105),f335(f16(f934(x45102,a922),x45101),f335(f335(f317(x45102),x45104),x45106)))),f335(f335(f262(x45101,x45102),f335(f335(f317(x45101),x45103),x45105)),f335(f16(f934(x45102,a922),x45101),x45106)))),f335(f335(f262(x45101,x45102),f335(f335(f317(x45101),x45103),x45105)),f335(f16(f934(x45102,a922),x45101),f335(f335(f317(x45102),x45104),x45106)))) % 186.01/186.02 [4589]E(f335(f335(f108(f934(x45891,a922)),f335(f319(x45891,x45892,f335(f78(f933(x45892,x45893),x45892,x45891,f259(x45892,x45893)),x45894)),x45895)),f335(f319(x45891,x45893,f335(f78(f933(x45892,x45893),x45893,x45891,f264(x45892,x45893)),x45894)),x45896)),f335(f319(x45891,f933(x45892,x45893),x45894),f335(f335(f262(x45892,x45893),x45895),f335(f16(f934(x45893,a922),x45892),x45896)))) % 186.01/186.02 [4439]E(f335(f335(f117(f934(f933(x44391,x44392),a922)),f335(f335(f297(x44391,x44393,x44392),x44394),x44395)),f335(f335(f297(x44391,x44393,x44392),x44396),x44395)),f335(f335(f297(x44391,x44393,x44392),f335(f335(f117(f934(f933(x44391,x44393),a922)),x44394),x44396)),x44395)) % 186.01/186.02 [4570]E(f335(f335(f45(x45701,f934(x45702,a922)),x45703),f335(f335(f7(x45701,f934(x45704,f934(x45702,a922)),f934(x45702,a922)),f335(f335(f8(f934(x45704,a922),f934(f934(x45704,f934(x45702,a922)),f934(x45702,a922)),x45701),f45(x45704,f934(x45702,a922))),x45705)),x45706)),f335(f335(f45(x45704,f934(x45702,a922)),f335(f335(f45(x45701,f934(x45704,a922)),x45703),x45705)),x45706)) % 186.01/186.02 [4571]E(f335(f335(f46(x45711,f934(x45712,a922)),x45713),f335(f335(f7(x45711,f934(x45714,f934(x45712,a922)),f934(x45712,a922)),f335(f335(f8(f934(x45714,a922),f934(f934(x45714,f934(x45712,a922)),f934(x45712,a922)),x45711),f46(x45714,f934(x45712,a922))),x45715)),x45716)),f335(f335(f46(x45714,f934(x45712,a922)),f335(f335(f45(x45711,f934(x45714,a922)),x45713),x45715)),x45716)) % 186.01/186.02 [4623]E(f335(f265(x46231,x46232,f933(x46233,x46234)),f335(f335(f7(x46231,f934(x46232,x46234),f934(x46232,f933(x46233,x46234))),f335(f335(f8(f934(x46234,f933(x46233,x46234)),f934(f934(x46232,x46234),f934(x46232,f933(x46233,x46234))),x46231),f8(x46234,f933(x46233,x46234),x46232)),f335(f335(f8(x46233,f934(x46234,f933(x46233,x46234)),x46231),f260(x46233,x46234)),x46235))),x46236)),f266(x46231,x46233,x46232,x46234,x46235,x46236)) % 186.01/186.02 [4646]E(f335(f318(x46461,x46462,f335(f335(f18(x46461,x46462,x46462),f335(f335(f18(x46461,x46462,f934(x46462,x46462)),f335(f335(f8(a922,f934(x46462,f934(x46462,x46462)),x46461),f103(x46462)),x46463)),x46464)),x46465)),x46466),f335(f335(f117(f934(x46462,a922)),f335(f318(x46461,x46462,x46464),f335(f335(f108(f934(x46461,a922)),x46466),f335(f270(x46461),x46463)))),f335(f318(x46461,x46462,x46465),f335(f335(f108(f934(x46461,a922)),x46466),f335(f270(x46461),f335(f335(f8(a922,a922,x46461),a330),x46463)))))) % 186.01/186.02 [4658]E(f335(f318(x46581,f933(x46582,x46583),f335(f335(f18(x46581,x46583,f933(x46582,x46583)),f335(f335(f8(x46582,f934(x46583,f933(x46582,x46583)),x46581),f260(x46582,x46583)),x46584)),x46585)),x46586),f335(f335(f262(x46582,x46583),f335(f318(x46581,x46582,x46584),x46586)),f335(f335(f8(f934(x46581,a922),f934(x46583,a922),x46582),f318(x46581,x46583,x46585)),f335(f335(f7(x46582,f934(x46581,a922),f934(x46581,a922)),f335(f335(f8(f934(x46581,a922),f934(f934(x46581,a922),f934(x46581,a922)),x46582),f108(f934(x46581,a922))),f335(f335(f8(f934(x46582,a922),f934(x46581,a922),x46582),f319(x46581,x46582,x46584)),f335(f335(f7(x46582,f934(x46582,a922),f934(x46582,a922)),f317(x46582)),f195(f934(x46582,a922)))))),x46586)))) % 186.01/186.02 [4685]E(f254(x46851,x46852,x46853,x46854,x46855,x46856),f335(x46854,f335(f270(x46851),f335(f335(f8(f934(f934(x46853,x46851),a922),a922,x46851),f93(f934(x46853,x46851))),f335(f335(f8(f934(f934(x46853,x46851),a922),f934(f934(x46853,x46851),a922),x46851),f335(f18(f934(x46853,x46851),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x46853,x46851)),a333),f335(f335(f7(f934(x46853,x46851),f934(f934(x46853,x46851),a922),a922),f337(f934(x46853,x46851))),x46855)))),f335(f335(f7(x46851,f934(f934(x46853,x46851),x46851),f934(f934(x46853,x46851),a922)),f335(f335(f8(f934(x46851,a922),f934(f934(f934(x46853,x46851),x46851),f934(f934(x46853,x46851),a922)),x46851),f8(x46851,a922,f934(x46853,x46851))),a332)),f335(f335(f7(f934(x46853,x46851),x46853,x46851),f5(f934(x46853,x46851))),x46856))))))) % 186.01/186.02 [4472]E(f335(f78(x44721,x44722,x44723,x44724),f80(x44723,x44721,x44725,x44726,x44727)),f80(x44723,x44722,f335(f78(x44721,x44722,x44723,x44724),x44725),x44726,f335(x44724,x44727))) % 186.01/186.02 [4606]E(f335(f264(x46061,x46062),f335(f266(x46063,x46061,x46064,x46062,x46065,x46066),x46067)),f335(x46066,f335(f264(x46063,x46064),x46067))) % 186.01/186.02 [4607]E(f335(f259(x46071,x46072),f335(f266(x46073,x46071,x46074,x46072,x46075,x46076),x46077)),f335(x46075,f335(f259(x46073,x46074),x46077))) % 186.01/186.02 [4319]E(f335(f335(f188(x43191,x43192),f335(f335(f166(x43191,x43193),x43194),x43195)),f335(f335(f166(x43192,x43196),x43194),x43197)),f335(f335(f166(f933(x43191,x43192),f335(f335(f188(x43191,x43192),x43193),x43196)),x43194),f335(f335(f260(x43191,x43192),x43195),x43197))) % 186.01/186.02 [4388]E(f335(f335(f335(f267(x43881,x43882,x43883,x43884),x43885),x43886),x43887),f335(f335(f265(x43882,x43883,x43884),x43886),f335(x43885,x43887))) % 186.01/186.02 [4398]E(f335(f335(f335(f267(x43981,x43982,x43983,x43984),x43985),x43986),x43987),f335(f335(x43986,f335(f259(x43982,x43983),f335(x43985,x43987))),f335(f264(x43982,x43983),f335(x43985,x43987)))) % 186.01/186.02 [4450]E(f335(f78(x44501,x44502,x44503,x44504),f335(f78(x44505,x44501,x44503,x44506),x44507)),f335(f78(x44505,x44502,x44503,f335(f78(x44501,x44502,x44505,x44504),x44506)),x44507)) % 186.01/186.02 [4627]E(f335(f266(x46271,x46272,x46273,x46273,x46274,f25(x46273)),f335(f266(x46271,x46271,x46275,x46273,f25(x46271),x46276),x46277)),f335(f335(f260(x46272,x46273),f335(x46274,f335(f259(x46271,x46275),x46277))),f335(x46276,f335(f264(x46271,x46275),x46277)))) % 186.01/186.02 [4628]E(f335(f266(x46281,x46281,x46282,x46283,f25(x46281),x46284),f335(f266(x46285,x46281,x46282,x46282,x46286,f25(x46282)),x46287)),f335(f335(f260(x46281,x46283),f335(x46286,f335(f259(x46285,x46282),x46287))),f335(x46284,f335(f264(x46285,x46282),x46287)))) % 186.01/186.02 [4644]E(f335(f266(x46441,x46442,x46443,x46443,x46444,f25(x46443)),f335(f266(x46445,x46441,x46443,x46443,x46446,f25(x46443)),x46447)),f335(f266(x46445,x46442,x46443,x46443,f335(f78(x46441,x46442,x46445,x46444),x46446),f25(x46443)),x46447)) % 186.01/186.02 [4645]E(f335(f266(x46451,x46451,x46452,x46453,f25(x46451),x46454),f335(f266(x46451,x46451,x46455,x46452,f25(x46451),x46456),x46457)),f335(f266(x46451,x46451,x46455,x46453,f25(x46451),f335(f78(x46452,x46453,x46455,x46454),x46456)),x46457)) % 186.01/186.02 [4655]E(f335(f266(x46551,x46552,x46553,x46553,x46554,f25(x46553)),f335(f266(x46551,x46551,x46555,x46553,f25(x46551),x46556),x46557)),f335(f266(x46552,x46552,x46555,x46553,f25(x46552),x46556),f335(f266(x46551,x46552,x46555,x46555,x46554,f25(x46555)),x46557))) % 186.01/186.02 [4353]E(f335(f335(f297(x43531,x43532,x43533),f335(f335(f297(x43531,x43534,x43532),x43535),x43536)),x43537),f335(f335(f297(x43531,x43534,x43533),x43535),f335(f335(f297(x43534,x43532,x43533),x43536),x43537))) % 186.01/186.02 [4422]E(f335(f335(f265(x44221,x44222,x44223),f335(f78(x44224,f934(x44222,x44223),x44221,x44225),x44226)),x44227),f335(f335(x44225,f335(x44226,f335(f259(x44221,x44222),x44227))),f335(f264(x44221,x44222),x44227))) % 186.01/186.02 [4503]E(f335(f149(x45031,x45032,f335(f7(x45032,x45031,x45031),x45033),x45034),f335(f175(x45032),f335(f335(f161(x45035,x45032),x45036),x45037))),f335(f149(x45031,x45035,f335(f7(x45035,x45031,x45031),f335(f78(x45032,f934(x45031,x45031),x45035,x45033),x45036)),x45034),f335(f175(x45035),x45037))) % 186.01/186.02 [4451]E(f335(f335(f45(x44511,f934(f933(x44512,x44513),a922)),x44514),f335(f335(f8(f934(f933(x44515,x44513),a922),f934(f933(x44512,x44513),a922),x44511),f335(f297(x44512,x44515,x44513),x44516)),x44517)),f335(f335(f297(x44512,x44515,x44513),x44516),f335(f335(f45(x44511,f934(f933(x44515,x44513),a922)),x44514),x44517))) % 186.01/186.02 [4594]E(f335(f335(f45(x45941,f934(f933(x45942,x45943),a922)),x45944),f335(f335(f7(x45941,f934(f933(x45945,x45943),a922),f934(f933(x45942,x45943),a922)),f335(f335(f8(f934(f933(x45942,x45945),a922),f934(f934(f933(x45945,x45943),a922),f934(f933(x45942,x45943),a922)),x45941),f297(x45942,x45945,x45943)),x45946)),x45947)),f335(f335(f297(x45942,x45945,x45943),f335(f335(f45(x45941,f934(f933(x45942,x45945),a922)),x45944),x45946)),x45947)) % 186.01/186.02 [4595]E(f335(f149(x45951,x45952,f335(f335(f7(x45951,f934(x45952,x45953),f934(x45952,x45951)),f335(f335(f8(f934(x45953,x45951),f934(f934(x45952,x45953),f934(x45952,x45951)),x45951),f8(x45953,x45951,x45952)),x45954)),x45955),x45956),x45957),f335(f149(x45951,x45953,x45954,x45956),f335(f335(f161(x45952,x45953),x45955),x45957))) % 186.01/186.02 [4656]E(f335(f335(f45(x46561,f934(x46562,a922)),x46563),f335(f335(f8(f934(x46564,f934(x46562,a922)),f934(x46562,a922),x46561),f335(f45(x46564,f934(x46562,a922)),x46565)),f335(f335(f7(x46561,f934(x46564,f934(x46562,a922)),f934(x46564,f934(x46562,a922))),f335(f335(f8(f934(f934(x46562,a922),f934(x46562,a922)),f934(f934(x46564,f934(x46562,a922)),f934(x46564,f934(x46562,a922))),x46561),f8(f934(x46562,a922),f934(x46562,a922),x46564)),f335(f335(f8(f934(x46562,a922),f934(f934(x46562,a922),f934(x46562,a922)),x46561),f108(f934(x46562,a922))),x46566))),x46567))),f335(f335(f108(f934(x46562,a922)),f335(f335(f45(x46561,f934(x46562,a922)),x46563),x46566)),f335(f335(f45(x46564,f934(x46562,a922)),x46565),x46567))) % 186.01/186.02 [4657]E(f335(f335(f46(x46571,f934(x46572,a922)),x46573),f335(f335(f8(f934(x46574,f934(x46572,a922)),f934(x46572,a922),x46571),f335(f46(x46574,f934(x46572,a922)),x46575)),f335(f335(f7(x46571,f934(x46574,f934(x46572,a922)),f934(x46574,f934(x46572,a922))),f335(f335(f8(f934(f934(x46572,a922),f934(x46572,a922)),f934(f934(x46574,f934(x46572,a922)),f934(x46574,f934(x46572,a922))),x46571),f8(f934(x46572,a922),f934(x46572,a922),x46574)),f335(f335(f8(f934(x46572,a922),f934(f934(x46572,a922),f934(x46572,a922)),x46571),f117(f934(x46572,a922))),x46576))),x46577))),f335(f335(f117(f934(x46572,a922)),f335(f335(f46(x46571,f934(x46572,a922)),x46573),x46576)),f335(f335(f46(x46574,f934(x46572,a922)),x46575),x46577))) % 186.01/186.02 [4649]E(f206(x46491,x46492,f335(f335(f335(x46493,x46494),x46495),x46496),f335(f335(f7(x46491,f933(a106,a106),f934(a106,f929(x46492))),f335(f335(f7(x46491,a106,f934(f933(a106,a106),f934(a106,f929(x46492)))),f335(f335(f7(x46491,a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(x46492))))),x46497),x46494)),x46495)),x46496)),f335(f335(f335(f218(x46491,x46492,x46493,x46497),x46494),x46495),x46496)) % 186.01/186.02 [4663]E(f207(x46631,x46632,f335(f335(f335(x46633,x46634),x46635),x46636),f335(f335(f7(x46631,f933(a106,a106),f934(a106,f929(x46632))),f335(f335(f7(x46631,a106,f934(f933(a106,a106),f934(a106,f929(x46632)))),f335(f335(f7(x46631,a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(x46632))))),x46637),x46634)),x46635)),x46636)),f220(x46631,x46632,x46633,x46637,x46634,x46635,x46636)) % 186.01/186.02 [4654]E(f202(x46541,x46542,f335(f335(f335(x46543,x46544),x46545),x46546),f335(f335(f7(x46541,f933(a106,a106),f934(a106,f929(f931(x46542)))),f335(f335(f7(x46541,a106,f934(f933(a106,a106),f934(a106,f929(f931(x46542))))),f335(f335(f7(x46541,a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(f931(x46542)))))),x46547),x46544)),x46545)),x46546)),f335(f335(f335(f214(x46541,x46542,x46543,x46547),x46544),x46545),x46546)) % 186.01/186.02 [4665]E(f205(x46651,x46652,f335(f335(f335(x46653,x46654),x46655),x46656),f335(f335(f7(x46651,f933(a106,a106),f934(a106,f929(f931(x46652)))),f335(f335(f7(x46651,a106,f934(f933(a106,a106),f934(a106,f929(f931(x46652))))),f335(f335(f7(x46651,a106,f934(a106,f934(f933(a106,a106),f934(a106,f929(f931(x46652)))))),x46657),x46654)),x46655)),x46656)),f216(x46651,x46652,x46653,x46657,x46654,x46655,x46656)) % 186.01/186.02 [4564]E(f335(f266(x45641,x45642,x45643,x45644,x45645,x45646),f335(f335(f260(x45641,x45643),x45647),x45648)),f335(f335(f260(x45642,x45644),f335(x45645,x45647)),f335(x45646,x45648))) % 186.01/186.02 [4667]E(f335(f335(f161(f933(x46671,x46672),f933(x46673,x46674)),f335(f265(x46671,x46672,f933(x46673,x46674)),f335(f335(f7(x46671,f934(x46672,x46674),f934(x46672,f933(x46673,x46674))),f335(f335(f8(f934(x46674,f933(x46673,x46674)),f934(f934(x46672,x46674),f934(x46672,f933(x46673,x46674))),x46671),f8(x46674,f933(x46673,x46674),x46672)),f335(f335(f8(x46673,f934(x46674,f933(x46673,x46674)),x46671),f260(x46673,x46674)),x46675))),x46676))),f335(f335(f188(x46671,x46672),x46677),x46678)),f335(f335(f188(x46673,x46674),f335(f335(f161(x46671,x46673),x46675),x46677)),f335(f335(f161(x46672,x46674),x46676),x46678))) % 186.01/186.02 [4672]E(f335(f335(f161(f933(x46721,x46722),x46723),f335(f265(x46721,x46722,x46723),f335(f335(f8(f934(x46722,f933(x46721,x46724)),f934(x46722,x46723),x46721),f335(f8(f933(x46721,x46724),x46723,x46722),x46725)),f335(f335(f7(x46721,f934(x46722,x46724),f934(x46722,f933(x46721,x46724))),f335(f335(f8(f934(x46724,f933(x46721,x46724)),f934(f934(x46722,x46724),f934(x46722,f933(x46721,x46724))),x46721),f8(x46724,f933(x46721,x46724),x46722)),f260(x46721,x46724))),x46726)))),f335(f335(f188(x46721,x46722),x46727),x46728)),f335(f335(f161(f933(x46721,x46724),x46723),x46725),f335(f335(f188(x46721,x46724),x46727),f335(f335(f161(x46722,x46724),x46726),x46728)))) % 186.01/186.02 [4598]E(f335(f335(f161(f933(x45981,x45982),x45983),f335(f265(x45981,x45982,x45983),f335(f335(f8(f934(x45982,f933(x45984,x45982)),f934(x45982,x45983),x45981),f335(f8(f933(x45984,x45982),x45983,x45982),x45985)),f335(f335(f8(x45984,f934(x45982,f933(x45984,x45982)),x45981),f260(x45984,x45982)),x45986)))),f335(f335(f188(x45981,x45982),x45987),x45988)),f335(f335(f161(f933(x45984,x45982),x45983),x45985),f335(f335(f188(x45984,x45982),f335(f335(f161(x45981,x45984),x45986),x45987)),x45988))) % 186.01/186.02 [4555]E(f335(f335(f265(x45551,x45552,x45553),f335(f335(f8(f934(x45552,f933(x45554,x45555)),f934(x45552,x45553),x45551),f335(f8(f933(x45554,x45555),x45553,x45552),f335(f265(x45554,x45555,x45553),x45556))),x45557)),x45558),f335(f335(f265(x45554,x45555,x45553),x45556),f335(f335(f265(x45551,x45552,f933(x45554,x45555)),x45557),x45558))) % 186.01/186.02 [4673]E(f335(f335(f45(f933(x46731,x46732),f934(f933(x46733,x46734),a922)),f335(f335(f262(x46731,x46732),x46735),f335(f16(f934(x46732,a922),x46731),x46736))),f335(f265(x46731,x46732,f934(f933(x46733,x46734),a922)),f335(f335(f7(x46731,f934(x46732,f934(x46733,f934(x46734,a922))),f934(x46732,f934(f933(x46733,x46734),a922))),f335(f335(f8(f934(f934(x46733,f934(x46734,a922)),f934(f933(x46733,x46734),a922)),f934(f934(x46732,f934(x46733,f934(x46734,a922))),f934(x46732,f934(f933(x46733,x46734),a922))),x46731),f8(f934(x46733,f934(x46734,a922)),f934(f933(x46733,x46734),a922),x46732)),f335(f335(f8(f934(x46733,a922),f934(f934(x46733,f934(x46734,a922)),f934(f933(x46733,x46734),a922)),x46731),f262(x46733,x46734)),x46737))),f335(f335(f8(f934(x46734,a922),f934(x46733,f934(x46734,a922)),x46732),f16(f934(x46734,a922),x46733)),x46738)))),f335(f335(f262(x46733,x46734),f335(f335(f45(x46731,f934(x46733,a922)),x46735),x46737)),f335(f16(f934(x46734,a922),x46733),f335(f335(f45(x46732,f934(x46734,a922)),x46736),x46738)))) % 186.01/186.02 [4612]E(f335(f335(f267(x46121,x46122,x46123,x46124),f335(f335(f267(x46121,x46125,x46126,f933(x46122,x46123)),x46127),x46128)),x46129),f335(f335(f267(x46121,x46125,x46126,x46124),x46127),f335(f335(f7(x46125,f934(x46122,f934(x46123,x46124)),f934(x46126,x46124)),f335(f335(f8(f934(x46126,f933(x46122,x46123)),f934(f934(x46122,f934(x46123,x46124)),f934(x46126,x46124)),x46125),f267(x46126,x46122,x46123,x46124)),x46128)),x46129))) % 186.01/186.02 [4641]E(f335(f78(f933(x46411,x46412),f933(x46413,x46414),f933(x46415,x46416),f266(x46411,x46413,x46412,x46414,x46417,x46418)),f266(x46415,x46411,x46416,x46412,x46419,x464110)),f266(x46415,x46413,x46416,x46414,f335(f78(x46411,x46413,x46415,x46417),x46419),f335(f78(x46412,x46414,x46416,x46418),x464110))) % 186.01/186.02 [4647]E(f335(f266(x46471,x46472,x46473,x46474,x46475,x46476),f335(f266(x46477,x46471,x46478,x46473,x46479,x464710),x464711)),f335(f266(x46477,x46472,x46478,x46474,f335(f78(x46471,x46472,x46477,x46475),x46479),f335(f78(x46473,x46474,x46478,x46476),x464710)),x464711)) % 186.01/186.02 [4810]~P62(x48101)+P62(f931(x48101)) % 186.01/186.02 [4811]~P65(x48111)+P65(f931(x48111)) % 186.01/186.02 [4812]~P105(x48121)+P105(f928(x48121)) % 186.01/186.02 [4815]~P144(x48151)+~E(f84(x48151),f2(x48151)) % 186.01/186.02 [4817]~E(x48171,f2(a106))+E(f335(a22,x48171),f2(a1)) % 186.01/186.02 [4818]~E(x48181,f2(a1))+E(f88(a1,x48181),f2(a1)) % 186.01/186.02 [4824]~P146(x48241)+P29(x48241,f2(x48241)) % 186.01/186.02 [4826]~P109(x48261)+P14(x48261,f120(x48261)) % 186.01/186.02 [4835]P1(x48351)+P1(f335(a330,x48351)) % 186.01/186.02 [4889]~P146(x48891)+~P29(x48891,f84(x48891)) % 186.01/186.02 [4932]~P1(x49321)+~P1(f335(a330,x49321)) % 186.01/186.02 [4953]E(f335(a111,x49531),f2(a927))+~P1(f335(a200,x49531)) % 186.01/186.02 [5019]~P96(x50191)+P15(x50191,x50191,f87(x50191)) % 186.01/186.02 [5020]~P97(x50201)+P15(x50201,x50201,f108(x50201)) % 186.01/186.02 [5021]~P103(x50211)+P15(x50211,x50211,f117(x50211)) % 186.01/186.02 [5022]~P109(x50221)+P15(x50221,x50221,f241(x50221)) % 186.01/186.02 [5023]~P109(x50231)+P15(x50231,x50231,f242(x50231)) % 186.01/186.02 [5024]~P70(x50241)+P17(x50241,x50241,f87(x50241)) % 186.01/186.02 [4821]~E(x48211,f2(a927))+E(f335(f107(a1),x48211),f2(a1)) % 186.01/186.02 [4828]~P94(x48281)+E(f335(f110(x48281),a89),f2(x48281)) % 186.01/186.02 [4831]~E(f574(x48311),f2(a927))+E(f335(f172(a927),x48311),f2(a927)) % 186.01/186.02 [4832]~P108(x48321)+E(f245(x48321,f243(x48321)),f241(x48321)) % 186.01/186.02 [4833]~P108(x48331)+E(f246(x48331,f243(x48331)),f242(x48331)) % 186.01/186.02 [4834]~P90(x48341)+E(f88(x48341,f2(x48341)),f2(x48341)) % 186.01/186.02 [4843]~P146(x48431)+E(f335(f107(x48431),f84(a927)),f84(x48431)) % 186.01/186.02 [4844]~P146(x48441)+E(f335(f107(x48441),f2(a927)),f2(x48441)) % 186.01/186.02 [4845]~P140(x48451)+E(f335(f109(x48451),f84(a1)),f84(x48451)) % 186.01/186.02 [4846]~P140(x48461)+E(f335(f109(x48461),f2(a1)),f2(x48461)) % 186.01/186.02 [4847]E(x48471,f2(a927))+~E(f335(f107(a1),x48471),f2(a1)) % 186.01/186.02 [4883]~P83(x48831)+E(f335(f85(x48831),f195(x48831)),f250(x48831)) % 186.01/186.02 [4884]~P83(x48841)+E(f335(f85(x48841),f250(x48841)),f195(x48841)) % 186.01/186.02 [4885]~P4(x48851)+E(f335(f85(x48851),f2(x48851)),f2(x48851)) % 186.01/186.02 [4886]~P113(x48861)+E(f335(f81(x48861),f84(x48861)),f84(x48861)) % 186.01/186.02 [4887]~P87(x48871)+E(f335(f81(x48871),f2(x48871)),f2(x48871)) % 186.01/186.02 [4888]~P82(x48881)+E(f335(f172(x48881),f120(x48881)),f2(x48881)) % 186.01/186.02 [4906]~P37(x49061)+P41(f335(f179(a1),x49061)) % 186.01/186.02 [4937]~P94(x49371)+E(f335(f85(x49371),f84(x49371)),f335(f110(x49371),a104)) % 186.01/186.02 [4952]~P94(x49521)+P29(x49521,f335(f110(x49521),a89)) % 186.01/186.02 [4978]P37(x49781)+~P41(f335(f179(a1),x49781)) % 186.01/186.02 [5025]E(f335(f107(a1),f335(a111,x50251)),x50251)+P1(f335(a200,x50251)) % 186.01/186.02 [5095]~P117(x50951)+E(f253(x50951,f84(x50951),f87(x50951)),f252(x50951)) % 186.01/186.02 [5128]~P94(x51281)+~P29(x51281,f335(f110(x51281),a104)) % 186.01/186.02 [5220]~E(x52201,f84(a927))+P1(f335(f335(f295(a927),x52201),f84(a927))) % 186.01/186.02 [5276]E(f335(f81(a1),x52761),x52761)+P1(f335(f335(f244(a1),x52761),f2(a1))) % 186.01/186.02 [5294]~E(f335(a111,x52941),f2(a927))+P1(f335(f335(f243(a1),x52941),f2(a1))) % 186.01/186.02 [5360]~P1(f335(a200,x53601))+P1(f335(f335(f244(a1),x53601),f2(a1))) % 186.01/186.02 [5400]~P140(x54001)+P1(f335(f335(f337(x54001),f84(x54001)),f116(x54001))) % 186.01/186.02 [5401]~P146(x54011)+P1(f335(f335(f337(x54011),f84(x54011)),f193(x54011))) % 186.01/186.02 [5402]~P140(x54021)+P1(f335(f335(f337(x54021),f2(x54021)),f116(x54021))) % 186.01/186.02 [5403]~P146(x54031)+P1(f335(f335(f337(x54031),f2(x54031)),f193(x54031))) % 186.01/186.02 [5404]~P125(x54041)+P1(f335(f335(f243(x54041),f2(x54041)),f84(x54041))) % 186.01/186.02 [5405]~P125(x54051)+P1(f335(f335(f244(x54051),f2(x54051)),f84(x54051))) % 186.01/186.02 [5457]E(x54571,f84(a927))+~P1(f335(f335(f295(a927),x54571),f84(a927))) % 186.01/186.02 [5458]E(x54581,f2(a927))+~P1(f335(f335(f243(a927),x54581),f2(a927))) % 186.01/186.02 [5500]E(f335(a111,x55001),f2(a927))+~P1(f335(f335(f243(a1),x55001),f2(a1))) % 186.01/186.02 [5561]P1(f335(a200,x55611))+~P1(f335(f335(f244(a1),x55611),f2(a1))) % 186.01/186.02 [5568]~P109(x55681)+P17(x55681,f928(x55681),f155(x55681,x55681,f5(x55681))) % 186.01/186.02 [5586]P41(x55861)+~P1(f335(f335(f243(a1),f2(a1)),f436(x55861))) % 186.01/186.02 [5591]E(f335(f81(a1),x55911),f335(f85(a1),x55911))+~P1(f335(f335(f244(a1),x55911),f2(a1))) % 186.01/186.02 [5762]~P125(x57621)+~P1(f335(f335(f243(x57621),f84(x57621)),f2(x57621))) % 186.01/186.02 [5763]~P125(x57631)+~P1(f335(f335(f244(x57631),f84(x57631)),f2(x57631))) % 186.01/186.02 [5777]~E(x57771,f2(a927))+P1(f335(f335(f243(a1),f335(f107(a1),x57771)),f2(a1))) % 186.01/186.02 [5778]~E(x57781,f2(a1))+P1(f335(f335(f244(a1),f335(f81(a1),x57781)),f84(a1))) % 186.01/186.02 [5899]~P82(x58991)+E(f149(x58991,x58991,f86(x58991),f2(x58991)),f172(x58991)) % 186.01/186.02 [6073]~P104(x60731)+P26(a927,x60731,f107(x60731),f250(f934(a927,a922))) % 186.01/186.02 [6272]E(x62721,f2(a927))+~P1(f335(f335(f243(a1),f335(f107(a1),x62721)),f2(a1))) % 186.01/186.02 [6273]E(x62731,f2(a1))+~P1(f335(f335(f244(a1),f335(f81(a1),x62731)),f84(a1))) % 186.01/186.02 [7067]~P1(f335(f335(f244(a1),x70671),f2(a1)))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x70671),x70671)),f2(a1))) % 186.01/186.02 [7618]P1(f335(f335(f244(a1),x76181),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x76181),x76181)),f2(a1))) % 186.01/186.02 [8157]E(x81571,f335(a3,f2(a927)))+P1(f335(f335(f244(a927),f335(f335(f23(a927),f335(a20,x81571)),f335(a119,f2(a927)))),f335(a20,x81571))) % 186.01/186.02 [8919]~P1(f335(f335(f244(a1),x89191),f2(a1)))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x89191),x89191)),a104)),f2(a1))) % 186.01/186.02 [9016]~P1(f335(f335(f244(a1),x90161),f2(a1)))+P1(f335(f335(f244(a1),f335(f335(f86(a1),f335(f335(f86(a1),f84(a1)),x90161)),x90161)),f2(a1))) % 186.01/186.02 [9339]P1(f335(f335(f244(a1),x93391),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93391),x93391)),a104)),f2(a1))) % 186.01/186.02 [9400]P1(f335(f335(f244(a1),x94001),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),f335(f335(f86(a1),f84(a1)),x94001)),x94001)),f2(a1))) % 186.01/186.02 [4926]~E(a89,x49261)+E(f335(f335(f86(a1),x49261),x49261),a89) % 186.01/186.02 [4927]~E(x49271,a89)+E(f335(f335(f86(a1),x49271),x49271),a89) % 186.01/186.02 [4938]E(x49381,f2(a1))+E(f335(f335(f42(a1),x49381),x49381),f84(a1)) % 186.01/186.02 [5072]E(x50721,a89)+~E(f335(f335(f86(a1),x50721),x50721),a89) % 186.01/186.02 [5073]E(a89,x50731)+~E(f335(f335(f86(a1),x50731),x50731),a89) % 186.01/186.02 [5085]~P6(x50851)+E(f44(x50851,f195(f934(x50851,a922))),f250(x50851)) % 186.01/186.02 [5086]~P6(x50861)+E(f44(x50861,f250(f934(x50861,a922))),f195(x50861)) % 186.01/186.02 [5087]~P6(x50871)+E(f43(x50871,f195(f934(x50871,a922))),f195(x50871)) % 186.01/186.02 [5088]~P6(x50881)+E(f43(x50881,f250(f934(x50881,a922))),f250(x50881)) % 186.01/186.02 [5089]~P109(x50891)+E(f146(x50891,f195(f934(x50891,a922))),f120(x50891)) % 186.01/186.02 [5232]E(x52321,f2(a927))+P1(f335(f335(f244(a927),f2(a927)),x52321)) % 186.01/186.02 [5251]~P7(x52511)+P1(f335(f335(f243(a1),f2(a1)),x52511)) % 186.01/186.02 [5285]~E(f335(f110(a927),x52851),f2(a927))+P1(f335(f335(f243(a1),x52851),a89)) % 186.01/186.02 [5290]P41(x52901)+P1(f335(f335(f337(a1),f436(x52901)),x52901)) % 186.01/186.02 [5291]E(x52911,f335(a3,f2(a927)))+P1(f335(f335(f243(a106),f84(a106)),x52911)) % 186.01/186.02 [5332]P1(f335(a200,x53321))+P1(f335(f335(f243(a1),f2(a1)),x53321)) % 186.01/186.02 [5382]E(f335(f107(a1),f335(a111,x53821)),f2(a1))+P1(f335(f335(f243(a1),f2(a1)),x53821)) % 186.01/186.02 [5439]E(f335(f107(a1),f335(f110(a927),x54391)),f335(f110(a1),x54391))+P1(f335(a200,f335(f110(a1),x54391))) % 186.01/186.02 [5464]E(f335(f110(a927),x54641),f2(a927))+~P1(f335(a200,f335(f110(a1),x54641))) % 186.01/186.02 [5465]E(f335(f110(a927),x54651),f2(a927))+~P1(f335(f335(f243(a1),x54651),a89)) % 186.01/186.02 [5497]P7(x54971)+~P1(f335(f335(f243(a1),f2(a1)),x54971)) % 186.01/186.02 [5571]E(f335(a119,f373(x55711)),x55711)+~P1(f335(f335(f244(a927),f2(a927)),x55711)) % 186.01/186.02 [5580]E(f335(a119,f335(f110(a927),x55801)),f84(a927))+~P1(f335(a200,f335(f110(a1),x55801))) % 186.01/186.02 [5587]E(f335(f107(a1),f464(x55871)),x55871)+~P1(f335(f335(f244(a1),f2(a1)),x55871)) % 186.01/186.02 [5594]~E(x55941,f335(a3,f2(a927)))+~P1(f335(f335(f243(a106),f84(a106)),x55941)) % 186.01/186.02 [5601]E(f335(f107(a1),f335(f110(a927),x56011)),f2(a1))+~P1(f335(a200,f335(f110(a1),x56011))) % 186.01/186.02 [5626]E(f335(f172(a927),x56261),f2(a927))+P1(f335(f335(f337(a927),f574(x56261)),f335(f179(a927),x56261))) % 186.01/186.02 [5646]E(f335(f107(a1),f335(a111,x56461)),x56461)+~P1(f335(f335(f243(a1),f2(a1)),x56461)) % 186.01/186.02 [5654]~P1(f335(a200,x56541))+~P1(f335(f335(f243(a1),f2(a1)),x56541)) % 186.01/186.02 [5755]E(f335(f335(f86(a927),f84(a927)),f335(f110(a927),x57551)),f84(a927))+~P1(f335(f335(f244(a1),x57551),a89)) % 186.01/186.02 [5819]E(x58191,f2(a927))+~P1(f335(f335(f244(a927),x58191),f335(a119,f2(a927)))) % 186.01/186.02 [5858]E(f335(f335(f23(a927),f335(f110(a927),x58581)),f84(a927)),f2(a927))+~P1(f335(f335(f243(a1),x58581),a89)) % 186.01/186.02 [5859]E(f335(f335(f86(a927),f335(f110(a927),x58591)),f84(a927)),f84(a927))+~P1(f335(f335(f244(a1),x58591),a89)) % 186.01/186.02 [5871]~P41(x58711)+E(f335(f41(a927),f335(f318(a1,a927,a111),x58711)),f335(f41(a1),x58711)) % 186.01/186.02 [5900]~P109(x59001)+E(f245(x59001,f335(f7(x59001,x59001,a922),f243(x59001))),f242(x59001)) % 186.01/186.02 [5901]~P109(x59011)+E(f246(x59011,f335(f7(x59011,x59011,a922),f243(x59011))),f241(x59011)) % 186.01/186.02 [5911]E(f51(a927,f335(a119,f2(a927)),f335(f110(a927),x59111)),f335(a119,f2(a927)))+~P1(f335(a200,f335(f110(a1),x59111))) % 186.01/186.02 [5920]~P1(f335(f335(f244(a1),f2(a1)),x59201))+P1(f335(f335(f243(a1),f84(a1)),x59201)) % 186.01/186.02 [5921]P1(f335(f335(f244(a1),f2(a1)),x59211))+~P1(f335(f335(f243(a1),f84(a1)),x59211)) % 186.01/186.02 [5932]E(f335(a119,f335(f335(f23(a927),x59321),f84(a927))),x59321)+~P1(f335(f335(f244(a927),f2(a927)),x59321)) % 186.01/186.02 [5988]P1(f335(f335(f244(a927),f2(a927)),f464(x59881)))+~P1(f335(f335(f244(a1),f2(a1)),x59881)) % 186.01/186.02 [6049]E(f51(a1,f335(f110(a1),a104),x60491),f335(f335(f23(a1),x60491),f84(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x60491)) % 186.01/186.02 [6086]~P1(f335(f335(f244(a1),a89),x60861))+P1(f335(f335(f244(a927),f2(a927)),f335(f110(a927),x60861))) % 186.01/186.02 [6091]E(f335(a20,f838(x60911)),x60911)+~P1(f335(f335(f337(a927),x60911),f250(f934(a927,a922)))) % 186.01/186.02 [6140]P1(f335(f335(f244(a927),f2(a927)),f335(a111,x61401)))+~P1(f335(f335(f244(a1),f2(a1)),x61401)) % 186.01/186.02 [6189]~P1(f335(f335(f244(a927),f2(a927)),x61891))+P1(f335(f335(f244(a1),f2(a1)),f335(f107(a1),x61891))) % 186.01/186.02 [6225]~P1(f335(f335(f244(a927),f2(a927)),f335(a111,x62251)))+P1(f335(f335(f244(a1),f2(a1)),x62251)) % 186.01/186.02 [6240]~P41(x62401)+E(f335(f318(a927,a1,f107(a1)),f335(f318(a1,a927,a111),x62401)),x62401) % 186.01/186.02 [6253]P1(f335(f335(f244(a1),a89),x62531))+~P1(f335(f335(f244(a927),f2(a927)),f335(f110(a927),x62531))) % 186.01/186.02 [6310]P1(f335(f335(f244(a927),f2(a927)),x63101))+~P1(f335(f335(f244(a1),f2(a1)),f335(f107(a1),x63101))) % 186.01/186.02 [6424]E(f335(f318(a927,a1,f107(a1)),f335(f290(a927),f335(a111,x64241))),f335(f310(a1,f2(a1)),x64241))+~P1(f335(f335(f243(a1),f2(a1)),x64241)) % 186.01/186.02 [6440]~P125(x64401)+P1(f335(f335(f244(x64401),f2(x64401)),f335(f335(f86(x64401),f84(x64401)),f84(x64401)))) % 186.01/186.02 [6489]P1(f335(f335(f244(a927),f335(a119,f2(a927))),f335(a111,x64891)))+~P1(f335(f335(f244(a1),f84(a1)),x64891)) % 186.01/186.02 [6586]E(x65861,f2(a1))+P1(f335(f55(f2(a1),x65861),f335(f335(f260(a1,a1),f2(a1)),f2(a1)))) % 186.01/186.02 [6753]~P1(f335(f335(f244(a927),f335(a119,f2(a927))),f335(a111,x67531)))+P1(f335(f335(f244(a1),f84(a1)),x67531)) % 186.01/186.02 [7175]~P115(x71751)+P38(x71751,f335(f270(f933(x71751,x71751)),f335(f265(x71751,x71751,a922),f244(x71751)))) % 186.01/186.02 [5806]E(f335(f110(a927),f335(f335(f23(a1),x58061),a104)),f335(a119,f335(f110(a927),x58061)))+P1(f335(a200,f335(f110(a1),x58061))) % 186.01/186.02 [5822]~P37(x58221)+E(f335(f335(f161(a927,a1),f107(a1)),f335(f335(f161(a1,a927),a111),x58221)),x58221) % 186.01/186.02 [5938]E(f335(f85(a1),f335(f107(a1),f335(a119,f465(x59381)))),x59381)+~P1(f335(f335(f244(a1),x59381),f2(a1))) % 186.01/186.02 [5948]E(f335(f335(f86(a927),f84(a927)),f335(f110(a927),x59481)),f335(f110(a927),f335(f335(f23(a1),x59481),a104)))+P1(f335(f335(f244(a1),x59481),a89)) % 186.01/186.02 [5990]E(f335(f335(f42(a1),f335(f110(a1),a104)),x59901),f335(f110(a1),a104))+~P1(f335(f335(f244(a1),f2(a1)),x59901)) % 186.01/186.02 [6082]E(f335(f335(f23(a927),f335(f110(a927),x60821)),f84(a927)),f335(f110(a927),f335(f335(f86(a1),x60821),a104)))+P1(f335(f335(f243(a1),x60821),a89)) % 186.01/186.02 [6083]E(f335(f335(f86(a927),f335(f110(a927),x60831)),f84(a927)),f335(f110(a927),f335(f335(f23(a1),x60831),a104)))+P1(f335(f335(f244(a1),x60831),a89)) % 186.01/186.02 [6127]E(f335(a111,f335(f335(f86(a1),f84(a1)),x61271)),f335(a119,f335(a111,x61271)))+~P1(f335(f335(f243(a1),f2(a1)),x61271)) % 186.01/186.02 [6161]E(f335(a119,f335(f335(f23(a927),x61611),f335(a119,f2(a927)))),x61611)+~P1(f335(f335(f244(a927),f2(a927)),x61611)) % 186.01/186.02 [6375]E(f51(a927,f335(a119,f2(a927)),f335(f110(a927),x63751)),f335(a111,f51(a1,f84(a1),f335(f110(a1),x63751))))+P1(f335(a200,f335(f110(a1),x63751))) % 186.01/186.02 [6417]~P1(f335(f335(f243(a1),a89),x64171))+P1(f335(f335(f243(a1),a89),f335(f335(f86(a1),x64171),x64171))) % 186.01/186.02 [6418]~P1(f335(f335(f244(a1),a104),x64181))+P1(f335(f335(f243(a1),a104),f335(f335(f86(a1),x64181),x64181))) % 186.01/186.02 [6419]~P1(f335(f335(f244(a1),a89),x64191))+P1(f335(f335(f244(a1),a89),f335(f335(f86(a1),x64191),x64191))) % 186.01/186.02 [6420]~P1(f335(f335(f244(a1),a104),x64201))+P1(f335(f335(f244(a1),a104),f335(f335(f86(a1),x64201),x64201))) % 186.01/186.02 [6599]~P1(f335(f67(x65991),f250(f934(x65991,a922))))+P1(f335(f67(f931(x65991)),f250(f934(f931(x65991),a922)))) % 186.01/186.02 [6685]~P1(f335(f335(f243(a1),f2(a1)),x66851))+P1(f335(f335(f244(a1),f2(a1)),f335(f335(f86(a1),f84(a1)),x66851))) % 186.01/186.02 [6692]E(f335(f259(a1,a1),f53(f84(a1),f335(f110(a1),x66921))),f335(f335(f42(a1),f84(a1)),f335(f110(a1),x66921)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x66921))) % 186.01/186.02 [6712]E(f335(f264(a1,a1),f53(f84(a1),f335(f110(a1),x67121))),f51(a1,f84(a1),f335(f110(a1),x67121)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x67121))) % 186.01/186.02 [6724]P1(f335(f67(x67241),f250(f934(x67241,a922))))+~P1(f335(f67(f931(x67241)),f250(f934(f931(x67241),a922)))) % 186.01/186.02 [6754]P1(f335(f335(f243(a1),a89),x67541))+~P1(f335(f335(f243(a1),a89),f335(f335(f86(a1),x67541),x67541))) % 186.01/186.02 [6755]P1(f335(f335(f244(a1),a89),x67551))+~P1(f335(f335(f244(a1),a89),f335(f335(f86(a1),x67551),x67551))) % 186.01/186.02 [6756]P1(f335(f335(f244(a1),a104),x67561))+~P1(f335(f335(f243(a1),a104),f335(f335(f86(a1),x67561),x67561))) % 186.01/186.02 [6757]P1(f335(f335(f244(a1),a104),x67571))+~P1(f335(f335(f244(a1),a104),f335(f335(f86(a1),x67571),x67571))) % 186.01/186.02 [7071]~P1(f335(f67(x70711),f250(f934(x70711,a922))))+P1(f335(f335(f244(a927),f2(a927)),f335(f41(x70711),f250(f934(x70711,a922))))) % 186.01/186.02 [7657]P1(f335(f67(a927),x76571))+~P1(f335(f67(a1),f335(f318(a927,a1,f107(a1)),x76571))) % 186.01/186.02 [5730]~E(a104,x57301)+E(f335(f335(f23(a1),f335(f335(f86(a1),x57301),x57301)),a104),a104) % 186.01/186.02 [5731]~E(x57311,a104)+E(f335(f335(f23(a1),f335(f335(f86(a1),x57311),x57311)),a104),a104) % 186.01/186.02 [6248]E(x62481,a104)+~E(f335(f335(f23(a1),f335(f335(f86(a1),x62481),x62481)),a104),a104) % 186.01/186.02 [6249]E(a104,x62491)+~E(f335(f335(f23(a1),f335(f335(f86(a1),x62491),x62491)),a104),a104) % 186.01/186.02 [6653]~E(f335(f110(a927),x66531),f2(a927))+P1(f335(a200,f335(f110(a1),f335(f335(f86(a1),x66531),a104)))) % 186.01/186.02 [7001]~P1(f335(a200,f335(f110(a1),x70011)))+P1(f335(a200,f335(f110(a1),f335(f335(f86(a1),x70011),x70011)))) % 186.01/186.02 [7002]~P1(f335(f335(f243(a1),x70021),a89))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x70021),x70021)),a89)) % 186.01/186.02 [7003]~P1(f335(f335(f243(a1),x70031),a104))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x70031),x70031)),a104)) % 186.01/186.02 [7004]~P1(f335(f335(f244(a1),x70041),a89))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x70041),x70041)),a89)) % 186.01/186.02 [7005]~P1(f335(f335(f243(a1),x70051),a104))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x70051),x70051)),a104)) % 186.01/186.02 [7321]E(f335(f110(a927),x73211),f2(a927))+~P1(f335(a200,f335(f110(a1),f335(f335(f86(a1),x73211),a104)))) % 186.01/186.02 [7574]~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x75741)))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),f335(f335(f86(a1),x75741),x75741)))) % 186.01/186.02 [7575]P1(f335(a200,f335(f110(a1),x75751)))+~P1(f335(a200,f335(f110(a1),f335(f335(f86(a1),x75751),x75751)))) % 186.01/186.02 [7576]P1(f335(f335(f243(a1),x75761),a89))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x75761),x75761)),a89)) % 186.01/186.02 [7577]P1(f335(f335(f243(a1),x75771),a104))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x75771),x75771)),a104)) % 186.01/186.02 [7578]P1(f335(f335(f243(a1),x75781),a104))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x75781),x75781)),a104)) % 186.01/186.02 [7579]P1(f335(f335(f244(a1),x75791),a89))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x75791),x75791)),a89)) % 186.01/186.02 [7931]E(f335(a113,f556(x79311)),x79311)+~P1(f335(f335(f337(f934(f933(a927,a927),a922)),x79311),a105)) % 186.01/186.02 [6573]~P94(x65731)+E(f335(f110(x65731),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f84(x65731)) % 186.01/186.02 [7051]~P1(f335(a200,f335(f110(a1),x70511)))+E(f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x70511),x70511)),a104)),f2(a927)) % 186.01/186.02 [8103]~P1(f335(f335(f244(a1),f335(f110(a1),x81031)),f2(a1)))+E(f335(f259(a1,a1),f335(a57,f56(f335(f85(a1),f84(a1)),f335(f85(a1),f335(f110(a1),x81031))))),f335(f335(f42(a1),f84(a1)),f335(f110(a1),x81031))) % 186.01/186.02 [8116]~P1(f335(f335(f244(a1),f335(f110(a1),x81161)),f2(a1)))+E(f335(f264(a1,a1),f335(a57,f56(f335(f85(a1),f84(a1)),f335(f85(a1),f335(f110(a1),x81161))))),f51(a1,f84(a1),f335(f110(a1),x81161))) % 186.01/186.02 [8164]~P1(f335(f335(f243(a1),a89),x81641))+P1(f335(f335(f243(a1),a89),f335(f335(f23(a1),f335(f335(f86(a1),x81641),x81641)),a104))) % 186.01/186.02 [8165]~P1(f335(f335(f243(a1),a104),x81651))+P1(f335(f335(f243(a1),a104),f335(f335(f23(a1),f335(f335(f86(a1),x81651),x81651)),a104))) % 186.01/186.02 [8166]~P1(f335(f335(f243(a1),a89),x81661))+P1(f335(f335(f244(a1),a89),f335(f335(f23(a1),f335(f335(f86(a1),x81661),x81661)),a104))) % 186.01/186.02 [8167]~P1(f335(f335(f244(a1),a104),x81671))+P1(f335(f335(f244(a1),a104),f335(f335(f23(a1),f335(f335(f86(a1),x81671),x81671)),a104))) % 186.01/186.02 [8461]~P94(x84611)+~P29(x84611,f335(f110(x84611),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))) % 186.01/186.02 [8644]P1(f335(f335(f243(a1),a89),x86441))+~P1(f335(f335(f243(a1),a89),f335(f335(f23(a1),f335(f335(f86(a1),x86441),x86441)),a104))) % 186.01/186.02 [8645]P1(f335(f335(f243(a1),a89),x86451))+~P1(f335(f335(f244(a1),a89),f335(f335(f23(a1),f335(f335(f86(a1),x86451),x86451)),a104))) % 186.01/186.02 [8646]P1(f335(f335(f243(a1),a104),x86461))+~P1(f335(f335(f243(a1),a104),f335(f335(f23(a1),f335(f335(f86(a1),x86461),x86461)),a104))) % 186.01/186.02 [8647]P1(f335(f335(f244(a1),a104),x86471))+~P1(f335(f335(f244(a1),a104),f335(f335(f23(a1),f335(f335(f86(a1),x86471),x86471)),a104))) % 186.01/186.02 [8966]E(f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x89661),x89661)),a104)),f335(f335(f92(a927,a927),f335(f110(a927),x89661)),f335(f335(f8(a927,a927,a927),a119),f335(f335(f18(a927,a927,a927),f86(a927)),f5(a927)))))+P1(f335(a200,f335(f110(a1),x89661))) % 186.01/186.02 [9819]E(x98191,f195(f934(f933(a927,a927),a922)))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x98191),f195(f934(f933(a927,a927),a922)))),a39)) % 186.01/186.02 [8893]~P1(f335(a200,f335(f110(a1),x88931)))+P1(f335(a200,f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x88931),x88931)),a104)))) % 186.01/186.02 [8894]~P1(f335(f335(f244(a1),x88941),a89))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x88941),x88941)),a104)),a89)) % 186.01/186.02 [8895]~P1(f335(f335(f243(a1),x88951),a104))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x88951),x88951)),a104)),a104)) % 186.01/186.02 [8896]~P1(f335(f335(f244(a1),x88961),a89))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x88961),x88961)),a104)),a89)) % 186.01/186.02 [8897]~P1(f335(f335(f244(a1),x88971),a104))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x88971),x88971)),a104)),a104)) % 186.01/186.02 [9007]~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x90071)))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x90071),x90071)),a104)))) % 186.01/186.02 [9169]~P94(x91691)+E(f335(f335(f86(x91691),f84(x91691)),f84(x91691)),f335(f110(x91691),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))) % 186.01/186.02 [9323]P1(f335(a200,f335(f110(a1),x93231)))+~P1(f335(a200,f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93231),x93231)),a104)))) % 186.01/186.02 [9324]P1(f335(f335(f243(a1),x93241),a104))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93241),x93241)),a104)),a104)) % 186.01/186.02 [9325]P1(f335(f335(f244(a1),x93251),a89))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93251),x93251)),a104)),a89)) % 186.01/186.02 [9326]P1(f335(f335(f244(a1),x93261),a89))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93261),x93261)),a104)),a89)) % 186.01/186.02 [9327]P1(f335(f335(f244(a1),x93271),a104))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93271),x93271)),a104)),a104)) % 186.01/186.02 [9864]~P1(f335(f67(f933(a927,a927)),x98641))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f195(f934(f933(a927,a927),a922))),x98641)),a75)) % 186.01/186.02 [9649]~P146(x96491)+E(f335(f335(f252(x96491),f84(x96491)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(x96491)) % 186.01/186.02 [9650]~P146(x96501)+E(f335(f335(f252(x96501),f2(x96501)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f2(x96501)) % 186.01/186.02 [10091]~P1(f335(f335(f244(a927),f84(a927)),x100911))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f42(a927),x100911),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.02 [10097]~P1(f335(f335(f244(a927),f2(a927)),x100971))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f42(a927),f335(f335(f86(a927),x100971),f84(a927))),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.02 [10136]~E(f51(a927,x101361,f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(a927))+P1(f335(f335(f244(a927),f2(a927)),f51(a927,x101361,f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.02 [10168]E(f51(a927,x101681,f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(a927))+~P1(f335(f335(f244(a927),f2(a927)),f51(a927,x101681,f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.02 [4851]~P38(x48511,x48512)+P59(x48511,x48512) % 186.01/186.02 [4852]~P44(x48521,x48522)+P59(x48521,x48522) % 186.01/186.02 [4854]~P8(x48541,x48542)+P49(x48541,x48542) % 186.01/186.02 [4856]~P8(x48561,x48562)+P51(x48561,x48562) % 186.01/186.02 [4858]~P16(x48581,x48582)+P51(x48581,x48582) % 186.01/186.02 [4860]~P8(x48601,x48602)+P52(x48601,x48602) % 186.01/186.02 [4862]~P16(x48621,x48622)+P52(x48621,x48622) % 186.01/186.02 [4863]~P8(x48631,x48632)+P16(x48631,x48632) % 186.01/186.02 [4808]E(x48081,x48082)+~E(f33(x48081),f33(x48082)) % 186.01/186.02 [4809]E(x48091,x48092)+~E(f34(x48091),f34(x48092)) % 186.01/186.02 [4813]~E(x48131,x48132)+E(f277(x48131,x48132),f84(a106)) % 186.01/186.02 [4816]E(f225(x48161,x48162),x48161)+~E(x48162,f2(a927)) % 186.01/186.02 [4823]~E(x48232,f120(x48231))+E(f159(x48231,x48232),f120(x48231)) % 186.01/186.02 [4842]~E(f159(x48422,x48421),f120(x48422))+E(x48421,f120(x48422)) % 186.01/186.02 [4867]~P2(x48672)+P2(f934(x48671,x48672)) % 186.01/186.02 [4868]~P3(x48682)+P3(f934(x48681,x48682)) % 186.01/186.02 [4869]~P107(x48692)+P107(f934(x48691,x48692)) % 186.01/186.02 [4870]~P111(x48702)+P111(f934(x48701,x48702)) % 186.01/186.02 [4871]~P108(x48712)+P108(f934(x48711,x48712)) % 186.01/186.02 [4872]~P110(x48722)+P110(f934(x48721,x48722)) % 186.01/186.02 [4873]~P83(x48732)+P83(f934(x48731,x48732)) % 186.01/186.02 [4874]~P84(x48742)+P84(f934(x48741,x48742)) % 186.01/186.02 [4875]~P6(x48752)+P6(f934(x48751,x48752)) % 186.01/186.02 [4876]~P98(x48762)+P97(f934(x48761,x48762)) % 186.01/186.02 [4877]~P98(x48772)+P98(f934(x48771,x48772)) % 186.01/186.02 [4878]~P100(x48782)+P99(f934(x48781,x48782)) % 186.01/186.02 [4879]~P100(x48792)+P101(f934(x48791,x48792)) % 186.01/186.02 [4880]~P98(x48802)+P103(f934(x48801,x48802)) % 186.01/186.02 [4881]~P102(x48812)+P102(f934(x48811,x48812)) % 186.01/186.02 [4882]~P100(x48822)+P100(f934(x48821,x48822)) % 186.01/186.02 [4895]E(x48951,x48952)+~E(f335(a119,x48951),f335(a119,x48952)) % 186.01/186.02 [4896]E(x48961,x48962)+~E(f335(a113,x48961),f335(a113,x48962)) % 186.01/186.02 [4897]E(x48971,x48972)+~E(f335(a3,x48971),f335(a3,x48972)) % 186.01/186.02 [4899]E(x48991,x48992)+~E(f335(a20,x48991),f335(a20,x48992)) % 186.01/186.02 [4954]P40(x49541,x49542)+~E(f729(x49542,x49541),f730(x49542,x49541)) % 186.01/186.02 [4984]~P59(x49841,x49842)+P40(x49841,f315(x49841,x49842)) % 186.01/186.02 [4985]~P53(x49851,x49852)+P53(x49851,f315(x49851,x49852)) % 186.01/186.02 [4998]~P63(x49981)+E(f51(x49981,x49982,x49982),f2(x49981)) % 186.01/186.02 [5032]~P38(x50321,x50322)+P38(f928(x50321),f153(x50321,x50322)) % 186.01/186.02 [5033]~P38(x50331,x50332)+P38(f928(x50331),f152(x50331,x50332)) % 186.01/186.02 [5034]~P39(x50341,x50342)+P39(f928(x50341),f154(x50341,x50342)) % 186.01/186.02 [5035]~P39(x50351,x50352)+P39(f928(x50351),f165(x50351,x50352)) % 186.01/186.02 [5036]~P53(x50361,x50362)+P53(f928(x50361),f165(x50361,x50362)) % 186.01/186.02 [5133]~P38(x51331,x51332)+P38(f934(x51331,a922),f326(x51331,x51332)) % 186.01/186.02 [5134]~P38(x51341,x51342)+P38(f934(x51341,a922),f327(x51341,x51342)) % 186.01/186.02 [5260]~P7(x52601)+P41(f311(a1,x52601,x52602)) % 186.01/186.02 [5363]~P38(x53631,x53632)+P61(x53631,f73(x53631,x53631,x53632)) % 186.01/186.02 [5865]~P79(x58651)+P26(x58651,x58651,f85(x58651),x58652) % 186.01/186.02 [4837]~E(x48372,f120(x48371))+E(f335(f174(x48371),x48372),f120(x48371)) % 186.01/186.02 [4838]~E(x48382,f120(x48381))+E(f335(f175(x48381),x48382),f120(x48381)) % 186.01/186.02 [4901]E(x49011,f335(a111,x49012))+~E(f335(f107(a1),x49011),x49012) % 186.01/186.02 [4904]E(x49041,f120(x49042))+~E(f335(f174(x49042),x49041),f120(x49042)) % 186.01/186.02 [4905]E(x49051,f120(x49052))+~E(f335(f175(x49052),x49051),f120(x49052)) % 186.01/186.02 [4923]~P94(x49231)+E(f335(f110(x49231),x49232),f335(f109(x49231),x49232)) % 186.01/186.02 [4931]~P62(x49311)+P1(f335(f67(x49311),x49312)) % 186.01/186.02 [4939]~E(f689(x49392,x49391),f120(x49391))+E(f186(x49391,x49392),f120(f928(x49391))) % 186.01/186.02 [4948]~E(x49482,f120(x49481))+E(f335(f179(x49481),x49482),f195(f934(x49481,a922))) % 186.01/186.02 [4949]~E(x49492,f120(x49491))+E(f195(f934(x49491,a922)),f335(f179(x49491),x49492)) % 186.01/186.02 [4951]E(x49511,x49512)+~E(f335(f107(a1),x49511),f335(f107(a1),x49512)) % 186.01/186.02 [4955]E(f223(x49551,x49552),f2(a927))+P1(f335(f67(x49551),x49552)) % 186.01/186.02 [4973]~P113(x49731)+E(f88(x49731,f88(x49731,x49732)),f88(x49731,x49732)) % 186.01/186.02 [4987]~P81(x49871)+E(f335(f335(f252(x49871),x49872),f84(a927)),x49872) % 186.01/186.02 [4988]~P118(x49881)+E(f335(f335(f252(x49881),x49882),f84(a927)),x49882) % 186.01/186.02 [4989]~P53(x49891,x49892)+E(f335(f294(x49891,x49891),x49892),x49892) % 186.01/186.02 [4993]E(x49931,x49932)+E(f277(x49931,x49932),f335(f335(f86(a106),x49932),f84(a106))) % 186.01/186.02 [4996]E(f335(f41(x49961),x49962),f2(a927))+P1(f335(f67(x49961),x49962)) % 186.01/186.02 [4999]~E(f159(x49991,x49992),x49992)+P1(f335(f144(x49991),x49992)) % 186.01/186.02 [5002]~P4(x50021)+E(f335(f335(f23(x50021),x50022),f2(x50021)),x50022) % 186.01/186.02 [5003]~P81(x50031)+E(f335(f335(f87(x50031),x50032),f84(x50031)),x50032) % 186.01/186.02 [5004]~P72(x50041)+E(f335(f335(f87(x50041),x50042),f84(x50041)),x50042) % 186.01/186.02 [5005]~P118(x50051)+E(f335(f335(f87(x50051),x50052),f84(x50051)),x50052) % 186.01/186.02 [5006]~P101(x50061)+E(f335(f335(f108(x50061),x50062),f250(x50061)),x50062) % 186.01/186.02 [5007]~P99(x50071)+E(f335(f335(f117(x50071),x50072),f195(x50071)),x50072) % 186.01/186.02 [5008]~P118(x50081)+E(f335(f335(f86(x50081),x50082),f2(x50081)),x50082) % 186.01/186.02 [5009]~P82(x50091)+E(f335(f335(f86(x50091),x50092),f2(x50091)),x50092) % 186.01/186.02 [5010]~P76(x50101)+E(f335(f335(f86(x50101),x50102),f2(x50101)),x50102) % 186.01/186.02 [5011]~P63(x50111)+E(f335(f335(f42(x50111),x50112),f84(x50111)),x50112) % 186.01/186.02 [5012]~P121(x50121)+E(f335(f335(f299(x50121),x50122),f84(x50121)),x50122) % 186.01/186.02 [5013]~P118(x50131)+E(f335(f335(f252(x50131),x50132),f2(a927)),f84(x50131)) % 186.01/186.02 [5014]~P117(x50141)+E(f335(f335(f252(x50141),x50142),f2(a927)),f84(x50141)) % 186.01/186.02 [5015]~E(x50152,f195(f934(x50151,a922)))+E(f335(f41(x50151),x50152),f2(a927)) % 186.01/186.02 [5026]~P63(x50261)+E(f51(x50261,x50262,f2(x50261)),x50262) % 186.01/186.02 [5037]~P118(x50371)+E(f335(f335(f87(x50371),x50372),f2(x50371)),f2(x50371)) % 186.01/186.02 [5038]~P130(x50381)+E(f335(f335(f87(x50381),x50382),f2(x50381)),f2(x50381)) % 186.01/186.02 [5039]~P99(x50391)+E(f335(f335(f108(x50391),x50392),f195(x50391)),f195(x50391)) % 186.01/186.02 [5040]~P101(x50401)+E(f335(f335(f117(x50401),x50402),f250(x50401)),f250(x50401)) % 186.01/186.02 [5041]~P63(x50411)+E(f335(f335(f42(x50411),x50412),f2(x50411)),f2(x50411)) % 186.01/186.02 [5042]~P122(x50421)+E(f335(f335(f299(x50421),x50422),f2(x50421)),f2(x50421)) % 186.01/186.02 [5044]~P63(x50441)+E(f51(x50441,x50442,f84(x50441)),f2(x50441)) % 186.01/186.02 [5045]~P63(x50451)+E(f51(x50451,f2(x50451),x50452),f2(x50451)) % 186.01/186.02 [5074]E(x50741,f2(a927))+E(f61(x50742,x50741,f120(x50742)),f120(f928(x50742))) % 186.01/186.02 [5097]P53(x50971,x50972)+~E(f335(f294(x50971,x50971),x50972),x50972) % 186.01/186.02 [5098]P38(x50981,x50982)+~E(f841(x50982,x50981),f195(f934(x50981,a922))) % 186.01/186.02 [5099]E(x50991,f120(x50992))+~E(f335(f179(x50992),x50991),f195(f934(x50992,a922))) % 186.01/186.02 [5100]E(x51001,f120(x51002))+~E(f195(f934(x51002,a922)),f335(f179(x51002),x51001)) % 186.01/186.02 [5103]~E(x51031,x51032)+P1(f335(f335(a332,x51031),x51032)) % 186.01/186.02 [5113]P1(x51131)+P1(f335(f335(a338,x51131),x51132)) % 186.01/186.02 [5114]E(x51141,f120(x51142))+E(f335(f335(f171(x51142),x51141),f2(a927)),f335(f148(x51142),x51141)) % 186.01/186.02 [5117]E(f159(x51171,x51172),x51172)+~P1(f335(f144(x51171),x51172)) % 186.01/186.02 [5124]~P1(x51242)+P1(f335(f335(a338,x51241),x51242)) % 186.01/186.02 [5125]~P1(x51252)+P1(f335(f335(a334,x51251),x51252)) % 186.01/186.02 [5126]~P1(x51261)+P1(f335(f335(a334,x51261),x51262)) % 186.01/186.02 [5136]~E(f690(x51362,x51361),f694(x51362,x51361))+P1(f335(f144(x51361),x51362)) % 186.01/186.02 [5143]E(f335(f270(x51431),x51432),f195(f934(x51431,a922)))+P1(f335(x51432,f340(x51432))) % 186.01/186.02 [5144]E(f195(f934(x51441,a922)),f335(f270(x51441),x51442))+P1(f335(x51442,f341(x51442))) % 186.01/186.02 [5213]~P113(x52131)+E(f335(f335(f87(x52131),x52132),f88(x52131,x52132)),f335(f81(x52131),x52132)) % 186.01/186.02 [5225]~E(x52251,f2(a1))+E(f52(x52251,x52252),f335(f335(f260(a1,a1),f2(a1)),f2(a1))) % 186.01/186.02 [5256]~P59(x52561,x52562)+P59(x52561,f335(f294(x52561,x52561),x52562)) % 186.01/186.02 [5257]~P39(x52571,x52572)+P39(x52571,f335(f294(x52571,x52571),x52572)) % 186.01/186.02 [5258]~P40(x52581,x52582)+P40(x52581,f335(f294(x52581,x52581),x52582)) % 186.01/186.02 [5259]~P53(x52591,x52592)+P53(x52591,f335(f294(x52591,x52591),x52592)) % 186.01/186.02 [5281]E(x52811,x52812)+~P1(f335(f335(a332,x52811),x52812)) % 186.01/186.02 [5292]P1(x52921)+~P1(f335(f335(a333,x52922),x52921)) % 186.01/186.02 [5293]P1(x52931)+~P1(f335(f335(a333,x52931),x52932)) % 186.01/186.02 [5298]~P111(x52981)+P1(f335(f335(f243(x52981),x52982),f250(x52981))) % 186.01/186.02 [5299]~P118(x52991)+P1(f335(f335(f295(x52991),x52992),f2(x52991))) % 186.01/186.02 [5303]E(x53031,x53032)+~E(f335(x53031,f444(x53032,x53031)),f335(x53032,f444(x53032,x53031))) % 186.01/186.02 [5334]E(x53341,f2(a927))+E(f225(x53341,f51(a927,x53342,x53341)),f225(x53342,x53341)) % 186.01/186.02 [5339]~P109(x53391)+P14(x53391,f335(f335(f158(x53391),x53392),f120(x53391))) % 186.01/186.02 [5341]E(x53411,f2(a1))+P1(f335(f55(x53412,x53411),f52(x53412,x53411))) % 186.01/186.02 [5358]~P16(x53582,x53581)+P1(f335(f335(x53581,f825(x53581)),f825(x53581))) % 186.01/186.02 [5361]~E(x53611,x53612)+P1(f335(f335(f244(a927),x53611),f335(a119,x53612))) % 186.01/186.02 [5371]~E(x53711,f2(a927))+P1(f335(f335(f244(a927),x53711),f335(a119,x53712))) % 186.01/186.02 [5381]P1(f335(x53811,x53812))+P1(f335(f335(f243(a1),f2(a1)),f440(x53811))) % 186.01/186.02 [5444]P59(x54441,x54442)+~P59(x54441,f335(f294(x54441,x54441),x54442)) % 186.01/186.02 [5445]P39(x54451,x54452)+~P39(x54451,f335(f294(x54451,x54451),x54452)) % 186.01/186.02 [5446]P40(x54461,x54462)+~P40(x54461,f335(f294(x54461,x54461),x54462)) % 186.01/186.02 [5447]P53(x54471,x54472)+~P53(x54471,f335(f294(x54471,x54471),x54472)) % 186.01/186.02 [5450]~E(f51(a927,x54502,x54501),f2(a927))+E(f335(f335(f87(a927),x54501),f450(x54501,x54502)),x54502) % 186.01/186.02 [5451]~E(f51(a1,x54512,x54511),f2(a1))+E(f335(f335(f87(a1),x54511),f463(x54511,x54512)),x54512) % 186.01/186.02 [5478]~P1(f335(x54781,x54782))+P1(f335(f335(f243(a1),f2(a1)),f437(x54781))) % 186.01/186.02 [5489]E(f335(f335(f23(a927),f335(a111,x54891)),f335(a111,x54892)),f335(a111,x54891))+~P1(f335(a200,x54892)) % 186.01/186.02 [5518]E(f280(x55181,x55182),f84(a106))+~P1(f335(f335(f243(a106),x55181),f84(a106))) % 186.01/186.02 [5612]E(f335(f335(f171(x56121),x56122),f690(x56122,x56121)),f335(f335(f171(x56121),x56122),f694(x56122,x56121)))+P1(f335(f144(x56121),x56122)) % 186.01/186.02 [5655]~P1(f335(x56551,f96(x56552,x56551)))+P1(f335(x56551,f575(x56552,x56551))) % 186.01/186.02 [5720]P61(x57201,x57202)+~P1(f335(f323(x57201,x57202),f451(x57202,x57201))) % 186.01/186.02 [5862]~P16(x58622,x58621)+P1(f335(f335(x58621,f826(x58621,x58622)),f826(x58621,x58622))) % 186.01/186.02 [5863]~P16(x58632,x58631)+P1(f335(f335(x58631,f830(x58631,x58632)),f830(x58631,x58632))) % 186.01/186.02 [5872]~E(f335(a119,f51(a927,x58721,x58722)),x58722)+E(f51(a927,f335(a119,x58721),x58722),f2(a927)) % 186.01/186.02 [5927]P38(x59271,x59272)+P1(f335(f335(f337(x59271),f912(x59272,x59271)),f913(x59272,x59271))) % 186.01/186.02 [5934]~P140(x59341)+P1(f335(f335(f337(x59341),f335(f107(x59341),x59342)),f116(x59341))) % 186.01/186.02 [5935]~P146(x59351)+P1(f335(f335(f337(x59351),f335(f107(x59351),x59352)),f193(x59351))) % 186.01/186.02 [5936]~P140(x59361)+P1(f335(f335(f337(x59361),f335(f109(x59361),x59362)),f116(x59361))) % 186.01/186.02 [5937]~P94(x59371)+P1(f335(f335(f337(x59371),f335(f110(x59371),x59372)),f116(x59371))) % 186.01/186.02 [6071]~P39(x60711,x60712)+E(f335(f335(f297(x60711,x60711,x60711),x60712),f315(x60711,x60712)),x60712) % 186.01/186.02 [6085]E(f335(a119,f51(a927,x60851,x60852)),x60852)+E(f51(a927,f335(a119,x60851),x60852),f335(a119,f51(a927,x60851,x60852))) % 186.01/186.02 [6501]P38(x65011,x65012)+~P1(f335(f335(f337(x65011),f544(x65012,x65011)),f324(x65011,x65012))) % 186.01/186.02 [6538]~P125(x65381)+~P1(f335(f335(f244(x65381),f335(f107(x65381),x65382)),f2(x65381))) % 186.01/186.02 [6539]~P87(x65391)+~P1(f335(f335(f244(x65391),f335(f81(x65391),x65392)),f2(x65391))) % 186.01/186.02 [6627]P1(f335(f335(f244(a1),x66271),f51(a1,x66272,x66271)))+~P1(f335(f335(f244(a1),x66271),f2(a1))) % 186.01/186.02 [6726]E(f335(f335(f317(a927),f335(a119,x67261)),f311(a927,x67262,x67261)),f311(a927,x67262,f335(a119,x67261)))+~P1(f335(f335(f243(a927),x67262),f335(a119,x67261))) % 186.01/186.02 [6816]~P109(x68161)+P14(x68161,f157(x68161,x68161,f5(x68161),x68162)) % 186.01/186.02 [6945]E(f335(f174(x69451),x69452),x69452)+~P1(f335(f335(f243(a927),f335(f196(f928(x69451)),x69452)),f84(a927))) % 186.01/186.02 [6966]~P87(x69661)+P1(f335(f335(f243(x69661),f335(f85(x69661),f335(f81(x69661),x69662))),f2(x69661))) % 186.01/186.02 [6997]~P38(x69971,x69972)+P38(x69971,f335(f335(f297(x69971,x69971,x69971),x69972),f315(x69971,x69972))) % 186.01/186.02 [6998]~P53(x69981,x69982)+P53(x69981,f335(f335(f297(x69981,x69981,x69981),x69982),f315(x69981,x69982))) % 186.01/186.02 [7216]~P1(f335(f335(f244(a1),x72162),f2(a1)))+P1(f335(f335(f243(a1),f51(a1,x72161,x72162)),f2(a1))) % 186.01/186.02 [7615]~P146(x76151)+E(f197(x76151,f335(f335(f7(x76151,x76151,x76151),f86(x76151)),f84(x76151)),x76152,f2(x76151)),f335(f107(x76151),x76152)) % 186.01/186.02 [7643]~P126(x76431)+~P1(f335(f335(f244(x76431),f335(f335(f87(x76431),x76432),x76432)),f2(x76431))) % 186.01/186.02 [10260]~P113(x102601)+~P1(f335(f335(f244(x102601),f335(f335(f252(x102601),x102602),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f2(x102601))) % 186.01/186.02 [4902]~E(x49022,f120(x49021))+E(f335(f196(f928(x49021)),x49022),f2(a927)) % 186.01/186.02 [4940]~E(x49401,f2(a927))+E(f335(f335(f86(a927),x49401),x49402),x49402) % 186.01/186.02 [4941]~E(x49412,f2(a927))+E(f335(f335(f87(a927),x49411),x49412),f2(a927)) % 186.01/186.02 [4943]~E(x49431,f2(a927))+E(f335(f335(f87(a927),x49431),x49432),f2(a927)) % 186.01/186.02 [4944]~E(x49442,f2(a927))+E(f335(f335(f252(a927),x49441),x49442),f84(a927)) % 186.01/186.02 [4945]~E(x49452,f2(a1))+E(f335(f335(f42(a1),x49451),x49452),f2(a1)) % 186.01/186.02 [4956]E(x49561,f120(x49562))+~E(f335(f196(f928(x49562)),x49561),f2(a927)) % 186.01/186.02 [4958]~P96(x49581)+E(f335(f335(f87(x49581),x49582),x49582),x49582) % 186.01/186.02 [4960]~P97(x49601)+E(f335(f335(f108(x49601),x49602),x49602),x49602) % 186.01/186.02 [4961]~P98(x49611)+E(f335(f335(f108(x49611),x49612),x49612),x49612) % 186.01/186.02 [4962]~P98(x49621)+E(f335(f335(f117(x49621),x49622),x49622),x49622) % 186.01/186.02 [4964]~P103(x49641)+E(f335(f335(f117(x49641),x49642),x49642),x49642) % 186.01/186.02 [4966]~P109(x49661)+E(f335(f335(f241(x49661),x49662),x49662),x49662) % 186.01/186.02 [4968]~P109(x49681)+E(f335(f335(f242(x49681),x49682),x49682),x49682) % 186.01/186.02 [4986]~P4(x49861)+E(f335(f335(f23(x49861),x49862),x49862),f2(x49861)) % 186.01/186.02 [5000]~P83(x50001)+E(f335(f85(x50001),f335(f85(x50001),x50002)),x50002) % 186.01/186.02 [5001]~P4(x50011)+E(f335(f85(x50011),f335(f85(x50011),x50012)),x50012) % 186.01/186.02 [5018]~E(x50182,f2(a927))+E(f335(f335(f252(a927),x50181),x50182),f335(a119,f2(a927))) % 186.01/186.02 [5053]~P81(x50531)+E(f335(f335(f87(x50531),f84(x50531)),x50532),x50532) % 186.01/186.02 [5054]~P72(x50541)+E(f335(f335(f87(x50541),f84(x50541)),x50542),x50542) % 186.01/186.02 [5055]~P118(x50551)+E(f335(f335(f87(x50551),f84(x50551)),x50552),x50552) % 186.01/186.02 [5056]~P101(x50561)+E(f335(f335(f108(x50561),f250(x50561)),x50562),x50562) % 186.01/186.02 [5057]~P99(x50571)+E(f335(f335(f117(x50571),f195(x50571)),x50572),x50572) % 186.01/186.02 [5058]~P118(x50581)+E(f335(f335(f86(x50581),f2(x50581)),x50582),x50582) % 186.01/186.02 [5059]~P82(x50591)+E(f335(f335(f86(x50591),f2(x50591)),x50592),x50592) % 186.01/186.02 [5060]~P76(x50601)+E(f335(f335(f86(x50601),f2(x50601)),x50602),x50602) % 186.01/186.02 [5078]~P118(x50781)+E(f335(f335(f87(x50781),f2(x50781)),x50782),f2(x50781)) % 186.01/186.02 [5079]~P130(x50791)+E(f335(f335(f87(x50791),f2(x50791)),x50792),f2(x50791)) % 186.01/186.02 [5080]~P99(x50801)+E(f335(f335(f108(x50801),f195(x50801)),x50802),f195(x50801)) % 186.01/186.02 [5081]~P101(x50811)+E(f335(f335(f117(x50811),f250(x50811)),x50812),f250(x50811)) % 186.01/186.02 [5082]~P81(x50821)+E(f335(f335(f252(x50821),f84(x50821)),x50822),f84(x50821)) % 186.01/186.02 [5083]~P63(x50831)+E(f335(f335(f42(x50831),f2(x50831)),x50832),f2(x50831)) % 186.01/186.02 [5084]~P121(x50841)+E(f335(f335(f299(x50841),f2(x50841)),x50842),f2(x50841)) % 186.01/186.02 [5092]E(x50921,f120(x50922))+E(f151(x50922,f335(f175(x50922),x50921)),f335(f148(x50922),x50921)) % 186.01/186.02 [5093]E(x50931,f120(x50932))+E(f335(f148(x50932),f335(f175(x50932),x50931)),f151(x50932,x50931)) % 186.01/186.02 [5094]E(x50941,f2(a927))+~E(f335(f335(f86(a927),x50942),x50941),x50942) % 186.01/186.02 [5101]~P140(x51011)+E(f335(f109(x51011),f335(f107(a1),x51012)),f335(f107(x51011),x51012)) % 186.01/186.02 [5102]~P94(x51021)+E(f335(f109(x51021),f335(f110(a1),x51022)),f335(f110(x51021),x51022)) % 186.01/186.02 [5109]E(x51091,f84(a927))+~E(f335(f335(f87(a927),x51092),x51091),f84(a927)) % 186.01/186.02 [5110]E(x51101,f84(a927))+~E(f335(f335(f87(a927),x51101),x51102),f84(a927)) % 186.01/186.02 [5111]E(x51111,f2(a927))+~E(f335(f335(f86(a927),x51112),x51111),f2(a927)) % 186.01/186.02 [5112]E(x51121,f2(a927))+~E(f335(f335(f86(a927),x51121),x51122),f2(a927)) % 186.01/186.02 [5129]~P87(x51291)+E(f335(f81(x51291),f335(f85(x51291),x51292)),f335(f81(x51291),x51292)) % 186.01/186.02 [5130]~P113(x51301)+E(f335(f81(x51301),f335(f107(x51301),x51302)),f335(f107(x51301),x51302)) % 186.01/186.02 [5131]~P87(x51311)+E(f335(f81(x51311),f335(f81(x51311),x51312)),f335(f81(x51311),x51312)) % 186.01/186.02 [5132]~P76(x51321)+E(f335(f172(x51321),f335(f175(x51321),x51322)),f335(f172(x51321),x51322)) % 186.01/186.02 [5137]~E(x51371,f335(a119,f2(a927)))+E(f335(f335(f252(a927),x51371),x51372),f335(a119,f2(a927))) % 186.01/186.02 [5146]~P4(x51461)+E(f335(f335(f23(x51461),f2(x51461)),x51462),f335(f85(x51461),x51462)) % 186.01/186.02 [5147]~E(x51472,f2(a927))+E(f146(a927,f335(f310(a927,x51471),x51472)),f120(a927)) % 186.01/186.02 [5156]~P94(x51561)+E(f335(f335(f86(x51561),x51562),f335(f110(x51561),a89)),x51562) % 186.01/186.02 [5157]E(x51571,f2(a1))+E(f53(f335(f81(a1),x51572),f335(f81(a1),x51571)),f59(x51572,x51571)) % 186.01/186.02 [5173]~E(x51731,x51732)+P1(f335(f335(f243(a927),x51731),x51732)) % 186.01/186.02 [5180]~E(x51801,f2(a106))+E(f335(f335(f86(a927),f335(a20,x51801)),x51802),x51802) % 186.01/186.02 [5181]~E(f335(f110(a1),x51812),f335(f107(a1),x51811))+E(x51811,f335(a111,f335(f110(a1),x51812))) % 186.01/186.02 [5194]~P7(x51941)+P7(f335(f335(f252(a1),x51941),x51942)) % 186.01/186.02 [5195]~P83(x51951)+E(f335(f335(f108(x51951),x51952),f335(f85(x51951),x51952)),f195(x51951)) % 186.01/186.02 [5196]~P83(x51961)+E(f335(f335(f117(x51961),x51962),f335(f85(x51961),x51962)),f250(x51961)) % 186.01/186.02 [5197]~P4(x51971)+E(f335(f335(f86(x51971),x51972),f335(f85(x51971),x51972)),f2(x51971)) % 186.01/186.02 [5222]E(x52221,f2(a927))+~E(f335(f85(a1),f335(f107(a1),x52222)),f335(f107(a1),x52221)) % 186.01/186.02 [5223]E(x52231,f2(a927))+~E(f335(f85(a1),f335(f107(a1),x52231)),f335(f107(a1),x52232)) % 186.01/186.02 [5233]E(f201(x52331,x52332),f2(a1))+P1(f335(f335(f243(a1),x52332),x52331)) % 186.01/186.02 [5234]E(f185(x52341,x52342),f120(a1))+P1(f335(f335(f243(a1),x52341),x52342)) % 186.01/186.02 [5235]E(f249(x52351,x52352),f2(a106))+P1(f335(f335(f244(a106),x52351),x52352)) % 186.01/186.02 [5248]E(x52481,f335(a119,f2(a927)))+~E(f335(f335(f87(a927),x52482),x52481),f335(a119,f2(a927))) % 186.01/186.02 [5249]E(x52491,f335(a119,f2(a927)))+~E(f335(f335(f87(a927),x52491),x52492),f335(a119,f2(a927))) % 186.01/186.02 [5250]~P107(x52501)+P1(f335(f335(f243(x52501),x52502),x52502)) % 186.01/186.02 [5253]~P94(x52531)+E(f335(f335(f87(x52531),x52532),f335(f110(x52531),a104)),f335(f85(x52531),x52532)) % 186.01/186.02 [5273]~P140(x52731)+E(f335(f85(x52731),f335(f109(x52731),x52732)),f335(f109(x52731),f335(f85(a1),x52732))) % 186.01/186.02 [5274]~P94(x52741)+E(f335(f85(x52741),f335(f110(x52741),x52742)),f335(f110(x52741),f335(f85(a1),x52742))) % 186.01/186.02 [5304]~E(x53041,f335(a119,x53042))+P1(f335(f335(f244(a927),f2(a927)),x53041)) % 186.01/186.02 [5322]~P109(x53221)+E(f335(f85(f934(x53221,a922)),f335(f290(x53221),x53222)),f335(f291(x53221),x53222)) % 186.01/186.02 [5323]~P109(x53231)+E(f335(f85(f934(x53231,a922)),f335(f312(x53231),x53232)),f335(f309(x53231),x53232)) % 186.01/186.02 [5324]~P109(x53241)+E(f335(f85(f934(x53241,a922)),f335(f291(x53241),x53242)),f335(f290(x53241),x53242)) % 186.01/186.02 [5325]~P109(x53251)+E(f335(f85(f934(x53251,a922)),f335(f309(x53251),x53252)),f335(f312(x53251),x53252)) % 186.01/186.02 [5333]~E(f335(f107(a1),x53332),x53331)+P1(f335(f335(f243(a1),f2(a1)),x53331)) % 186.01/186.02 [5340]~E(x53402,f2(a1))+E(f59(x53401,x53402),f335(f335(f260(a1,a1),f2(a1)),f335(f81(a1),x53401))) % 186.01/186.02 [5342]~P2(x53421)+P1(f335(f335(f243(x53421),f195(x53421)),x53422)) % 186.01/186.02 [5343]~P118(x53431)+P1(f335(f335(f295(x53431),f84(x53431)),x53432)) % 186.01/186.02 [5376]E(x53761,x53762)+~E(f335(f335(f86(a1),x53761),x53761),f335(f335(f86(a1),x53762),x53762)) % 186.01/186.02 [5380]~P1(f335(x53801,x53802))+P1(f335(x53801,f335(a111,f437(x53801)))) % 186.01/186.02 [5406]~P113(x54061)+E(f335(f335(f87(x54061),f88(x54061,x54062)),f335(f81(x54061),x54062)),x54062) % 186.01/186.02 [5413]~E(x54132,f2(a927))+E(f91(f933(a927,a927),f54(x54131,x54132)),f335(f335(f260(a927,a927),f2(a927)),x54131)) % 186.01/186.02 [5418]~E(x54181,x54182)+~P1(f335(f335(f244(a927),x54181),x54182)) % 186.01/186.02 [5419]~E(x54191,x54192)+~P1(f335(f335(f244(a1),x54191),x54192)) % 186.01/186.02 [5422]~P146(x54221)+E(f335(f335(f86(x54221),f84(x54221)),f335(f107(x54221),x54222)),f335(f107(x54221),f335(a119,x54222))) % 186.01/186.02 [5426]~E(x54261,f2(a927))+~P1(f335(f335(f244(a927),x54262),x54261)) % 186.01/186.02 [5440]E(f159(x54401,x54402),x54402)+~E(f335(f196(f928(x54401)),f159(x54401,x54402)),f335(f196(f928(x54401)),x54402)) % 186.01/186.02 [5441]E(f335(f41(x54411),f335(f179(x54411),x54412)),f335(f196(f928(x54411)),x54412))+~P1(f335(f144(x54411),x54412)) % 186.01/186.02 [5455]~P1(f335(x54551,f424(x54551)))+P1(f335(x54551,f335(f107(a1),x54552))) % 186.01/186.02 [5466]E(f249(x54661,x54662),x54662)+~P1(f335(f335(f244(a106),x54661),x54662)) % 186.01/186.02 [5468]E(f280(x54681,x54682),f84(a106))+~P1(f335(f335(f244(a106),x54682),x54681)) % 186.01/186.02 [5469]E(f185(x54691,x54692),f120(a1))+~P1(f335(f335(f244(a1),x54692),x54691)) % 186.01/186.02 [5470]E(f135(x54701,x54702),f122(a1))+~P1(f335(f335(f244(a1),x54701),x54702)) % 186.01/186.02 [5472]~P110(x54721)+E(f311(x54721,x54722,x54722),f335(f335(f317(x54721),x54722),f195(f934(x54721,a922)))) % 186.01/186.02 [5492]~E(f335(f335(f23(a927),x54921),x54922),f2(a927))+P1(f335(f335(f243(a927),x54921),x54922)) % 186.01/186.02 [5515]~E(x55152,f2(a927))+E(f61(x55151,x55152,f120(x55151)),f335(f335(f158(f928(x55151)),f120(x55151)),f120(f928(x55151)))) % 186.01/186.02 [5519]~P107(x55191)+~P1(f335(f335(f244(x55191),x55192),x55192)) % 186.01/186.02 [5521]~E(f51(a1,x55211,x55212),f2(a1))+E(f51(a1,x55211,f335(f85(a1),x55212)),f2(a1)) % 186.01/186.02 [5523]~E(f51(a1,x55231,x55232),f2(a1))+E(f51(a1,f335(f85(a1),x55231),x55232),f2(a1)) % 186.01/186.02 [5530]E(f335(f310(a927,x55301),f335(a119,x55302)),f195(f934(a927,a922)))+P1(f335(f335(f243(a927),x55301),x55302)) % 186.01/186.02 [5553]E(f146(a927,f335(f310(a927,x55531),x55532)),f120(a927))+P1(f335(f335(f244(a927),x55531),x55532)) % 186.01/186.02 [5558]~E(f335(f41(x55581),f335(f179(x55581),x55582)),f335(f196(f928(x55581)),x55582))+P1(f335(f144(x55581),x55582)) % 186.01/186.02 [5562]~P1(f335(f144(x55621),x55622))+P1(f335(f144(x55621),f335(f174(x55621),x55622))) % 186.01/186.02 [5563]~P1(f335(f144(x55631),x55632))+P1(f335(f144(x55631),f335(f178(x55631),x55632))) % 186.01/186.02 [5564]~P1(f335(f144(x55641),x55642))+P1(f335(f144(x55641),f335(f175(x55641),x55642))) % 186.01/186.02 [5572]P1(f335(x55721,x55722))+~P1(f335(x55721,f335(a111,f440(x55721)))) % 186.01/186.02 [5573]P1(f335(f335(f243(a927),x55732),x55731))+P1(f335(f335(f243(a927),x55731),x55732)) % 186.01/186.02 [5574]P1(f335(f335(f243(a1),x55742),x55741))+P1(f335(f335(f243(a1),x55741),x55742)) % 186.01/186.02 [5578]~P87(x55781)+P1(f335(f335(f243(x55781),x55782),f335(f81(x55781),x55782))) % 186.01/186.02 [5581]P1(f335(x55811,f432(x55811)))+~P1(f335(x55811,f335(f107(a1),x55812))) % 186.01/186.02 [5605]E(f335(f335(f23(a927),x56051),x56052),f2(a927))+~P1(f335(f335(f243(a927),x56051),x56052)) % 186.01/186.02 [5606]E(f335(f335(f42(a927),x56061),x56062),f2(a927))+~P1(f335(f335(f244(a927),x56061),x56062)) % 186.01/186.02 [5624]E(f51(a927,x56241,x56242),x56241)+~P1(f335(f335(f244(a927),x56241),x56242)) % 186.01/186.02 [5632]E(f51(a1,x56321,f335(f85(a1),x56322)),f300(x56321,x56322))+P1(f335(f335(f243(a1),f2(a1)),x56322)) % 186.01/186.02 [5644]E(f335(f335(f23(a1),x56441),x56442),f201(x56441,x56442))+~P1(f335(f335(f243(a1),x56442),x56441)) % 186.01/186.02 [5664]P1(f335(f335(f243(a1),f2(a1)),f424(x56641)))+P1(f335(x56641,f335(f107(a1),x56642))) % 186.01/186.02 [5677]~P125(x56771)+P1(f335(f335(f243(x56771),f2(x56771)),f335(f107(x56771),x56772))) % 186.01/186.02 [5678]~P87(x56781)+P1(f335(f335(f243(x56781),f2(x56781)),f335(f81(x56781),x56782))) % 186.01/186.02 [5706]E(f335(f335(f86(a927),x57061),f374(x57062,x57061)),x57062)+~P1(f335(f335(f243(a927),x57061),x57062)) % 186.01/186.02 [5718]~E(f335(f110(a1),x57181),f335(f107(a1),x57182))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x57181))) % 186.01/186.02 [5721]E(f311(a1,x57211,x57212),f195(f934(a1,a922)))+~P1(f335(f335(f244(a1),x57212),x57211)) % 186.01/186.02 [5724]~P113(x57241)+E(f335(f335(f87(x57241),f335(f81(x57241),x57242)),f335(f81(x57241),x57242)),f335(f335(f87(x57241),x57242),x57242)) % 186.01/186.02 [5729]E(f146(a927,f335(f310(a927,x57291),f335(a119,x57292))),f120(a927))+P1(f335(f335(f243(a927),x57291),x57292)) % 186.01/186.02 [5733]E(f335(f335(f42(a1),x57331),x57332),f301(x57331,x57332))+~P1(f335(f335(f243(a1),f2(a1)),x57332)) % 186.01/186.02 [5753]P1(f335(f144(x57531),x57532))+~P1(f335(f144(x57531),f335(f174(x57531),x57532))) % 186.01/186.02 [5754]P1(f335(f144(x57541),x57542))+~P1(f335(f144(x57541),f335(f175(x57541),x57542))) % 186.01/186.02 [5779]P1(f335(f67(a927),x57791))+P1(f335(f335(f337(a927),f342(x57791,x57792)),x57791)) % 186.01/186.02 [5780]P1(f335(f67(a927),x57801))+P1(f335(f335(f337(a927),f349(x57801,x57802)),x57801)) % 186.01/186.02 [5783]P1(f335(f335(f244(a927),x57832),f335(a119,x57831)))+P1(f335(f335(f244(a927),x57831),x57832)) % 186.01/186.02 [5784]E(f51(a1,x57841,x57842),f300(x57841,x57842))+~P1(f335(f335(f243(a1),f2(a1)),x57842)) % 186.01/186.02 [5787]E(f146(a927,f335(f310(a927,x57871),x57872)),f120(a927))+~P1(f335(f335(f243(a927),x57872),x57871)) % 186.01/186.02 [5788]~P79(x57881)+E(f335(f318(x57881,x57881,f85(x57881)),f335(f290(x57881),x57882)),f335(f312(x57881),f335(f85(x57881),x57882))) % 186.01/186.02 [5789]~P79(x57891)+E(f335(f318(x57891,x57891,f85(x57891)),f335(f312(x57891),x57892)),f335(f290(x57891),f335(f85(x57891),x57892))) % 186.01/186.02 [5790]~P79(x57901)+E(f335(f318(x57901,x57901,f85(x57901)),f335(f291(x57901),x57902)),f335(f309(x57901),f335(f85(x57901),x57902))) % 186.01/186.02 [5791]~P79(x57911)+E(f335(f318(x57911,x57911,f85(x57911)),f335(f309(x57911),x57912)),f335(f291(x57911),f335(f85(x57911),x57912))) % 186.01/186.02 [5802]E(x58021,f195(f934(x58022,a922)))+P1(f335(f335(f337(x58022),f382(x58021,x58022)),x58021)) % 186.01/186.02 [5803]E(x58031,f195(f934(x58032,a922)))+P1(f335(f335(f337(x58032),f391(x58031,x58032)),x58031)) % 186.01/186.02 [5814]~P1(f335(f335(f244(a927),x58141),x58142))+P1(f335(f335(f243(a927),x58141),x58142)) % 186.01/186.02 [5815]~P1(f335(f335(f244(a1),x58151),x58152))+P1(f335(f335(f243(a1),x58151),x58152)) % 186.01/186.02 [5831]E(f53(x58311,x58312),f335(f335(f260(a1,a1),f2(a1)),x58311))+~P1(f335(f335(f244(a1),x58311),x58312)) % 186.01/186.02 [5833]E(f224(f335(f85(a1),x58331),f335(f85(a1),x58332)),f224(x58331,x58332))+~P1(f335(f335(f244(a1),x58332),f2(a1))) % 186.01/186.02 [5844]E(x58441,x58442)+~E(f335(a3,f335(a119,f335(a20,x58441))),f335(a3,f335(a119,f335(a20,x58442)))) % 186.01/186.02 [5849]E(f53(x58491,x58492),f335(f335(f260(a1,a1),f2(a1)),x58491))+~P1(f335(f335(f243(a1),x58492),f2(a1))) % 186.01/186.02 [5878]E(f51(a927,f335(f110(a927),x58781),f335(f110(a927),x58782)),f2(a927))+~P1(f335(a200,f335(f110(a1),x58781))) % 186.01/186.02 [5892]P1(f335(f335(f243(a1),f2(a1)),f432(x58921)))+~P1(f335(x58921,f335(f107(a1),x58922))) % 186.01/186.02 [5925]P41(f311(a1,x59251,x59252))+~P1(f335(f335(f243(a1),f2(a1)),x59251)) % 186.01/186.02 [5930]~P1(f335(f67(x59301),x59302))+P1(f335(f67(f934(x59301,a922)),f335(f316(x59301),x59302))) % 186.01/186.02 [5943]E(f335(f335(f86(a1),x59431),f335(f107(a1),f425(x59432,x59431))),x59432)+~P1(f335(f335(f243(a1),x59431),x59432)) % 186.01/186.02 [5951]P1(f335(f335(f243(a927),x59511),x59512))+P1(f335(f335(f243(a927),f335(a119,x59512)),x59511)) % 186.01/186.02 [5995]E(f335(f335(f42(a927),f335(f110(a927),x59951)),f335(f110(a927),x59952)),f2(a927))+~P1(f335(a200,f335(f110(a1),x59951))) % 186.01/186.02 [5996]E(f335(f335(f87(a927),f335(f110(a927),x59961)),f335(f110(a927),x59962)),f2(a927))+~P1(f335(f335(f244(a1),x59961),a89)) % 186.01/186.02 [5998]P1(f335(f335(f243(a927),x59981),f335(a119,x59982)))+~P1(f335(f335(f243(a927),x59981),x59982)) % 186.01/186.02 [6000]P1(f335(f335(f244(a927),x60001),f335(a119,x60002)))+~P1(f335(f335(f243(a927),x60001),x60002)) % 186.01/186.02 [6002]P1(f335(f335(f244(a927),x60021),f335(a119,x60022)))+~P1(f335(f335(f244(a927),x60021),x60022)) % 186.01/186.02 [6005]~E(x60051,x60052)+P1(f335(f335(f244(a1),x60051),f335(f335(f86(a1),x60052),f84(a1)))) % 186.01/186.02 [6008]E(f51(a1,x60081,x60082),f2(a1))+E(f335(f335(f23(a1),x60082),f51(a1,x60081,x60082)),f51(a1,f335(f85(a1),x60081),x60082)) % 186.01/186.02 [6017]E(x60171,f120(x60172))+P1(f335(f335(f337(x60172),f151(x60172,x60171)),f335(f179(x60172),x60171))) % 186.01/186.02 [6029]E(f91(f933(a927,a927),f54(x60291,x60292)),f335(f335(f260(a927,a927),f2(a927)),x60291))+~P1(f335(f335(f244(a927),x60291),x60292)) % 186.01/186.02 [6064]E(f335(f335(f23(a927),f335(f110(a927),x60641)),f335(f110(a927),x60642)),f335(f110(a927),x60641))+~P1(f335(f335(f244(a1),x60642),a89)) % 186.01/186.02 [6065]E(f335(f335(f86(a927),f335(f110(a927),x60651)),f335(f110(a927),x60652)),f335(f110(a927),x60652))+~P1(f335(f335(f244(a1),x60651),a89)) % 186.01/186.02 [6072]E(f335(a119,f335(f335(f86(a927),x60721),f383(x60722,x60721))),x60722)+~P1(f335(f335(f244(a927),x60721),x60722)) % 186.01/186.02 [6096]P1(f335(x60961,x60962))+~P1(f335(x60961,f335(a95,f576(x60962,x60961)))) % 186.01/186.02 [6097]P1(f335(x60971,x60972))+~P1(f335(x60971,f335(a3,f840(x60972,x60971)))) % 186.01/186.02 [6106]~P1(f335(f335(f244(a927),x61061),f335(a119,x61062)))+P1(f335(f335(f243(a927),x61061),x61062)) % 186.01/186.02 [6152]E(f335(f335(f317(a927),x61521),f335(f310(a927,x61522),x61521)),f335(f310(a927,x61522),f335(a119,x61521)))+~P1(f335(f335(f243(a927),x61522),x61521)) % 186.01/186.02 [6154]E(x61541,f120(x61542))+E(f335(f335(f141(x61542),f121(x61542,x61541)),f335(f335(f158(x61542),f151(x61542,x61541)),f120(x61542))),x61541) % 186.01/186.02 [6171]P1(f335(f67(x61711),x61712))+~P1(f335(f335(f244(a927),f2(a927)),f335(f41(x61711),x61712))) % 186.01/186.02 [6174]~E(x61741,f195(f934(x61742,a922)))+~P1(f335(f335(f244(a927),f2(a927)),f335(f41(x61742),x61741))) % 186.01/186.02 [6186]~P1(f335(f335(f244(a927),x61861),x61862))+P1(f335(f335(f243(a927),f335(a119,x61861)),x61862)) % 186.01/186.02 [6190]~P109(x61901)+E(f157(x61901,x61901,f5(x61901),f159(x61901,x61902)),f146(x61901,f335(f179(x61901),x61902))) % 186.01/186.02 [6193]E(x61931,f120(x61932))+P1(f335(f335(f337(x61932),f335(f148(x61932),x61931)),f335(f179(x61932),x61931))) % 186.01/186.02 [6199]~P125(x61991)+P1(f335(f335(f244(x61991),x61992),f335(f335(f86(x61991),x61992),f84(x61991)))) % 186.01/186.02 [6201]~P87(x62011)+P1(f335(f335(f243(x62011),f335(f85(x62011),x62012)),f335(f81(x62011),x62012))) % 186.01/186.02 [6215]~E(x62151,x62152)+E(f298(a927,f295(a927),x62151,x62152),f335(f335(f317(a927),x62151),f195(f934(a927,a922)))) % 186.01/186.02 [6233]P1(f335(f67(a927),x62331))+~P1(f335(f335(f243(a927),f349(x62331,x62332)),x62332)) % 186.01/186.02 [6234]P1(f335(f67(a927),x62341))+~P1(f335(f335(f244(a927),f342(x62341,x62342)),x62342)) % 186.01/186.02 [6237]~P1(f335(f67(f933(x62371,x62371)),x62372))+P1(f335(f67(x62371),f335(f289(x62371),x62372))) % 186.01/186.02 [6291]E(f298(a927,f295(a927),x62911,x62912),f195(f934(a927,a922)))+P1(f335(f335(f295(a927),x62911),x62912)) % 186.01/186.02 [6294]~P1(f335(f335(f244(a927),x62942),f335(a119,x62941)))+~P1(f335(f335(f244(a927),x62941),x62942)) % 186.01/186.02 [6295]~P110(x62951)+E(f335(f335(f108(f934(x62951,a922)),f335(f309(x62951),x62952)),f335(f291(x62951),x62952)),f335(f335(f317(x62951),x62952),f195(f934(x62951,a922)))) % 186.01/186.02 [6307]P1(f335(f67(x63071),x63072))+~P1(f335(f67(f934(x63071,a922)),f335(f316(x63071),x63072))) % 186.01/186.02 [6329]P1(f335(f335(f243(a927),f335(a119,x63291)),f335(a119,x63292)))+~P1(f335(f335(f243(a927),x63291),x63292)) % 186.01/186.02 [6330]P1(f335(f335(f243(a927),f335(a20,x63301)),f335(a20,x63302)))+~P1(f335(f335(f243(a106),x63301),x63302)) % 186.01/186.02 [6331]P1(f335(f335(f243(a106),f335(a3,x63311)),f335(a3,x63312)))+~P1(f335(f335(f243(a927),x63311),x63312)) % 186.01/186.02 [6333]P1(f335(f335(f244(a927),f335(a119,x63331)),f335(a119,x63332)))+~P1(f335(f335(f244(a927),x63331),x63332)) % 186.01/186.02 [6334]P1(f335(f335(f244(a927),f335(a20,x63341)),f335(a20,x63342)))+~P1(f335(f335(f244(a106),x63341),x63342)) % 186.01/186.02 [6335]P1(f335(f335(f244(a106),f335(a3,x63351)),f335(a3,x63352)))+~P1(f335(f335(f244(a927),x63351),x63352)) % 186.01/186.02 [6340]E(x63401,x63402)+~E(f335(f318(a927,a1,f107(a1)),x63401),f335(f318(a927,a1,f107(a1)),x63402)) % 186.01/186.02 [6356]P1(f335(f335(f243(a927),x63561),x63562))+~P1(f335(f335(f243(a927),f335(a119,x63561)),x63562)) % 186.01/186.02 [6359]P1(f335(f335(f244(a927),x63591),x63592))+~P1(f335(f335(f243(a927),f335(a119,x63591)),x63592)) % 186.01/186.02 [6360]P1(f335(f335(f244(a927),x63601),x63602))+~P1(f335(f335(f244(a927),f335(a119,x63601)),x63602)) % 186.01/186.02 [6378]E(f51(a1,x63781,x63782),f2(a1))+E(f335(f335(f23(a1),f51(a1,x63781,x63782)),x63782),f51(a1,x63781,f335(f85(a1),x63782))) % 186.01/186.02 [6443]E(f335(f41(f934(x64431,a922)),f335(f316(x64431),x64432)),f335(f335(f252(a927),f335(a119,f335(a119,f2(a927)))),f335(f41(x64431),x64432)))+~P1(f335(f67(x64431),x64432)) % 186.01/186.02 [6446]E(x64461,f120(x64462))+E(f335(f335(f171(x64462),x64461),f335(f335(f23(a927),f335(f196(f928(x64462)),x64461)),f84(a927))),f151(x64462,x64461)) % 186.01/186.02 [6468]E(x64681,f120(x64682))+E(f335(f335(f141(x64682),f335(f178(x64682),x64681)),f335(f335(f158(x64682),f335(f148(x64682),x64681)),f120(x64682))),f335(f174(x64682),x64681)) % 186.01/186.02 [6498]~P1(f335(f67(x64981),f43(f934(x64981,a922),x64982)))+P1(f335(f67(f934(x64981,a922)),x64982)) % 186.01/186.02 [6520]P1(f335(f335(f243(a927),f335(f110(a927),x65201)),f335(f110(a927),x65202)))+~P1(f335(f335(f243(a1),x65201),a89)) % 186.01/186.02 [6540]~P1(f335(f335(f244(a1),x65401),x65402))+P1(f335(f335(f243(a1),x65401),f335(f335(f23(a1),x65402),f84(a1)))) % 186.01/186.02 [6541]~P1(f335(f335(f243(a1),x65411),x65412))+P1(f335(f335(f244(a1),x65411),f335(f335(f86(a1),x65412),f84(a1)))) % 186.01/186.02 [6542]~P1(f335(f335(f244(a1),x65421),x65422))+P1(f335(f335(f244(a1),x65421),f335(f335(f86(a1),x65422),f84(a1)))) % 186.01/186.02 [6544]~P1(f335(f335(f243(a1),x65441),x65442))+P1(f335(f335(f243(a927),f335(f110(a927),x65441)),f335(f110(a927),x65442))) % 186.01/186.02 [6546]~P1(f335(f335(f243(a927),x65461),x65462))+P1(f335(f335(f243(a1),f335(f107(a1),x65461)),f335(f107(a1),x65462))) % 186.01/186.02 [6547]~P1(f335(f335(f243(a1),x65471),x65472))+P1(f335(f335(f243(a1),f335(f110(a1),x65471)),f335(f110(a1),x65472))) % 186.01/186.02 [6549]~P1(f335(f335(f244(a927),x65491),x65492))+P1(f335(f335(f244(a1),f335(f107(a1),x65491)),f335(f107(a1),x65492))) % 186.01/186.02 [6550]~P1(f335(f335(f244(a1),x65501),x65502))+P1(f335(f335(f244(a1),f335(f110(a1),x65501)),f335(f110(a1),x65502))) % 186.01/186.02 [6570]~P1(f335(f335(f243(a927),x65701),x65702))+~P1(f335(f335(f243(a927),f335(a119,x65702)),x65701)) % 186.01/186.02 [6612]~P1(f335(f335(f243(a927),f335(a119,x66121)),f335(a119,x66122)))+P1(f335(f335(f243(a927),x66121),x66122)) % 186.01/186.02 [6613]~P1(f335(f335(f243(a106),f335(a3,x66131)),f335(a3,x66132)))+P1(f335(f335(f243(a927),x66131),x66132)) % 186.01/186.02 [6614]~P1(f335(f335(f243(a927),f335(a20,x66141)),f335(a20,x66142)))+P1(f335(f335(f243(a106),x66141),x66142)) % 186.01/186.02 [6616]~P1(f335(f335(f244(a927),f335(a119,x66161)),f335(a119,x66162)))+P1(f335(f335(f244(a927),x66161),x66162)) % 186.01/186.02 [6617]~P1(f335(f335(f244(a106),f335(a3,x66171)),f335(a3,x66172)))+P1(f335(f335(f244(a927),x66171),x66172)) % 186.01/186.02 [6618]~P1(f335(f335(f244(a927),f335(a111,x66181)),f335(a111,x66182)))+P1(f335(f335(f244(a1),x66181),x66182)) % 186.01/186.02 [6619]~P1(f335(f335(f244(a927),f335(a20,x66191)),f335(a20,x66192)))+P1(f335(f335(f244(a106),x66191),x66192)) % 186.01/186.02 [6659]~P1(f335(f335(f244(a927),f335(a111,x66592)),f335(a111,x66591)))+P1(f335(f335(f244(a1),f2(a1)),x66591)) % 186.01/186.02 [6691]P1(f335(f335(f243(a1),f2(a1)),f51(a1,x66911,x66912)))+~P1(f335(f335(f244(a1),f2(a1)),x66912)) % 186.01/186.02 [6850]P38(x68501,x68502)+~E(f335(f335(f297(x68501,x68501,x68501),x68502),x68502),f195(f934(f933(x68501,x68501),a922))) % 186.01/186.02 [6864]~P38(x68641,x68642)+P38(x68641,f335(f335(f297(x68641,x68641,x68641),x68642),x68642)) % 186.01/186.02 [6875]P1(f335(f335(f243(a1),x68751),x68752))+~P1(f335(f335(f244(a1),x68751),f335(f335(f86(a1),x68752),f84(a1)))) % 186.01/186.02 [6876]P1(f335(f335(f244(a1),x68761),x68762))+~P1(f335(f335(f243(a1),x68761),f335(f335(f23(a1),x68762),f84(a1)))) % 186.01/186.02 [6879]P1(f335(f335(f243(a927),x68791),x68792))+~P1(f335(f335(f243(a1),f335(f107(a1),x68791)),f335(f107(a1),x68792))) % 186.01/186.02 [6880]P1(f335(f335(f243(a1),x68801),x68802))+~P1(f335(f335(f243(a1),f335(f110(a1),x68801)),f335(f110(a1),x68802))) % 186.01/186.02 [6882]P1(f335(f335(f244(a927),x68821),x68822))+~P1(f335(f335(f244(a1),f335(f107(a1),x68821)),f335(f107(a1),x68822))) % 186.01/186.02 [6883]P1(f335(f335(f244(a1),x68831),x68832))+~P1(f335(f335(f244(a927),f335(f110(a927),x68831)),f335(f110(a927),x68832))) % 186.01/186.02 [6884]P1(f335(f335(f244(a1),x68841),x68842))+~P1(f335(f335(f244(a1),f335(f110(a1),x68841)),f335(f110(a1),x68842))) % 186.01/186.02 [6956]~E(f298(a927,f295(a927),x69561,x69562),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x69561),x69562)) % 186.01/186.02 [6979]~E(f720(x69792,x69791),f120(x69791))+E(f335(f149(f928(x69791),f928(x69791),f141(x69791),f120(x69791)),x69792),f120(x69791)) % 186.01/186.02 [6980]~E(f721(x69802,x69801),f120(x69801))+E(f335(f149(f928(x69801),f928(x69801),f141(x69801),f120(x69801)),x69802),f120(x69801)) % 186.01/186.02 [6984]~P6(x69841)+E(f335(f149(x69841,x69841,f108(x69841),f250(x69841)),x69842),f44(x69841,f335(f179(x69841),x69842))) % 186.01/186.02 [6985]~P6(x69851)+E(f335(f149(x69851,x69851,f117(x69851),f195(x69851)),x69852),f43(x69851,f335(f179(x69851),x69852))) % 186.01/186.02 [6999]E(x69991,f2(a106))+E(f335(f335(f86(a927),f335(a20,f335(f335(f23(a106),x69991),f84(a106)))),f335(a119,x69992)),f335(f335(f86(a927),f335(a20,x69991)),x69992)) % 186.01/186.02 [7048]P1(f335(f335(f244(a1),f335(f335(f23(a1),x70481),x70482)),f2(a1)))+~P1(f335(f335(f244(a1),x70481),x70482)) % 186.01/186.02 [7073]~P109(x70731)+E(f335(f335(f117(f934(x70731,a922)),f335(f335(f317(x70731),x70732),f195(f934(x70731,a922)))),f335(f312(x70731),x70732)),f335(f291(x70731),x70732)) % 186.01/186.02 [7145]~P61(x71451,x71452)+P38(x71451,f335(f270(f933(x71451,x71451)),f335(f265(x71451,x71451,a922),x71452))) % 186.01/186.02 [7146]~P61(x71461,x71462)+P59(x71461,f335(f270(f933(x71461,x71461)),f335(f265(x71461,x71461,a922),x71462))) % 186.01/186.02 [7147]~P51(x71471,x71472)+P39(x71471,f335(f270(f933(x71471,x71471)),f335(f265(x71471,x71471,a922),x71472))) % 186.01/186.02 [7148]~P52(x71481,x71482)+P53(x71481,f335(f270(f933(x71481,x71481)),f335(f265(x71481,x71481,a922),x71482))) % 186.01/186.02 [7149]E(x71491,f195(f934(x71492,a922)))+~P1(f335(f335(f243(f934(x71492,a922)),x71491),f195(f934(x71492,a922)))) % 186.01/186.02 [7231]~P1(f335(f335(f244(a927),f2(a927)),x72312))+P1(f335(f335(f243(a927),f51(a927,x72311,x72312)),x72312)) % 186.01/186.02 [7232]~P1(f335(f335(f243(a1),f2(a1)),x72321))+P1(f335(f335(f243(a1),f51(a1,x72321,x72322)),x72321)) % 186.01/186.02 [7233]~P1(f335(f335(f244(a927),f2(a927)),x72332))+P1(f335(f335(f244(a927),f51(a927,x72331,x72332)),x72332)) % 186.01/186.02 [7235]~P1(f335(f335(f244(a1),f2(a1)),x72352))+P1(f335(f335(f244(a1),f51(a1,x72351,x72352)),x72352)) % 186.01/186.02 [7311]~P110(x73111)+E(f335(f335(f23(f934(x73111,a922)),f335(f335(f317(x73111),x73112),f195(f934(x73111,a922)))),f335(f290(x73111),x73112)),f335(f335(f317(x73111),x73112),f195(f934(x73111,a922)))) % 186.01/186.02 [7384]~P49(x73841,x73842)+P54(x73841,f250(f934(x73841,a922)),f335(f270(f933(x73841,x73841)),f335(f265(x73841,x73841,a922),x73842))) % 186.01/186.02 [7385]P1(f335(x73851,x73852))+P1(f335(f335(f337(f934(f933(a927,a927),a922)),f576(x73852,x73851)),a105)) % 186.01/186.02 [7429]E(f335(f335(f141(a927),f146(a927,f335(f310(a927,x74291),x74292))),f335(f335(f158(a927),x74292),f120(a927))),f146(a927,f335(f310(a927,x74291),f335(a119,x74292))))+~P1(f335(f335(f243(a927),x74291),x74292)) % 186.01/186.02 [7583]E(x75831,f2(a927))+~E(f335(f149(a927,a927,f86(a927),x75831),x75832),f2(a927)) % 186.01/186.02 [7607]~P1(f335(f335(f244(a1),f335(f335(f23(a1),x76071),x76072)),f2(a1)))+P1(f335(f335(f244(a1),x76071),x76072)) % 186.01/186.02 [7634]P38(x76341,x76342)+~P38(x76341,f335(f335(f297(x76341,x76341,x76341),x76342),x76342)) % 186.01/186.02 [7660]~P1(f335(f335(f243(a927),f335(a119,x76601)),x76602))+P1(f192(a922,a247,f335(f243(a927),x76601),x76602)) % 186.01/186.02 [7811]P26(a927,a927,f335(f335(f7(a927,a927,a927),f23(a927)),x78111),x78112)+P1(f335(f335(f337(a927),f590(x78111,x78112)),x78112)) % 186.01/186.02 [7867]E(f335(f335(f335(f71(a927,x78671,f86(a927)),f335(f16(a927,x78671),f84(a927))),f2(a927)),x78672),f335(f41(x78671),x78672))+~P1(f335(f67(x78671),x78672)) % 186.01/186.02 [7908]P26(a927,a927,f335(f335(f7(a927,a927,a927),f23(a927)),x79081),x79082)+~P1(f335(f335(f243(a927),x79081),f590(x79081,x79082))) % 186.01/186.02 [7963]P38(x79631,x79632)+P1(f335(f335(f243(f934(x79631,a922)),f841(x79632,x79631)),f335(f293(x79631,x79631,x79632),f841(x79632,x79631)))) % 186.01/186.02 [7968]P61(x79681,x79682)+~P38(x79681,f335(f270(f933(x79681,x79681)),f335(f265(x79681,x79681,a922),x79682))) % 186.01/186.02 [7969]P51(x79691,x79692)+~P39(x79691,f335(f270(f933(x79691,x79691)),f335(f265(x79691,x79691,a922),x79692))) % 186.01/186.02 [7970]P52(x79701,x79702)+~P53(x79701,f335(f270(f933(x79701,x79701)),f335(f265(x79701,x79701,a922),x79702))) % 186.01/186.02 [8036]P1(f335(f335(f243(a927),f335(a119,x80361)),x80362))+~P1(f192(a922,a247,f335(f243(a927),x80361),x80362)) % 186.01/186.02 [8091]P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x80911),x80912)),f315(a927,a325)))+~P1(f335(f335(f243(a927),x80911),x80912)) % 186.01/186.02 [8187]P49(x81871,x81872)+~P54(x81871,f250(f934(x81871,a922)),f335(f270(f933(x81871,x81871)),f335(f265(x81871,x81871,a922),x81872))) % 186.01/186.02 [8242]~P1(f335(f144(x82421),x82422))+P1(f335(f144(f934(x82421,a922)),f335(f335(f161(f928(x82421),f934(x82421,a922)),f179(x82421)),f60(x82421,x82422)))) % 186.01/186.02 [8438]~P38(x84381,f335(f294(x84381,x84381),x84382))+P38(x84381,f335(f294(x84381,x84381),f335(f335(f297(x84381,x84381,x84381),x84382),f315(x84381,x84382)))) % 186.01/186.02 [8538]P27(x85381,a927,f604(x85382,x85381),x85382,f335(f310(a927,f2(a927)),f335(f41(x85381),x85382)))+~P1(f335(f67(x85381),x85382)) % 186.01/186.02 [8539]P27(a927,x85391,f593(x85392,x85391),f335(f310(a927,f2(a927)),f335(f41(x85391),x85392)),x85392)+~P1(f335(f67(x85391),x85392)) % 186.01/186.02 [8556]P27(a927,x85561,f591(x85562,x85561),f311(a927,f84(a927),f335(f41(x85561),x85562)),x85562)+~P1(f335(f67(x85561),x85562)) % 186.01/186.02 [8565]P1(f335(f67(f933(x85651,x85651)),f335(f335(f297(x85651,x85651,x85651),x85652),f315(x85651,x85652))))+~P1(f335(f67(f933(x85651,x85651)),x85652)) % 186.01/186.02 [8592]E(x85921,f2(a1))+P1(f335(f55(x85922,x85921),f335(f335(f260(a1,a1),f335(f335(f42(a1),x85922),x85921)),f51(a1,x85922,x85921)))) % 186.01/186.02 [8606]~P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x86061),x86062)),f315(a927,a325)))+P1(f335(f335(f243(a927),x86061),x86062)) % 186.01/186.02 [8622]~P82(x86221)+E(f335(f149(x86221,x86221,f335(f7(x86221,x86221,x86221),f86(x86221)),f2(x86221)),f335(f175(x86221),x86222)),f335(f149(x86221,x86221,f86(x86221),f2(x86221)),x86222)) % 186.01/186.02 [8793]~P109(x87931)+E(f335(f149(f928(x87931),x87931,f335(f7(x87931,f928(x87931),f928(x87931)),f155(x87931,x87931,f5(x87931))),f120(x87931)),x87932),f157(x87931,x87931,f5(x87931),x87932)) % 186.01/186.02 [8904]~P59(x89041,f335(f270(f933(x89041,x89041)),f335(f265(x89041,x89041,a922),x89042)))+P59(x89041,f335(f270(f933(x89041,x89041)),f335(f265(x89041,x89041,a922),f251(x89041,x89041,x89042)))) % 186.01/186.02 [8918]P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x89181),x89182)),f335(f335(f297(a927,a927,a927),a325),f315(a927,a325))))+~P1(f335(f335(f244(a927),x89181),x89182)) % 186.01/186.02 [8964]~P1(f335(f67(f933(x89641,x89641)),f335(f335(f297(x89641,x89641,x89641),x89642),f315(x89641,x89642))))+P1(f335(f67(f933(x89641,x89641)),x89642)) % 186.01/186.02 [9022]~P59(x90221,f335(f270(f933(x90221,x90221)),f335(f265(x90221,x90221,a922),f251(x90221,x90221,x90222))))+P59(x90221,f335(f270(f933(x90221,x90221)),f335(f265(x90221,x90221,a922),x90222))) % 186.01/186.02 [9223]P59(x92231,x92232)+P1(f335(f335(f337(f933(x92231,x92231)),f335(f335(f260(x92231,x92231),f618(x92232,x92231)),f618(x92232,x92231))),f335(f335(f297(x92231,x92231,x92231),x92232),f315(x92231,x92232)))) % 186.01/186.02 [9224]P59(x92241,x92242)+P1(f335(f335(f337(f933(x92241,x92241)),f335(f335(f260(x92241,x92241),f620(x92242,x92241)),f620(x92242,x92241))),f335(f335(f297(x92241,x92241,x92241),x92242),f315(x92241,x92242)))) % 186.01/186.02 [9342]~P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x93421),x93422)),f335(f335(f297(a927,a927,a927),a325),f315(a927,a325))))+P1(f335(f335(f244(a927),x93421),x93422)) % 186.01/186.02 [5318]~P94(x53181)+E(f335(f335(f86(x53181),f335(f110(x53181),a89)),x53182),x53182) % 186.01/186.02 [5348]~P83(x53481)+E(f335(f335(f108(x53481),f335(f85(x53481),x53482)),x53482),f195(x53481)) % 186.01/186.02 [5349]~P83(x53491)+E(f335(f335(f117(x53491),f335(f85(x53491),x53492)),x53492),f250(x53491)) % 186.01/186.02 [5350]~P4(x53501)+E(f335(f335(f86(x53501),f335(f85(x53501),x53502)),x53502),f2(x53501)) % 186.01/186.02 [5351]~P5(x53511)+E(f335(f335(f86(x53511),f335(f85(x53511),x53512)),x53512),f2(x53511)) % 186.01/186.02 [5384]~P94(x53841)+E(f335(f335(f87(x53841),f335(f110(x53841),a104)),x53842),f335(f85(x53841),x53842)) % 186.01/186.02 [5545]~P116(x55451)+E(f335(f335(f87(x55451),f335(f85(x55451),f84(x55451))),x55452),f335(f85(x55451),x55452)) % 186.01/186.02 [5590]E(f335(f81(a1),x55901),f84(a1))+~E(f335(f81(a1),f335(f335(f87(a1),x55901),x55902)),f84(a1)) % 186.01/186.02 [5680]~P94(x56801)+E(f335(f335(f86(x56801),f84(x56801)),f335(f110(x56801),x56802)),f335(f110(x56801),f335(f335(f23(a1),x56802),a104))) % 186.01/186.02 [5734]~P6(x57341)+E(f44(x57341,f335(f335(f317(x57341),x57342),f195(f934(x57341,a922)))),x57342) % 186.01/186.02 [5735]~P98(x57351)+E(f13(x57351,f335(f335(f317(x57351),x57352),f195(f934(x57351,a922)))),x57352) % 186.01/186.02 [5736]~P98(x57361)+E(f10(x57361,f335(f335(f317(x57361),x57362),f195(f934(x57361,a922)))),x57362) % 186.01/186.02 [5737]~P109(x57371)+E(f14(x57371,f335(f335(f317(x57371),x57372),f195(f934(x57371,a922)))),x57372) % 186.01/186.02 [5738]~P109(x57381)+E(f15(x57381,f335(f335(f317(x57381),x57382),f195(f934(x57381,a922)))),x57382) % 186.01/186.02 [5739]~P6(x57391)+E(f43(x57391,f335(f335(f317(x57391),x57392),f195(f934(x57391,a922)))),x57392) % 186.01/186.02 [5761]E(f335(f335(f86(a927),x57611),f335(f335(f23(a927),x57612),x57611)),x57612)+P1(f335(f335(f244(a927),x57612),x57611)) % 186.01/186.02 [5797]E(x57971,f120(x57972))+P1(f335(f335(f244(a927),f2(a927)),f335(f196(f928(x57972)),x57971))) % 186.01/186.02 [5922]~P109(x59221)+E(f11(x59221,f242(x59221),f335(f335(f317(x59221),x59222),f195(f934(x59221,a922)))),x59222) % 186.01/186.02 [5923]~P109(x59231)+E(f12(x59231,f241(x59231),f335(f335(f317(x59231),x59232),f195(f934(x59231,a922)))),x59232) % 186.01/186.02 [5984]E(f335(f335(f23(a927),x59841),f335(f335(f23(a927),x59841),x59842)),x59842)+~P1(f335(f335(f243(a927),x59842),x59841)) % 186.01/186.02 [5985]E(f335(f335(f86(a927),x59851),f335(f335(f23(a927),x59852),x59851)),x59852)+~P1(f335(f335(f243(a927),x59851),x59852)) % 186.01/186.02 [6007]E(f51(a927,f335(f335(f23(a927),x60071),x60072),x60072),f51(a927,x60071,x60072))+P1(f335(f335(f244(a927),x60071),x60072)) % 186.01/186.02 [6018]E(f335(f85(a1),f335(f335(f42(a1),x60181),f335(f85(a1),x60182))),f301(x60181,x60182))+P1(f335(f335(f243(a1),f2(a1)),x60182)) % 186.01/186.02 [6020]~E(x60202,f2(a927))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f252(a927),x60201),x60202))) % 186.01/186.02 [6074]~P94(x60741)+E(f335(f335(f86(x60741),f335(f85(x60741),f84(x60741))),f335(f110(x60741),x60742)),f335(f110(x60741),f335(f335(f86(a1),x60742),a104))) % 186.01/186.02 [6076]E(f335(f335(f252(a927),f335(f110(a927),x60761)),x60762),f335(f335(f252(a927),f2(a927)),x60762))+~P1(f335(a200,f335(f110(a1),x60761))) % 186.01/186.02 [6178]E(f335(f148(a927),f146(a927,f335(f310(a927,x61781),x61782))),x61781)+~P1(f335(f335(f244(a927),x61781),x61782)) % 186.01/186.02 [6194]E(f335(f335(f87(a927),f335(f110(a927),x61941)),f335(f110(a927),x61942)),f335(f110(a927),f335(f335(f87(a1),x61941),x61942)))+P1(f335(f335(f244(a1),x61941),a89)) % 186.01/186.02 [6200]~P126(x62001)+P1(f335(f335(f243(x62001),f2(x62001)),f335(f335(f87(x62001),x62002),x62002))) % 186.01/186.02 [6212]E(f335(f335(f23(a927),f335(a119,x62121)),x62122),f335(a119,f335(f335(f23(a927),x62121),x62122)))+~P1(f335(f335(f243(a927),x62122),x62121)) % 186.01/186.02 [6216]E(f51(a927,f335(f335(f23(a927),x62161),x62162),x62162),f51(a927,x62161,x62162))+~P1(f335(f335(f243(a927),x62162),x62161)) % 186.01/186.02 [6268]E(f335(f335(f252(a927),f335(a111,x62681)),x62682),f335(a111,f335(f335(f252(a1),x62681),x62682)))+~P1(f335(f335(f243(a1),f2(a1)),x62681)) % 186.01/186.02 [6286]P1(f335(f144(x62861),x62862))+P1(f335(f335(f244(a927),f690(x62862,x62861)),f335(f196(f928(x62861)),x62862))) % 186.01/186.02 [6287]P1(f335(f144(x62871),x62872))+P1(f335(f335(f244(a927),f694(x62872,x62871)),f335(f196(f928(x62871)),x62872))) % 186.01/186.02 [6301]~E(x63011,f120(x63012))+~P1(f335(f335(f244(a927),f2(a927)),f335(f196(f928(x63012)),x63011))) % 186.01/186.02 [6312]E(f151(a927,f146(a927,f335(f310(a927,x63121),x63122))),f335(f335(f23(a927),x63122),f84(a927)))+~P1(f335(f335(f244(a927),x63121),x63122)) % 186.01/186.02 [6315]E(f335(f335(f86(a1),x63151),f335(f107(a1),f335(a119,f426(x63152,x63151)))),x63152)+~P1(f335(f335(f244(a1),x63151),x63152)) % 186.01/186.02 [6322]E(x63221,f2(a927))+E(f335(f335(f87(a927),x63222),f335(f335(f252(a927),x63222),f335(f335(f23(a927),x63221),f84(a927)))),f335(f335(f252(a927),x63222),x63221)) % 186.01/186.02 [6350]E(f335(f335(f87(a927),f335(a111,x63501)),f335(a111,x63502)),f335(a111,f335(f335(f87(a1),x63501),x63502)))+~P1(f335(f335(f243(a1),f2(a1)),x63501)) % 186.01/186.02 [6351]E(f335(f335(f42(a927),f335(a111,x63511)),f335(a111,x63512)),f335(a111,f335(f335(f42(a1),x63511),x63512)))+~P1(f335(f335(f243(a1),f2(a1)),x63511)) % 186.01/186.02 [6365]~P118(x63651)+E(f335(f335(f86(x63651),x63652),x63652),f335(f335(f87(x63651),f335(f335(f86(x63651),f84(x63651)),f84(x63651))),x63652)) % 186.01/186.02 [6387]E(f335(f335(f23(a1),f335(f107(a1),x63871)),f335(f107(a1),x63872)),f335(f107(a1),f335(f335(f23(a927),x63871),x63872)))+~P1(f335(f335(f243(a927),x63872),x63871)) % 186.01/186.02 [6389]E(f335(f335(f260(a1,a1),f335(f110(a1),a104)),f335(f335(f86(a1),x63891),x63892)),f56(x63891,x63892))+~P1(f335(f335(f243(a1),x63892),f2(a1))) % 186.01/186.02 [6421]E(f186(x64211,x64212),f120(f928(x64211)))+P1(f335(f335(f337(f928(x64211)),f689(x64212,x64211)),f335(f179(f928(x64211)),x64212))) % 186.01/186.02 [6430]E(f123(a1,f335(f136(a1),x64301),f135(x64302,f335(f335(f86(a1),x64301),f84(a1)))),f135(x64302,x64301))+P1(f335(f335(f244(a1),x64302),x64301)) % 186.01/186.02 [6504]E(f335(f335(f158(a1),x65041),f185(f335(f335(f86(a1),x65041),f84(a1)),x65042)),f185(x65041,x65042))+~P1(f335(f335(f243(a1),x65041),x65042)) % 186.01/186.02 [6543]~P1(f335(f335(f244(a927),x65432),x65431))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f23(a927),x65431),x65432))) % 186.01/186.02 [6575]~P1(f335(f335(f244(a927),x65751),f335(a111,x65752)))+P1(f335(f335(f244(a1),f335(f107(a1),x65751)),x65752)) % 186.01/186.02 [6603]~P109(x66031)+E(f335(f335(f117(f934(x66031,a922)),f335(f290(x66031),x66032)),f335(f335(f317(x66031),x66032),f195(f934(x66031,a922)))),f335(f309(x66031),x66032)) % 186.01/186.02 [6604]~P1(f335(f335(f243(a1),f2(a1)),x66041))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f252(a1),x66041),x66042))) % 186.01/186.02 [6607]~P1(f335(f335(f244(a927),f2(a927)),x66071))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f252(a927),x66071),x66072))) % 186.01/186.02 [6635]~E(f335(x66351,f2(a927)),f2(a927))+E(f335(f335(f6(a927,a927),x66351),f311(a927,f335(a119,f2(a927)),x66352)),f335(f335(f6(a927,a927),x66351),f311(a927,f2(a927),x66352))) % 186.01/186.02 [6699]~P94(x66991)+E(f335(f335(f87(x66991),f335(f335(f86(x66991),f84(x66991)),f84(x66991))),f335(f110(x66991),x66992)),f335(f110(x66991),f335(f335(f86(a1),x66992),x66992))) % 186.01/186.02 [6714]E(f335(f335(f317(a1),x67141),f311(a1,f335(f335(f86(a1),x67141),f84(a1)),x67142)),f311(a1,x67141,x67142))+P1(f335(f335(f244(a1),x67142),x67141)) % 186.01/186.02 [6715]P1(f335(f335(f244(a927),x67151),f335(a111,x67152)))+~P1(f335(f335(f244(a1),f335(f107(a1),x67151)),x67152)) % 186.01/186.02 [6819]E(f335(a111,f335(f335(f42(a1),f335(f110(a1),x68191)),f335(f110(a1),x68192))),f335(f335(f42(a927),f335(f110(a927),x68191)),f335(f110(a927),x68192)))+P1(f335(a200,f335(f110(a1),x68191))) % 186.01/186.02 [6877]P1(f335(f335(f244(a927),x68771),x68772))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f23(a927),x68772),x68771))) % 186.01/186.02 [6921]P1(f335(f335(f244(a927),f2(a927)),x69211))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f87(a927),x69212),x69211))) % 186.01/186.02 [6922]P1(f335(f335(f244(a927),f2(a927)),x69221))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f87(a927),x69221),x69222))) % 186.01/186.02 [6940]~P1(f335(f335(f243(a1),x69401),f2(a1)))+E(f335(f335(f87(a927),f335(a111,f335(f85(a1),x69401))),f335(a111,f335(f85(a1),x69402))),f335(a111,f335(f335(f87(a1),x69401),x69402))) % 186.01/186.02 [6996]~E(x69962,f195(f934(x69961,a922)))+P1(f335(f335(f243(f934(x69961,a922)),x69962),f335(f85(f934(x69961,a922)),x69962))) % 186.01/186.02 [7058]~P94(x70581)+E(f335(f335(f86(x70581),f335(f335(f86(x70581),f2(x70581)),f335(f110(x70581),x70582))),f335(f110(x70581),x70582)),f335(f110(x70581),f335(f335(f86(a1),x70582),x70582))) % 186.01/186.02 [7112]~P1(f335(f335(f244(a1),x71121),x71122))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x71121),f84(a1))),x71122)) % 186.01/186.02 [7176]E(x71761,f2(a927))+~P1(f335(f335(f243(a1),f335(f107(a1),x71762)),f335(f85(a1),f335(f107(a1),x71761)))) % 186.01/186.02 [7177]E(x71771,f2(a927))+~P1(f335(f335(f243(a1),f335(f107(a1),x71771)),f335(f85(a1),f335(f107(a1),x71772)))) % 186.01/186.02 [7279]E(f335(f335(f260(a1,a1),f335(f110(a1),a104)),f335(f335(f86(a1),x72791),x72792)),f56(x72791,x72792))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),x72791),x72792))) % 186.01/186.02 [7323]~P28(x73231,x73232)+P38(x73231,f335(f259(f934(f933(x73231,x73231),a922),f934(f933(x73231,x73231),a922)),x73232)) % 186.01/186.02 [7342]~P1(f335(f335(f243(a927),f335(a119,f2(a927))),x73421))+P1(f335(f335(f243(a927),f335(a119,f2(a927))),f335(f335(f252(a927),x73421),x73422))) % 186.01/186.02 [7522]~P1(f335(f335(f243(a1),x75221),x75222))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x75221),x75221)),f335(f335(f86(a1),x75222),x75222))) % 186.01/186.02 [7527]~P1(f335(f335(f244(a1),x75271),x75272))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x75271),x75271)),f335(f335(f86(a1),x75272),x75272))) % 186.01/186.02 [7584]~P1(f335(f335(f244(a927),f2(a927)),x75841))+P1(f335(f335(f244(a927),f335(f335(f23(a927),x75841),f335(a119,x75842))),x75841)) % 186.01/186.02 [7616]P1(f335(f335(f243(a927),f335(a119,f2(a927))),x76161))+~P1(f335(f335(f243(a927),f335(a119,f2(a927))),f335(f335(f87(a927),x76162),x76161))) % 186.01/186.02 [7617]P1(f335(f335(f243(a927),f335(a119,f2(a927))),x76171))+~P1(f335(f335(f243(a927),f335(a119,f2(a927))),f335(f335(f87(a927),x76171),x76172))) % 186.01/186.02 [7621]P1(f335(f335(f243(a927),f335(f335(f171(a927),x76211),x76212)),f335(f172(a927),x76211)))+~P1(f335(f335(f244(a927),x76212),f335(f196(f928(a927)),x76211))) % 186.01/186.02 [7659]P1(f335(f335(f244(a1),x76591),x76592))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x76591),f84(a1))),x76592)) % 186.01/186.02 [7701]P1(f335(f67(x77011),f250(f934(x77011,a922))))+~P1(f335(f67(f934(x77012,x77011)),f250(f934(f934(x77012,x77011),a922)))) % 186.01/186.02 [7702]P1(f335(f67(x77021),f250(f934(x77021,a922))))+~P1(f335(f67(f935(x77022,x77021)),f250(f934(f935(x77022,x77021),a922)))) % 186.01/186.02 [7703]P1(f335(f67(x77031),f250(f934(x77031,a922))))+~P1(f335(f67(f935(x77031,x77032)),f250(f934(f935(x77031,x77032),a922)))) % 186.01/186.02 [7741]E(x77411,f195(f934(x77412,a922)))+~P1(f335(f335(f243(f934(x77412,a922)),x77411),f335(f85(f934(x77412,a922)),x77411))) % 186.01/186.02 [7877]E(f335(f149(f928(x78771),f928(x78771),f141(x78771),f120(x78771)),x78772),f120(x78771))+P1(f335(f335(f337(f928(x78771)),f720(x78772,x78771)),f335(f179(f928(x78771)),x78772))) % 186.01/186.02 [7878]E(f335(f149(f928(x78781),f928(x78781),f141(x78781),f120(x78781)),x78782),f120(x78781))+P1(f335(f335(f337(f928(x78781)),f721(x78782,x78781)),f335(f179(f928(x78781)),x78782))) % 186.01/186.02 [8109]P1(f335(f335(f243(a1),x81091),x81092))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x81091),x81091)),f335(f335(f86(a1),x81092),x81092))) % 186.01/186.02 [8114]P1(f335(f335(f244(a1),x81141),x81142))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x81141),x81141)),f335(f335(f86(a1),x81142),x81142))) % 186.01/186.02 [8207]~P118(x82071)+E(f335(f335(f87(x82071),f335(f335(f86(x82071),f84(x82071)),f84(x82071))),f335(f335(f6(a927,x82071),f107(x82071)),f311(a927,f84(a927),x82072))),f335(f335(f87(x82071),f335(f107(x82071),x82072)),f335(f335(f86(x82071),f335(f107(x82071),x82072)),f84(x82071)))) % 186.01/186.02 [8256]P1(f335(f335(f337(a927),x82561),x82562))+~P1(f335(f335(f337(a1),f335(f107(a1),x82561)),f335(f318(a927,a1,f107(a1)),x82562))) % 186.01/186.02 [8410]~P1(f335(f67(x84101),x84102))+E(f335(f318(a927,x84101,f354(x84102,x84101)),f335(f270(a927),f335(f335(f7(a927,a927,a922),f244(a927)),f355(x84102,x84101)))),x84102) % 186.01/186.02 [8690]P55(x86901,x86902)+P1(f335(f335(f337(f933(x86901,x86901)),f335(f335(f260(x86901,x86901),f807(x86902,x86901)),f807(x86902,x86901))),x86902)) % 186.01/186.02 [8691]P39(x86911,x86912)+P1(f335(f335(f337(f933(x86911,x86911)),f335(f335(f260(x86911,x86911),f813(x86912,x86911)),f816(x86912,x86911))),x86912)) % 186.01/186.02 [8692]P39(x86921,x86922)+P1(f335(f335(f337(f933(x86921,x86921)),f335(f335(f260(x86921,x86921),f816(x86922,x86921)),f817(x86922,x86921))),x86922)) % 186.01/186.02 [8693]P40(x86931,x86932)+P1(f335(f335(f337(f933(x86931,x86931)),f335(f335(f260(x86931,x86931),f730(x86932,x86931)),f729(x86932,x86931))),x86932)) % 186.01/186.02 [8694]P40(x86941,x86942)+P1(f335(f335(f337(f933(x86941,x86941)),f335(f335(f260(x86941,x86941),f729(x86942,x86941)),f730(x86942,x86941))),x86942)) % 186.01/186.02 [8695]P53(x86951,x86952)+P1(f335(f335(f337(f933(x86951,x86951)),f335(f335(f260(x86951,x86951),f828(x86952,x86951)),f829(x86952,x86951))),x86952)) % 186.01/186.02 [8836]~P94(x88361)+E(f335(f335(f23(x88361),f84(x88361)),f335(f110(x88361),x88362)),f335(f110(x88361),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f85(a1),x88362)))) % 186.01/186.02 [8961]~P1(f335(f335(f244(f934(a927,a922)),x89611),x89612))+P1(f335(f335(f244(f934(a1,a922)),f335(f318(a927,a1,f107(a1)),x89611)),f335(f318(a927,a1,f107(a1)),x89612))) % 186.01/186.02 [8995]~P1(f335(f335(f244(a1),x89951),x89952))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x89951),x89951)),a104)),f335(f335(f86(a1),x89952),x89952))) % 186.01/186.02 [8997]~P1(f335(f335(f244(a1),x89971),x89972))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x89971),x89971)),a104)),f335(f335(f86(a1),x89972),x89972))) % 186.01/186.02 [9070]~P1(f335(f335(f337(a927),x90701),f335(f179(a927),x90702)))+P1(f335(f335(f243(a927),x90701),f335(f149(a927,a927,f86(a927),f2(a927)),x90702))) % 186.01/186.02 [9163]P46(x91631,x91632)+~P1(f335(f335(f337(f933(x91631,x91631)),f335(f335(f260(x91631,x91631),f776(x91632,x91631)),f776(x91632,x91631))),x91632)) % 186.01/186.02 [9164]P39(x91641,x91642)+~P1(f335(f335(f337(f933(x91641,x91641)),f335(f335(f260(x91641,x91641),f813(x91642,x91641)),f817(x91642,x91641))),x91642)) % 186.01/186.02 [9165]P53(x91651,x91652)+~P1(f335(f335(f337(f933(x91651,x91651)),f335(f335(f260(x91651,x91651),f829(x91652,x91651)),f828(x91652,x91651))),x91652)) % 186.01/186.02 [9304]~P1(f335(f335(f243(f934(a1,a922)),f335(f318(a927,a1,f107(a1)),x93041)),f335(f318(a927,a1,f107(a1)),x93042)))+P1(f335(f335(f243(f934(a927,a922)),x93041),x93042)) % 186.01/186.02 [9305]~P1(f335(f335(f244(f934(a1,a922)),f335(f318(a927,a1,f107(a1)),x93051)),f335(f318(a927,a1,f107(a1)),x93052)))+P1(f335(f335(f244(f934(a927,a922)),x93051),x93052)) % 186.01/186.02 [9390]P1(f335(f335(f244(a1),x93901),x93902))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93901),x93901)),a104)),f335(f335(f86(a1),x93902),x93902))) % 186.01/186.02 [9392]P1(f335(f335(f244(a1),x93921),x93922))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x93921),x93921)),a104)),f335(f335(f86(a1),x93922),x93922))) % 186.01/186.02 [10280]~P105(x102801)+E(f123(f928(x102801),f335(f136(f928(x102801)),f120(x102801)),f335(f335(f335(f103(f929(f928(x102801))),f335(f335(f244(a1),f2(a1)),x102802)),f335(f125(f933(x102801,f928(x102801)),f928(x102801),f138(x102801,f928(x102801),f139(x102801,f335(f335(f23(a1),x102802),f84(a1))),f139(f928(x102801),f335(f335(f23(a1),x102802),f84(a1))))),f335(f265(x102801,f928(x102801),f929(f928(x102801))),f335(f335(f8(f934(f928(x102801),f928(x102801)),f934(f928(x102801),f929(f928(x102801))),x102801),f335(f8(f928(x102801),f929(f928(x102801)),f928(x102801)),f136(f928(x102801)))),f158(x102801))))),f122(f928(x102801)))),f139(f928(x102801),x102802)) % 186.01/186.02 [10302]~P1(f335(f67(x103021),x103022))+E(f335(f196(f928(x103021)),f96(f928(x103021),f335(f335(f18(f928(x103021),a922,a922),f335(f335(f8(a922,f934(a922,a922),f928(x103021)),a333),f335(f335(f7(f928(x103021),f934(x103021,a922),a922),f335(f335(f8(f934(x103021,a922),f934(f934(x103021,a922),a922),f928(x103021)),a332),f179(x103021))),x103022))),f144(x103021)))),f223(x103021,x103022)) % 186.01/186.02 [6311]E(f335(f335(f86(a927),f335(f335(f23(a927),x63111),x63112)),x63112),x63111)+~P1(f335(f335(f243(a927),x63112),x63111)) % 186.01/186.02 [6383]E(f335(f335(f42(a927),f335(f335(f87(a927),x63831),x63832)),x63832),x63831)+~P1(f335(f335(f244(a927),f2(a927)),x63832)) % 186.01/186.02 [6384]E(f335(f335(f42(a927),f335(f335(f87(a927),x63841),x63842)),x63841),x63842)+~P1(f335(f335(f244(a927),f2(a927)),x63841)) % 186.01/186.02 [6388]~P76(x63881)+E(f335(f335(f6(a927,x63881),f335(f171(x63881),x63882)),f335(f310(a927,f2(a927)),f335(f196(f928(x63881)),x63882))),f335(f172(x63881),x63882)) % 186.01/186.02 [6496]E(f51(a927,f335(a119,f335(f335(f87(a927),x64961),x64962)),x64961),f84(a927))+~P1(f335(f335(f244(a927),f84(a927)),x64961)) % 186.01/186.02 [6502]E(f335(a119,f335(f335(f86(a927),f335(f110(a927),x65021)),x65022)),f335(f335(f86(a927),f84(a927)),x65022))+~P1(f335(a200,f335(f110(a1),x65021))) % 186.01/186.02 [6531]E(f335(a111,f335(f335(f252(a1),f335(f110(a1),x65311)),x65312)),f335(f335(f252(a927),f335(f110(a927),x65311)),x65312))+P1(f335(a200,f335(f110(a1),x65311))) % 186.01/186.02 [6769]E(f335(f335(f23(a927),x67691),f335(f110(a927),f335(f335(f86(a1),x67692),a104))),f335(f335(f23(a927),f335(a119,x67691)),f335(f110(a927),x67692)))+~P1(f335(f335(f244(a1),a89),x67692)) % 186.01/186.02 [6849]E(x68491,f2(a927))+E(f335(a119,f335(f335(f86(a927),f335(f335(f23(a927),x68491),f84(a927))),x68492)),f335(f335(f86(a927),x68491),x68492)) % 186.01/186.02 [6890]E(x68901,f2(a1))+P1(f335(f335(f244(a1),f2(a1)),f335(f335(f252(a1),f335(f81(a1),x68901)),x68902))) % 186.01/186.02 [6905]~E(x69052,f2(a927))+P1(f335(f335(f244(a1),f2(a1)),f335(f335(f252(a1),f335(f81(a1),x69051)),x69052))) % 186.01/186.02 [6943]E(x69431,f2(a927))+E(f335(f335(f86(a927),x69432),f335(f335(f87(a927),f335(f335(f23(a927),x69431),f84(a927))),x69432)),f335(f335(f87(a927),x69431),x69432)) % 186.01/186.02 [6989]~P1(f335(f335(f243(a1),x69891),x69892))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x69891),a104)),x69892)) % 186.01/186.02 [7115]E(f335(f335(f158(a927),x71151),f146(a927,f335(f310(a927,f335(a119,x71151)),x71152))),f146(a927,f335(f310(a927,x71151),x71152)))+~P1(f335(f335(f244(a927),x71151),x71152)) % 186.01/186.02 [7314]E(x73141,x73142)+~E(f335(f335(f23(a1),f335(f335(f86(a1),x73141),x73141)),a104),f335(f335(f23(a1),f335(f335(f86(a1),x73142),x73142)),a104)) % 186.01/186.02 [7317]E(x73171,f120(x73172))+E(f274(x73172,f335(f335(f161(x73172,f933(a106,x73172)),f335(f260(a106,x73172),f84(a106))),x73171)),f283(x73172,x73171)) % 186.01/186.02 [7554]P1(f335(f335(f243(a1),x75541),x75542))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x75541),a104)),x75542)) % 186.01/186.02 [8016]~P1(f335(f335(f244(a927),x80161),x80162))+P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x80161),x80162)),a248)) % 186.01/186.02 [8233]~P1(f335(f335(f244(a106),f2(a106)),x82331))+P1(f335(f335(f244(a106),f335(f259(a106,f933(a106,a106)),f335(f275(x82331),x82332))),x82331)) % 186.01/186.02 [8492]~P39(x84921,x84922)+P39(x84921,f335(f335(f117(f934(f933(x84921,x84921),a922)),x84922),f315(x84921,f195(f934(f933(x84921,x84921),a922))))) % 186.01/186.02 [8493]~P40(x84931,x84932)+P40(x84931,f335(f335(f117(f934(f933(x84931,x84931),a922)),x84932),f315(x84931,f195(f934(f933(x84931,x84931),a922))))) % 186.01/186.02 [8542]~P87(x85421)+P1(f335(f335(f243(x85421),f335(f81(x85421),f335(f172(x85421),x85422))),f335(f172(x85421),f335(f335(f161(x85421,x85421),f81(x85421)),x85422)))) % 186.01/186.02 [8567]P1(f335(f335(f244(a927),x85671),x85672))+~P1(f335(f335(f337(f933(a927,a927)),f335(f335(f260(a927,a927),x85671),x85672)),a248)) % 186.01/186.02 [8714]E(f335(f335(f260(x87141,x87141),f916(x87142,x87141)),f916(x87142,x87141)),x87142)+~P1(f335(f335(f337(f933(x87141,x87141)),x87142),f315(x87141,f195(f934(f933(x87141,x87141),a922))))) % 186.01/186.02 [8758]E(f335(f310(a927,x87581),f335(f335(f86(a927),x87581),f335(f41(a927),x87582))),x87582)+~P1(f335(f335(f243(f934(a927,a922)),x87582),f335(f310(a927,x87581),f335(f335(f86(a927),x87581),f335(f41(a927),x87582))))) % 186.01/186.02 [8988]P40(x89881,x89882)+~P40(x89881,f335(f335(f117(f934(f933(x89881,x89881),a922)),x89882),f315(x89881,f195(f934(f933(x89881,x89881),a922))))) % 186.01/186.02 [9114]E(f335(f335(f42(a1),f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x91141),x91141)),a104))),f335(f110(a1),f335(f335(f86(a1),x91142),x91142))),f335(f335(f42(a1),f335(f110(a1),x91141)),f335(f110(a1),x91142)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x91142))) % 186.01/186.02 [9208]~P39(x92081,x92082)+P1(f335(f335(f243(f934(f933(x92081,x92081),a922)),f335(f335(f297(x92081,x92081,x92081),x92082),x92082)),x92082)) % 186.01/186.02 [9234]E(f184(f928(x92341),f335(f335(f8(a922,a922,f928(x92341)),a330),f335(f335(f7(f928(x92341),f928(x92341),a922),a332),f120(x92341))),x92342),f186(x92341,f186(x92341,x92342)))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x92341),a927),f196(f928(x92341))),x92342))) % 186.01/186.02 [9237]E(f335(f335(f42(a1),f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x92371),x92371)),a104))),f335(f110(a1),f335(f335(f86(a1),x92372),x92372))),f335(f335(f42(a1),f335(f335(f86(a1),f335(f110(a1),x92371)),f84(a1))),f335(f110(a1),x92372)))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x92372))) % 186.01/186.02 [10072]P1(f335(a200,x100722))+E(f335(f335(f92(a1,a927),f335(f335(f23(a1),x100721),x100722)),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f2(a927))),a111)),f335(f335(f23(a927),f335(a111,x100721)),f335(a111,x100722))) % 186.01/186.02 [10080]E(f335(f335(f92(a1,a927),f335(f110(a1),f335(f335(f86(a1),x100801),f335(f85(a1),x100802)))),f335(f335(f18(a1,a927,a927),f335(f335(f7(a1,a927,f934(a927,a927)),f335(f335(f8(a922,f934(a927,f934(a927,a927)),a1),f103(a927)),a200)),f2(a927))),a111)),f335(f335(f23(a927),f335(f110(a927),x100801)),f335(f110(a927),x100802)))+P1(f335(f335(f244(a1),x100802),a89)) % 186.01/186.02 [10081]~P28(x100811,x100812)+P1(f335(f335(f243(f934(f933(x100811,x100811),a922)),f335(f335(f297(x100811,x100811,x100811),f335(f259(f934(f933(x100811,x100811),a922),f934(f933(x100811,x100811),a922)),x100812)),f335(f264(f934(f933(x100811,x100811),a922),f934(f933(x100811,x100811),a922)),x100812))),f335(f259(f934(f933(x100811,x100811),a922),f934(f933(x100811,x100811),a922)),x100812))) % 186.01/186.02 [10137]~E(f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,f934(a927,a922),a922),f337(a927)),x101371))),f335(f335(f7(a927,a927,a922),f244(a927)),f335(a119,x101372))))),f2(a927))+~P1(f335(f335(f337(a927),f2(a927)),x101371)) % 186.01/186.02 [10150]E(f307(a927,f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x101501,x101502),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x101502),x101501)) % 186.01/186.02 [10155]E(f308(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x101551,x101552),f195(f934(a927,a922)))+P1(f335(f335(f295(a927),x101551),x101552)) % 186.01/186.02 [10156]E(f305(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x101561,x101562),f195(f934(a927,a922)))+P1(f335(f335(f295(a927),x101561),x101562)) % 186.01/186.02 [10160]E(f308(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x101601,x101602),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x101602),x101601)) % 186.01/186.02 [10162]E(f305(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x101621,x101622),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x101622),x101621)) % 186.01/186.02 [10206]E(f51(a1,f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x102061),x102061)),a104)),f335(f110(a1),f335(f335(f86(a1),x102062),x102062))),f335(f335(f86(a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a1,f335(f110(a1),x102061),f335(f110(a1),x102062)))),f84(a1)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x102062))) % 186.01/186.02 [10215]E(f51(a1,f335(f110(a1),f335(f335(f23(a1),f335(f335(f86(a1),x102151),x102151)),a104)),f335(f110(a1),f335(f335(f86(a1),x102152),x102152))),f335(f335(f23(a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a1,f335(f335(f86(a1),f335(f110(a1),x102151)),f84(a1)),f335(f110(a1),x102152)))),f84(a1)))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x102152))) % 186.01/186.02 [10269]~P6(x102691)+E(f43(x102691,f335(f270(x102691),f335(f335(f8(f934(x102691,a922),a922,x102691),f94(x102691)),f335(f335(f8(f934(x102691,a922),f934(x102691,a922),x102691),f335(f18(x102691,a922,a922),f335(f335(f8(a922,f934(a922,a922),x102691),a338),f335(f335(f7(x102691,f934(x102691,a922),a922),f337(x102691)),x102692)))),f243(x102691))))),f44(x102691,x102692)) % 186.01/186.02 [10295]~P38(x102951,x102952)+P61(x102951,f335(f335(f7(x102951,f934(f933(x102951,x102951),a922),f934(x102951,a922)),f335(f335(f8(f934(x102951,f934(f934(f933(x102951,x102951),a922),a922)),f934(f934(f933(x102951,x102951),a922),f934(x102951,a922)),x102951),f7(x102951,f934(f933(x102951,x102951),a922),a922)),f335(f335(f8(f934(x102951,f933(x102951,x102951)),f934(x102951,f934(f934(f933(x102951,x102951),a922),a922)),x102951),f335(f8(f933(x102951,x102951),f934(f934(f933(x102951,x102951),a922),a922),x102951),f337(f933(x102951,x102951)))),f260(x102951,x102951)))),x102952)) % 186.01/186.02 [10296]~P9(x102961,f250(f934(x102961,a922)),x102962)+P8(x102961,f335(f335(f7(x102961,f934(f933(x102961,x102961),a922),f934(x102961,a922)),f335(f335(f8(f934(x102961,f934(f934(f933(x102961,x102961),a922),a922)),f934(f934(f933(x102961,x102961),a922),f934(x102961,a922)),x102961),f7(x102961,f934(f933(x102961,x102961),a922),a922)),f335(f335(f8(f934(x102961,f933(x102961,x102961)),f934(x102961,f934(f934(f933(x102961,x102961),a922),a922)),x102961),f335(f8(f933(x102961,x102961),f934(f934(f933(x102961,x102961),a922),a922),x102961),f337(f933(x102961,x102961)))),f260(x102961,x102961)))),x102962)) % 186.01/186.02 [10339]P38(x103391,x103392)+~P61(x103391,f335(f335(f7(x103391,f934(f933(x103391,x103391),a922),f934(x103391,a922)),f335(f335(f8(f934(x103391,f934(f934(f933(x103391,x103391),a922),a922)),f934(f934(f933(x103391,x103391),a922),f934(x103391,a922)),x103391),f7(x103391,f934(f933(x103391,x103391),a922),a922)),f335(f335(f8(f934(x103391,f933(x103391,x103391)),f934(x103391,f934(f934(f933(x103391,x103391),a922),a922)),x103391),f335(f8(f933(x103391,x103391),f934(f934(f933(x103391,x103391),a922),a922),x103391),f337(f933(x103391,x103391)))),f260(x103391,x103391)))),x103392)) % 186.01/186.02 [10340]P9(x103401,f250(f934(x103401,a922)),x103402)+~P8(x103401,f335(f335(f7(x103401,f934(f933(x103401,x103401),a922),f934(x103401,a922)),f335(f335(f8(f934(x103401,f934(f934(f933(x103401,x103401),a922),a922)),f934(f934(f933(x103401,x103401),a922),f934(x103401,a922)),x103401),f7(x103401,f934(f933(x103401,x103401),a922),a922)),f335(f335(f8(f934(x103401,f933(x103401,x103401)),f934(x103401,f934(f934(f933(x103401,x103401),a922),a922)),x103401),f335(f8(f933(x103401,x103401),f934(f934(f933(x103401,x103401),a922),a922),x103401),f337(f933(x103401,x103401)))),f260(x103401,x103401)))),x103402)) % 186.01/186.02 [7502]E(f335(f335(f86(a927),f335(f110(a927),f335(f335(f23(a1),x75021),a104))),x75022),f335(a119,f335(f335(f86(a927),f335(f110(a927),x75021)),x75022)))+P1(f335(a200,f335(f110(a1),x75021))) % 186.01/186.02 [7934]~P94(x79341)+E(f335(f335(f86(x79341),f335(f335(f86(x79341),f84(x79341)),f335(f110(x79341),x79342))),f335(f110(x79341),x79342)),f335(f110(x79341),f335(f335(f23(a1),f335(f335(f86(a1),x79342),x79342)),a104))) % 186.01/186.02 [8569]~P1(f335(f335(f243(a1),x85691),x85692))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x85691),x85691)),f335(f335(f23(a1),f335(f335(f86(a1),x85692),x85692)),a104))) % 186.01/186.02 [8571]~P1(f335(f335(f243(a1),x85711),x85712))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x85711),x85711)),f335(f335(f23(a1),f335(f335(f86(a1),x85712),x85712)),a104))) % 186.01/186.02 [8999]P1(f335(f335(f243(a1),x89991),x89992))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x89991),x89991)),f335(f335(f23(a1),f335(f335(f86(a1),x89992),x89992)),a104))) % 186.01/186.02 [9001]P1(f335(f335(f243(a1),x90011),x90012))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),x90011),x90011)),f335(f335(f23(a1),f335(f335(f86(a1),x90012),x90012)),a104))) % 186.01/186.02 [9293]~P1(f335(f335(f243(a1),x92931),x92932))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x92931),x92931)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x92932),x92932)),a104))) % 186.01/186.02 [9295]~P1(f335(f335(f244(a1),x92951),x92952))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x92951),x92951)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x92952),x92952)),a104))) % 186.01/186.02 [9560]P1(f335(f335(f243(a1),x95601),x95602))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),x95601),x95601)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x95602),x95602)),a104))) % 186.01/186.02 [9562]P1(f335(f335(f244(a1),x95621),x95622))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),x95621),x95621)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),x95622),x95622)),a104))) % 186.01/186.02 [9595]~P1(f335(f67(x95951),x95952))+P1(f335(f67(f934(x95951,a922)),f335(f270(f934(x95951,a922)),f335(f335(f7(f934(x95951,a922),f934(x95951,a922),a922),f243(f934(x95951,a922))),x95952)))) % 186.01/186.02 [9644]~E(f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),x96441),f195(f934(f933(a927,a927),a922)))),f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),x96442),f195(f934(f933(a927,a927),a922)))))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x96441),x96442)),a115)) % 186.01/186.02 [9730]E(f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),x97301),f195(f934(f933(a927,a927),a922)))),f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),x97302),f195(f934(f933(a927,a927),a922)))))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x97301),x97302)),a115)) % 186.01/186.02 [9766]P1(f335(f335(f243(a1),f2(a1)),f662(x97661,x97662)))+E(f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97661)),f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97662))) % 186.01/186.02 [10277]~P6(x102771)+E(f44(x102771,f335(f270(x102771),f335(f335(f8(f934(x102771,a922),a922,x102771),f94(x102771)),f335(f335(f8(f934(x102771,a922),f934(x102771,a922),x102771),f335(f18(x102771,a922,a922),f335(f335(f8(a922,f934(a922,a922),x102771),a338),f335(f335(f7(x102771,f934(x102771,a922),a922),f337(x102771)),x102772)))),f335(f7(x102771,x102771,a922),f243(x102771)))))),f43(x102771,x102772)) % 186.01/186.02 [10301]P1(f335(f335(f337(a927),f2(a927)),x103011))+E(f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),a927),f337(a927)),a119)),x103011))),f335(f335(f7(a927,a927,a922),f244(a927)),x103012)))),f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,f934(a927,a922),a922),f337(a927)),x103011))),f335(f335(f7(a927,a927,a922),f244(a927)),f335(a119,x103012)))))) % 186.01/186.02 [7805]~P94(x78051)+E(f335(f335(f87(x78051),x78052),f335(f110(x78051),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),x78052) % 186.01/186.02 [8061]~P94(x80611)+E(f335(f335(f86(x80611),f335(f110(x80611),x80612)),f84(x80611)),f335(f110(x80611),f335(f335(f86(a1),x80612),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))) % 186.01/186.02 [8205]P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x82052)))+E(f335(f335(f252(a1),x82051),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x82052),x82052)),a104))),f84(a1)) % 186.01/186.02 [9620]~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x96202)))+E(f335(f335(f252(a1),x96201),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x96202),x96202)),a104))),f335(f335(f92(a1,a1),f335(f335(f252(a1),x96201),f335(f110(a927),x96202))),f335(f335(f18(a1,a1,a1),f335(f335(f8(a1,f934(a1,a1),a1),f87(a1)),f335(f87(a1),x96201))),f5(a1)))) % 186.01/186.02 [9990]~P1(f335(f335(f243(a927),f673(x99902,x99901)),f335(x99901,f673(x99902,x99901))))+P1(f335(f67(a927),f335(f270(a927),f335(f335(f7(a927,a927,a922),f335(f335(f8(a927,f934(a927,a922),a927),f243(a927)),x99901)),x99902)))) % 186.01/186.02 [10127]~P1(f335(f335(f243(a927),f335(f110(a927),x101271)),f335(a119,x101272)))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x101271),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),f243(a927)),a111)),x101272)))) % 186.01/186.02 [10128]~P1(f335(f335(f244(a927),f335(f110(a927),x101281)),f335(a119,x101282)))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x101281),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),f244(a927)),a111)),x101282)))) % 186.01/186.02 [10190]P1(f335(f335(f243(a927),f335(f110(a927),x101901)),f335(a119,x101902)))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x101901),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),f243(a927)),a111)),x101902)))) % 186.01/186.02 [10191]P1(f335(f335(f244(a927),f335(f110(a927),x101911)),f335(a119,x101912)))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x101911),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),f244(a927)),a111)),x101912)))) % 186.01/186.02 [10221]~P1(f335(f335(f243(a927),f335(a119,x102212)),f335(f110(a927),x102211)))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102211),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f8(a927,a922,a1),f335(f243(a927),x102212)),a111))))) % 186.01/186.02 [10222]~P1(f335(f335(f244(a927),f335(a119,x102222)),f335(f110(a927),x102221)))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102221),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f8(a927,a922,a1),f335(f244(a927),x102222)),a111))))) % 186.01/186.02 [10267]P1(f335(f335(f243(a927),f335(a119,x102671)),f335(f110(a927),x102672)))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102672),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f8(a927,a922,a1),f335(f243(a927),x102671)),a111))))) % 186.01/186.02 [10268]P1(f335(f335(f244(a927),f335(a119,x102681)),f335(f110(a927),x102682)))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102682),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f8(a927,a922,a1),f335(f244(a927),x102681)),a111))))) % 186.01/186.02 [10349]~P1(f335(f335(f337(a927),f2(a927)),x103491))+E(f335(a119,f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,f934(a927,a922),a922),f335(f335(f8(a927,f934(f934(a927,a922),a922),a927),f337(a927)),a119)),x103491))),f335(f335(f7(a927,a927,a922),f244(a927)),x103492))))),f335(f41(a927),f335(f270(a927),f335(f335(f18(a927,a922,a922),f335(f335(f8(a922,f934(a922,a922),a927),a333),f335(f335(f7(a927,f934(a927,a922),a922),f337(a927)),x103491))),f335(f335(f7(a927,a927,a922),f244(a927)),f335(a119,x103492)))))) % 186.01/186.02 [8741]~P94(x87411)+E(f335(f335(f87(x87411),f335(f110(x87411),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),x87412),x87412) % 186.01/186.02 [8802]~P94(x88021)+E(f335(f335(f86(x88021),f84(x88021)),f335(f110(x88021),x88022)),f335(f110(x88021),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),x88022))) % 186.01/186.02 [8864]~P94(x88641)+E(f335(f335(f23(x88641),f335(f110(x88641),x88642)),f84(x88641)),f335(f110(x88641),f335(f335(f86(a1),x88642),f335(f85(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [9018]~P1(f335(f335(f244(a927),f335(f110(a927),a89)),x90182))+E(f335(f335(f23(a927),x90181),f335(f335(f23(a927),x90182),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f23(a927),f335(a119,x90181)),x90182)) % 186.01/186.02 [9662]~P118(x96621)+E(f335(f335(f87(x96621),x96622),x96622),f335(f335(f252(x96621),x96622),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [9663]~P81(x96631)+E(f335(f335(f252(x96631),x96632),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f87(x96631),x96632),x96632)) % 186.01/186.02 [9665]~P94(x96651)+E(f335(f335(f87(x96651),x96652),f335(f110(x96651),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f86(x96651),x96652),x96652)) % 186.01/186.02 [9906]~P140(x99061)+E(f335(f335(f252(x99061),f335(f85(x99061),x99062)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f252(x99061),x99062),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [9907]~P113(x99071)+E(f335(f335(f252(x99071),f335(f81(x99071),x99072)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f252(x99071),x99072),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [9903]~P94(x99031)+E(f335(f335(f87(x99031),f335(f110(x99031),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x99032),f335(f335(f86(x99031),x99032),x99032)) % 186.01/186.02 [10023]~P113(x100231)+E(f335(f81(x100231),f335(f335(f252(x100231),x100232),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x100231),x100232),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [10088]~P113(x100881)+P1(f335(f335(f243(x100881),f2(x100881)),f335(f335(f252(x100881),x100882),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.02 [10258]~E(f335(a119,x102582),f335(f110(a927),x102581))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102581),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),a332),a111)),x102582))))) % 186.01/186.02 [10259]~E(f335(f110(a927),x102591),f335(a119,x102592))+P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x102591),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),a332),a111)),x102592))))) % 186.01/186.02 [10304]E(f335(a119,x103041),f335(f110(a927),x103042))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x103042),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),a332),a111)),x103041))))) % 186.01/186.02 [10305]E(f335(f110(a927),x103051),f335(a119,x103052))+~P1(f335(f335(f92(a1,a922),f335(f110(a1),f335(f335(f86(a1),x103051),a104))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a338),f335(f335(f8(a922,a922,a1),a330),a200))),f335(f335(f7(a1,a927,a922),f335(f335(f8(a927,f934(a927,a922),a1),a332),a111)),x103052))))) % 186.01/186.02 [10350]~P16(x103501,x103502)+P1(f335(f335(f337(f934(x103501,a922)),f835(x103502,x103501)),f335(f335(f8(f934(x103501,a922),a922,f934(x103501,a922)),f93(x103501)),f335(f335(f8(f934(x103501,a922),f934(x103501,a922),f934(x103501,a922)),f335(f18(x103501,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103501),a333),f335(f335(f18(x103501,x103501,a922),x103502),f5(x103501))))),f335(f335(f7(f934(x103501,a922),f934(x103501,f934(x103501,a922)),f934(x103501,a922)),f335(f335(f8(f934(f934(x103501,a922),a922),f934(f934(x103501,f934(x103501,a922)),f934(x103501,a922)),f934(x103501,a922)),f8(f934(x103501,a922),a922,x103501)),a332)),x103502))))) % 186.01/186.02 [10086]~P94(x100861)+E(f335(f335(f252(x100861),f335(f110(x100861),a104)),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x100862)),f84(x100861)) % 186.01/186.02 [10087]~P140(x100871)+E(f335(f335(f252(x100871),f335(f85(x100871),f84(x100871))),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x100872)),f84(x100871)) % 186.01/186.02 [10090]~P81(x100901)+E(f335(f335(f252(x100901),x100902),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),a104))),f335(f335(f87(x100901),f335(f335(f87(x100901),x100902),x100902)),x100902)) % 186.01/186.02 [10284]~P1(f335(f335(f243(a1),f2(a1)),x102842))+E(f51(a1,f335(f335(f86(a1),f84(a1)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x102841)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x102842)),f335(f335(f86(a1),f84(a1)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a1,x102841,x102842)))) % 186.01/186.02 [10307]~P1(f335(f335(f243(a1),f2(a1)),x103072))+E(f335(f335(f42(a1),f335(f335(f86(a1),f84(a1)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103071))),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103072)),f335(f335(f42(a1),x103071),x103072)) % 186.01/186.02 [10309]~P1(f335(f335(f243(a1),x103092),f2(a1)))+E(f335(f335(f42(a1),f335(f335(f86(a1),f84(a1)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103091))),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103092)),f335(f335(f42(a1),f335(f335(f86(a1),x103091),f84(a1))),x103092)) % 186.01/186.02 [10310]~P1(f335(f335(f243(a1),x103102),f2(a1)))+E(f51(a1,f335(f335(f86(a1),f84(a1)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103101)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103102)),f335(f335(f23(a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f51(a1,f335(f335(f86(a1),x103101),f84(a1)),x103102))),f84(a1))) % 186.01/186.02 [10181]~P94(x101811)+E(f335(f335(f252(x101811),f335(f110(x101811),a104)),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101812))),f335(f110(x101811),a104)) % 186.01/186.02 [10183]~P140(x101831)+E(f335(f335(f252(x101831),f335(f85(x101831),f84(x101831))),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101832))),f335(f85(x101831),f84(x101831))) % 186.01/186.02 [5183]P39(x51831,x51832)+~P9(x51831,x51833,x51832) % 186.01/186.02 [5185]P53(x51851,x51852)+~P9(x51851,x51853,x51852) % 186.01/186.02 [5357]~P9(x53571,x53572,x53573)+P54(x53571,x53572,x53573) % 186.01/186.02 [8271]~E(x82712,x82713)+P35(x82711,x82711,a332,x82712,x82713) % 186.01/186.02 [8815]E(x88151,x88152)+~P35(x88153,x88153,a332,x88151,x88152) % 186.01/186.02 [4991]E(f176(x49911,x49912,x49913),f120(x49911))+~E(x49912,f2(a927)) % 186.01/186.02 [5159]~E(f176(x51592,x51591,x51593),f120(x51592))+E(x51591,f2(a927)) % 186.01/186.02 [5362]~P38(x53621,x53623)+P38(x53621,f329(x53621,x53622,x53623)) % 186.01/186.02 [5471]~P30(x54711,x54712,x54713)+P32(a1,x54711,f185(x54712,x54713)) % 186.01/186.02 [5543]P30(x55431,x55432,x55433)+~P32(a1,x55431,f185(x55432,x55433)) % 186.01/186.02 [5613]~P9(x56131,x56132,x56133)+P9(f928(x56131),f168(x56131,x56132),f165(x56131,x56133)) % 186.01/186.02 [5614]~P54(x56141,x56142,x56143)+P54(f928(x56141),f168(x56141,x56142),f165(x56141,x56143)) % 186.01/186.02 [5726]P57(x57261,x57262,x57263)+~E(f843(x57263,x57262,x57261),f844(x57263,x57262,x57261)) % 186.01/186.02 [5727]P56(x57271,x57272,x57273)+~E(f600(x57273,x57272,x57271),f601(x57273,x57272,x57271)) % 186.01/186.02 [8277]~E(x82772,x82773)+P27(x82771,x82771,f25(x82771),x82772,x82773) % 186.01/186.02 [8823]E(x88231,x88232)+~P27(x88233,x88233,f25(x88233),x88231,x88232) % 186.01/186.02 [4946]~E(f335(f175(x49462),x49461),x49463)+E(x49461,f335(f175(x49462),x49463)) % 186.01/186.02 [4947]~E(x49472,f335(f175(x49471),x49473))+E(f335(f175(x49471),x49472),x49473) % 186.01/186.02 [4997]E(x49971,x49972)+~E(f335(f175(x49973),x49971),f335(f175(x49973),x49972)) % 186.01/186.02 [5209]~P8(x52093,x52091)+P1(f335(f335(x52091,x52092),x52092)) % 186.01/186.02 [5210]~P49(x52103,x52101)+P1(f335(f335(x52101,x52102),x52102)) % 186.01/186.02 [5212]~P61(x52121,x52122)+P1(f335(f323(x52121,x52122),x52123)) % 186.01/186.02 [5277]~P38(x52771,x52772)+P38(f928(x52771),f335(f150(x52771,x52772),x52773)) % 186.01/186.02 [5282]~P1(f335(x52822,x52823))+~E(f335(f270(x52821),x52822),f195(f934(x52821,a922))) % 186.01/186.02 [5283]~P1(f335(x52832,x52833))+~E(f195(f934(x52831,a922)),f335(f270(x52831),x52832)) % 186.01/186.02 [5295]E(x52951,f2(a927))+E(f151(x52952,f176(x52952,x52951,x52953)),x52953) % 186.01/186.02 [5314]~P1(f335(x53141,x53143))+P1(f335(x53141,f96(x53142,x53141))) % 186.01/186.02 [5315]~P1(f335(x53151,x53153))+P1(f335(x53151,f760(x53151,x53152))) % 186.01/186.02 [5327]E(x53271,f2(a927))+E(f335(f148(x53272),f176(x53272,x53271,x53273)),x53273) % 186.01/186.02 [5433]~E(x54332,x54333)+P1(f335(f335(f337(x54331),x54332),f335(a332,x54333))) % 186.01/186.02 [5448]~E(x54482,f2(a927))+E(f335(f179(x54481),f176(x54481,x54482,x54483)),f195(f934(x54481,a922))) % 186.01/186.02 [5493]E(f335(f175(x54931),x54932),f335(f335(f158(x54931),x54933),f120(x54931)))+~E(x54932,f335(f335(f158(x54931),x54933),f120(x54931))) % 186.01/186.02 [5494]~E(x54943,f335(f335(f158(x54941),x54942),f120(x54941)))+E(f335(f335(f158(x54941),x54942),f120(x54941)),f335(f175(x54941),x54943)) % 186.01/186.02 [5539]~P34(x55391,x55392,x55393)+P34(x55391,x55392,f335(f175(x55391),x55393)) % 186.01/186.02 [5540]~P32(x55401,x55402,x55403)+P32(x55401,x55402,f335(f175(x55401),x55403)) % 186.01/186.02 [5544]E(f335(f41(x55441),f400(x55442,x55443,x55441)),x55442)+~E(f335(f41(x55441),x55443),f335(a119,x55442)) % 186.01/186.02 [5551]~P38(x55511,x55513)+P1(f335(f335(f337(x55511),x55512),f324(x55511,x55513))) % 186.01/186.02 [5555]~E(f335(f175(x55552),x55551),f335(f335(f158(x55552),x55553),f120(x55552)))+E(x55551,f335(f335(f158(x55552),x55553),f120(x55552))) % 186.01/186.02 [5556]~E(f335(f335(f158(x55562),x55563),f120(x55562)),f335(f175(x55562),x55561))+E(x55561,f335(f335(f158(x55562),x55563),f120(x55562))) % 186.01/186.02 [5579]E(f91(f933(a927,a927),f54(x55791,x55792)),x55793)+~P1(f335(f54(x55791,x55792),x55793)) % 186.01/186.02 [5617]P34(x56171,x56172,x56173)+~P34(x56171,x56172,f335(f175(x56171),x56173)) % 186.01/186.02 [5618]P32(x56181,x56182,x56183)+~P32(x56181,x56182,f335(f175(x56181),x56183)) % 186.01/186.02 [5656]P1(f335(f335(x56561,x56562),x56562))+~P1(f335(f278(x56563,x56561),x56562)) % 186.01/186.02 [5657]~P1(f335(f335(x56572,x56573),x56573))+P1(f335(f278(x56571,x56572),x56573)) % 186.01/186.02 [5679]~E(x56792,f120(x56791))+P1(f335(f335(f337(f928(x56791)),x56792),f168(x56791,x56793))) % 186.01/186.02 [5689]~P57(x56891,x56892,x56893)+P57(x56891,x56892,f335(f294(x56891,x56891),x56893)) % 186.01/186.02 [5690]~P54(x56901,x56902,x56903)+P54(x56901,x56902,f335(f294(x56901,x56901),x56903)) % 186.01/186.02 [5707]~P63(x57071)+E(f51(x57071,f51(x57071,x57072,x57073),x57073),f51(x57071,x57072,x57073)) % 186.01/186.02 [5808]E(x58081,x58082)+~P1(f335(f335(f337(x58083),x58081),f335(a332,x58082))) % 186.01/186.02 [5854]~P146(x58541)+E(f197(x58541,x58542,f2(a927),x58543),x58543) % 186.01/186.02 [5876]P57(x58761,x58762,x58763)+~P57(x58761,x58762,f335(f294(x58761,x58761),x58763)) % 186.01/186.02 [5877]P54(x58771,x58772,x58773)+~P54(x58771,x58772,f335(f294(x58771,x58771),x58773)) % 186.01/186.02 [5881]~P109(x58812)+E(f157(x58811,x58812,x58813,f120(x58811)),f120(x58811)) % 186.01/186.02 [5893]E(f177(x58931,x58932,f159(x58931,x58933)),f159(x58931,f177(x58931,x58932,x58933)))+~P1(f335(f144(x58931),x58933)) % 186.01/186.02 [5992]~P1(f335(f335(x59923,x59922),x59922))+P1(f335(f335(f337(x59921),x59922),f278(x59921,x59923))) % 186.01/186.02 [5994]E(f335(f143(x59941,x59942),x59943),f120(x59941))+P1(f335(x59942,f696(x59943,x59942,x59941))) % 186.01/186.02 [6053]E(f74(x60531,x60532,x60533),x60532)+P1(f335(x60533,f761(x60532,x60531,x60533))) % 186.01/186.02 [6145]~P1(f335(f144(x61451),x61452))+P1(f335(f144(x61451),f183(x61451,x61452,x61453))) % 186.01/186.02 [6146]~P1(f335(f144(x61461),x61463))+P1(f335(f144(x61461),f177(x61461,x61462,x61463))) % 186.01/186.02 [6147]~P1(f335(f144(x61471),x61473))+P1(f335(f144(x61471),f184(x61471,x61472,x61473))) % 186.01/186.02 [6148]~P1(f335(f144(x61481),x61483))+P1(f335(f144(x61481),f147(x61481,x61482,x61483))) % 186.01/186.02 [6149]~P147(x61491,x61493,x61492)+P1(f335(x61491,f51(a1,x61492,x61493))) % 186.01/186.02 [6165]~P34(x61653,x61651,x61652)+P1(f335(x61651,f773(x61652,x61651,x61653))) % 186.01/186.02 [6166]~P36(x61663,x61661,x61662)+P1(f335(x61661,f780(x61662,x61661,x61663))) % 186.01/186.02 [6167]~P36(x61673,x61671,x61672)+P1(f335(x61671,f793(x61672,x61671,x61673))) % 186.01/186.02 [6168]~P34(x61683,x61681,x61682)+P1(f335(x61681,f819(x61681,x61682,x61683))) % 186.01/186.02 [6169]~P34(x61693,x61691,x61692)+P1(f335(x61691,f821(x61692,x61691,x61693))) % 186.01/186.02 [6173]P1(f335(f335(x61731,x61732),x61732))+~P1(f335(f335(f337(x61733),x61732),f278(x61733,x61731))) % 186.01/186.02 [6188]E(f335(f143(x61881,x61882),x61883),f184(x61881,x61882,x61883))+P1(f335(x61882,f745(x61883,x61882,x61881))) % 186.01/186.02 [6228]~P1(f335(f144(x62281),x62283))+P1(f335(f144(f928(x62281)),f61(x62281,x62282,x62283))) % 186.01/186.02 [6262]~P110(x62621)+E(f335(f335(f108(f934(x62621,a922)),f335(f290(x62621),x62622)),f311(x62621,x62622,x62623)),f195(f934(x62621,a922))) % 186.01/186.02 [6263]~P110(x62631)+E(f335(f335(f108(f934(x62631,a922)),f335(f309(x62631),x62632)),f314(x62631,x62632,x62633)),f195(f934(x62631,a922))) % 186.01/186.02 [6264]~P110(x62641)+E(f335(f335(f108(f934(x62641,a922)),f335(f309(x62641),x62642)),f313(x62641,x62642,x62643)),f195(f934(x62641,a922))) % 186.01/186.02 [6492]E(f335(f143(x64921,x64922),x64923),x64923)+~P1(f335(x64922,f697(x64923,x64922,x64921))) % 186.01/186.02 [6494]E(f335(f335(f317(x64941),f406(x64942,x64943,x64941)),f400(x64942,x64943,x64941)),x64943)+~E(f335(f41(x64941),x64943),f335(a119,x64942)) % 186.01/186.02 [6509]P147(x65091,x65092,x65093)+~P1(f335(x65091,f51(a1,x65093,x65092))) % 186.01/186.02 [6558]P32(x65581,x65582,x65583)+~P1(f335(x65582,f781(x65583,x65582,x65581))) % 186.01/186.02 [6559]P32(x65591,x65592,x65593)+~P1(f335(x65592,f791(x65592,x65593,x65591))) % 186.01/186.02 [6560]P32(x65601,x65602,x65603)+~P1(f335(x65602,f792(x65603,x65602,x65601))) % 186.01/186.02 [6561]P30(x65611,x65612,x65613)+~P1(f335(x65611,f805(x65613,x65612,x65611))) % 186.01/186.02 [6562]P31(x65621,x65622,x65623)+~P1(f335(x65621,f848(x65623,x65622,x65621))) % 186.01/186.02 [6564]E(f184(x65641,x65642,x65643),x65643)+~P1(f335(x65642,f740(x65643,x65642,x65641))) % 186.01/186.02 [6642]~P1(f335(x66422,f577(x66423,x66422,x66421)))+P1(f335(f256(x66421,x66422),x66423)) % 186.01/186.02 [6643]~P1(f335(x66432,f698(x66433,x66432,x66431)))+P1(f335(f167(x66431,x66432),x66433)) % 186.01/186.02 [6891]~P1(f335(f323(x68911,x68912),f453(x68913,x68912,x68911)))+P1(f335(f323(x68911,x68912),x68913)) % 186.01/186.02 [6892]~P1(f335(f323(x68921,x68922),f461(x68923,x68922,x68921)))+P1(f335(f323(x68921,x68922),x68923)) % 186.01/186.02 [7503]~P63(x75031)+E(f335(f335(f86(x75031),f335(f335(f87(x75031),x75032),f335(f335(f42(x75031),x75033),x75032))),f51(x75031,x75033,x75032)),x75033) % 186.01/186.02 [7532]P30(x75321,x75322,x75323)+P1(f335(f335(f337(a1),f805(x75323,x75322,x75321)),f311(a1,x75322,x75323))) % 186.01/186.02 [7955]E(f335(f335(f260(x79551,x79551),f893(x79552,x79553,x79551)),f893(x79552,x79553,x79551)),x79553)+~P1(f335(f335(f337(f933(x79551,x79551)),x79553),f271(x79551,x79552))) % 186.01/186.02 [8069]~P1(f335(f335(f337(x80691),f558(x80693,x80692,x80691)),f324(x80691,x80693)))+P1(f335(f335(f337(x80691),x80692),f324(x80691,x80693))) % 186.01/186.02 [8070]~P1(f335(f335(f337(x80701),f603(x80703,x80702,x80701)),f324(x80701,x80703)))+P1(f335(f335(f337(x80701),x80702),f324(x80701,x80703))) % 186.01/186.02 [8071]~P1(f335(f335(f337(x80711),f606(x80713,x80712,x80711)),f324(x80711,x80713)))+P1(f335(f335(f337(x80711),x80712),f324(x80711,x80713))) % 186.01/186.02 [8163]P34(a1,x81631,f185(x81632,x81633))+P30(f335(f78(a922,a922,a1,a330),x81631),x81632,x81633) % 186.01/186.02 [8252]~P63(x82521)+E(f335(f335(f86(x82521),f335(f335(f87(x82521),f335(f335(f42(x82521),x82522),x82523)),x82523)),f51(x82521,x82522,x82523)),x82522) % 186.01/186.02 [8298]~E(f335(f41(x82981),x82982),f335(a119,x82983))+~P1(f335(f335(f337(x82981),f406(x82983,x82982,x82981)),f400(x82983,x82982,x82981))) % 186.01/186.02 [8733]~P34(a1,x87331,f185(x87332,x87333))+~P30(f335(f78(a922,a922,a1,a330),x87331),x87332,x87333) % 186.01/186.02 [8920]P1(f335(f335(f243(f934(f933(x89201,x89201),a922)),f315(x89201,x89202)),f315(x89201,x89203)))+~P1(f335(f335(f243(f934(f933(x89201,x89201),a922)),x89202),f315(x89201,x89203))) % 186.01/186.02 [9204]E(x92041,f120(x92042))+~P1(f335(f335(f337(f933(f928(x92042),f928(x92042))),f335(f335(f260(f928(x92042),f928(x92042)),x92041),f120(x92042))),f165(x92042,x92043))) % 186.01/186.02 [9228]E(x92281,f120(x92282))+~P1(f335(f335(f337(f933(f928(x92282),f928(x92282))),f335(f335(f260(f928(x92282),f928(x92282)),f120(x92282)),x92281)),f165(x92282,x92283))) % 186.01/186.02 [9354]E(f335(f335(f158(x93541),f714(x93542,x93543,x93541)),f715(x93542,x93543,x93541)),x93543)+~P1(f335(f335(f337(f933(f928(x93541),f928(x93541))),f335(f335(f260(f928(x93541),f928(x93541)),f120(x93541)),x93543)),f154(x93541,x93542))) % 186.01/186.02 [9588]~P126(x95881)+~P1(f335(f335(f244(x95881),f335(f335(f86(x95881),f335(f335(f87(x95881),x95882),x95882)),f335(f335(f87(x95881),x95883),x95883))),f2(x95881))) % 186.01/186.02 [9637]P1(f335(f67(x96371),x96372))+~P1(f335(f335(f337(f933(f934(x96371,a922),f934(x96371,a922))),f335(f335(f260(f934(x96371,a922),f934(x96371,a922)),x96373),x96372)),f322(x96371))) % 186.01/186.02 [9932]~P47(x99321,x99322,x99323)+P1(f335(f335(f243(a1),f335(f335(f78(f933(a1,a1),a1,x99321,f259(a1,a1)),f221(x99321)),f239(x99321,x99322,f236(x99321,x99323)))),f2(a1))) % 186.01/186.02 [9933]~P48(x99331,x99332,x99333)+P1(f335(f335(f244(a1),f335(f335(f78(f933(a1,a1),a1,x99331,f259(a1,a1)),f221(x99331)),f239(x99331,x99332,f236(x99331,x99333)))),f2(a1))) % 186.01/186.02 [10054]P48(x100541,x100542,x100543)+~P1(f335(f335(f244(a1),f335(f335(f78(f933(a1,a1),a1,x100541,f259(a1,a1)),f221(x100541)),f239(x100541,x100542,f236(x100541,x100543)))),f2(a1))) % 186.01/186.02 [10055]P47(x100551,x100552,x100553)+~P1(f335(f335(f243(a1),f335(f335(f78(f933(a1,a1),a1,x100551,f259(a1,a1)),f221(x100551)),f239(x100551,x100552,f236(x100551,x100553)))),f2(a1))) % 186.01/186.02 [10411]~P113(x104111)+~P1(f335(f335(f244(x104111),f335(f335(f86(x104111),f335(f335(f252(x104111),x104112),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x104111),x104113),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f2(x104111))) % 186.01/186.02 [4976]~E(x49763,f120(x49761))+E(f335(f335(f141(x49761),x49762),x49763),x49762) % 186.01/186.02 [4977]~E(x49772,f120(x49771))+E(f335(f335(f141(x49771),x49772),x49773),x49773) % 186.01/186.02 [4983]~E(x49832,f2(a927))+E(f335(f335(f182(x49831),x49832),x49833),f120(x49831)) % 186.01/186.02 [4992]~E(x49923,f120(x49921))+E(f335(f335(f182(x49921),x49922),x49923),f120(x49921)) % 186.01/186.02 [5031]~E(x50311,x50313)+E(x50311,f335(f335(f141(x50312),f120(x50312)),x50313)) % 186.01/186.02 [5122]~P2(x51222)+E(f335(f195(f934(x51221,x51222)),x51223),f195(x51222)) % 186.01/186.02 [5123]~P111(x51232)+E(f335(f250(f934(x51231,x51232)),x51233),f250(x51232)) % 186.01/186.02 [5141]E(x51411,f120(x51412))+~E(f335(f335(f141(x51412),x51413),x51411),x51413) % 186.01/186.02 [5142]E(x51421,f120(x51422))+~E(f335(f335(f141(x51422),x51421),x51423),x51423) % 186.01/186.02 [5150]E(x51501,f120(x51502))+~E(f335(f335(f141(x51502),x51503),x51501),f120(x51502)) % 186.01/186.02 [5151]E(x51511,f120(x51512))+~E(f335(f335(f141(x51512),x51511),x51513),f120(x51512)) % 186.01/186.02 [5176]~E(x51762,f2(a927))+E(f335(f335(f87(a927),x51761),x51762),f335(f335(f87(a927),x51763),x51762)) % 186.01/186.02 [5178]~E(x51781,f2(a927))+E(f335(f335(f87(a927),x51781),x51782),f335(f335(f87(a927),x51781),x51783)) % 186.01/186.02 [5236]~P118(x52361)+E(f335(f335(f87(x52361),x52362),x52363),f335(f335(f87(x52361),x52363),x52362)) % 186.01/186.02 [5238]~P97(x52381)+E(f335(f335(f108(x52381),x52382),x52383),f335(f335(f108(x52381),x52383),x52382)) % 186.01/186.02 [5239]~P98(x52391)+E(f335(f335(f108(x52391),x52392),x52393),f335(f335(f108(x52391),x52393),x52392)) % 186.01/186.02 [5240]~P98(x52401)+E(f335(f335(f117(x52401),x52402),x52403),f335(f335(f117(x52401),x52403),x52402)) % 186.01/186.02 [5242]~P103(x52421)+E(f335(f335(f117(x52421),x52422),x52423),f335(f335(f117(x52421),x52423),x52422)) % 186.01/186.02 [5243]~P118(x52431)+E(f335(f335(f86(x52431),x52432),x52433),f335(f335(f86(x52431),x52433),x52432)) % 186.01/186.02 [5245]~P109(x52451)+E(f335(f335(f241(x52451),x52452),x52453),f335(f335(f241(x52451),x52453),x52452)) % 186.01/186.02 [5247]~P109(x52471)+E(f335(f335(f242(x52471),x52472),x52473),f335(f335(f242(x52471),x52473),x52472)) % 186.01/186.02 [5309]E(f51(a927,x53091,x53092),f2(a927))+~E(x53091,f335(f335(f87(a927),x53092),x53093)) % 186.01/186.02 [5310]E(f51(a1,x53101,x53102),f2(a1))+~E(x53101,f335(f335(f87(a1),x53102),x53103)) % 186.01/186.02 [5374]E(x53741,x53742)+~E(f335(f335(f86(a927),x53743),x53741),f335(f335(f86(a927),x53743),x53742)) % 186.01/186.02 [5375]E(x53751,x53752)+~E(f335(f335(f86(a927),x53751),x53753),f335(f335(f86(a927),x53752),x53753)) % 186.01/186.02 [5385]~P83(x53851)+E(f335(f335(f108(x53851),x53852),f335(f85(x53851),x53853)),f335(f335(f23(x53851),x53852),x53853)) % 186.01/186.02 [5386]~P4(x53861)+E(f335(f335(f86(x53861),x53862),f335(f85(x53861),x53863)),f335(f335(f23(x53861),x53862),x53863)) % 186.01/186.02 [5387]~P5(x53871)+E(f335(f335(f86(x53871),x53872),f335(f85(x53871),x53873)),f335(f335(f23(x53871),x53872),x53873)) % 186.01/186.02 [5388]~P116(x53881)+E(f335(f335(f86(x53881),x53882),f335(f85(x53881),x53883)),f335(f335(f23(x53881),x53882),x53883)) % 186.01/186.02 [5389]~P4(x53891)+E(f335(f335(f23(x53891),x53892),f335(f85(x53891),x53893)),f335(f335(f86(x53891),x53892),x53893)) % 186.01/186.02 [5427]~P1(f335(x54273,x54272))+P1(f335(f335(f337(x54271),x54272),x54273)) % 186.01/186.02 [5429]~P76(x54292)+E(f335(f335(f6(x54291,x54292),x54293),f195(f934(x54291,a922))),f2(x54292)) % 186.01/186.02 [5431]~P72(x54312)+E(f335(f335(f9(x54311,x54312),x54313),f195(f934(x54311,a922))),f84(x54312)) % 186.01/186.02 [5483]~E(x54832,f335(f335(f86(a927),x54831),x54833))+P1(f335(f335(f243(a927),x54831),x54832)) % 186.01/186.02 [5486]~E(x54862,f195(f934(x54861,a922)))+E(f335(f335(f66(x54861),x54862),x54863),f195(f934(f934(x54861,a922),a922))) % 186.01/186.02 [5487]~E(x54872,f195(f934(x54871,a922)))+E(f195(f934(f934(x54871,a922),a922)),f335(f335(f66(x54871),x54872),x54873)) % 186.01/186.02 [5559]~E(f335(f292(x55592,x55593),x55591),f195(f934(x55593,a922)))+E(x55591,f195(f934(f933(x55592,x55593),a922))) % 186.01/186.02 [5560]~E(f335(f272(x55602,x55603),x55601),f195(f934(x55602,a922)))+E(x55601,f195(f934(f933(x55602,x55603),a922))) % 186.01/186.02 [5592]E(f335(f292(x55921,x55922),x55923),f195(f934(x55922,a922)))+~E(x55923,f195(f934(f933(x55921,x55922),a922))) % 186.01/186.02 [5593]E(f335(f272(x55931,x55932),x55933),f195(f934(x55931,a922)))+~E(x55933,f195(f934(f933(x55931,x55932),a922))) % 186.01/186.02 [5596]E(f282(x55961,x55962,x55963),f335(f335(f23(a106),x55962),x55963))+P1(f335(f335(f244(a106),x55962),x55963)) % 186.01/186.02 [5611]P1(f335(x56111,x56112))+~P1(f335(f335(f337(x56113),x56112),x56111)) % 186.01/186.02 [5649]E(x56491,x56492)+~E(f335(f85(f934(x56493,a922)),x56491),f335(f85(f934(x56493,a922)),x56492)) % 186.01/186.02 [5660]~E(x56601,f195(f934(x56602,a922)))+~P1(f335(f335(f337(x56602),x56603),x56601)) % 186.01/186.02 [5691]~E(x56912,f335(f335(f86(a1),x56911),f335(f107(a1),x56913)))+P1(f335(f335(f243(a1),x56911),x56912)) % 186.01/186.02 [5705]E(f335(f335(f317(x57051),x57052),x57053),x57053)+~P1(f335(f335(f337(x57051),x57052),x57053)) % 186.01/186.02 [5716]E(x57161,f195(f934(x57162,a922)))+~E(f335(f335(f66(x57162),x57161),x57163),f195(f934(f934(x57162,a922),a922))) % 186.01/186.02 [5717]E(x57171,f195(f934(x57172,a922)))+~E(f195(f934(f934(x57172,a922),a922)),f335(f335(f66(x57172),x57171),x57173)) % 186.01/186.02 [5723]~P112(x57231)+E(f335(f335(f87(x57231),f335(f85(x57231),x57232)),f335(f85(x57231),x57233)),f335(f335(f87(x57231),x57232),x57233)) % 186.01/186.02 [5725]~P66(x57251)+E(f335(f335(f299(x57251),f335(f85(x57251),x57252)),f335(f85(x57251),x57253)),f335(f335(f299(x57251),x57252),x57253)) % 186.01/186.02 [5757]~P1(f335(x57573,x57572))+P1(f335(f335(f337(x57571),x57572),f335(f270(x57571),x57573))) % 186.01/186.02 [5782]E(x57821,f2(a927))+E(f335(f179(x57822),f176(x57822,x57821,x57823)),f335(f335(f317(x57822),x57823),f195(f934(x57822,a922)))) % 186.01/186.02 [5801]E(f177(x58011,x58012,x58013),x58013)+P1(f335(f335(f337(x58011),x58012),f335(f179(x58011),x58013))) % 186.01/186.02 [5885]~P1(f335(f144(x58851),x58853))+P1(f335(f144(x58851),f335(f143(x58851,x58852),x58853))) % 186.01/186.02 [5928]~P63(x59281)+E(f335(f335(f42(x59281),f51(x59281,x59282,x59283)),x59283),f2(x59281)) % 186.01/186.02 [5947]E(f183(x59471,f335(f335(f158(x59471),x59472),f120(x59471)),x59473),f120(x59471))+P1(f335(f335(f337(a927),f2(a927)),x59473)) % 186.01/186.02 [5953]E(x59531,f2(a927))+E(f335(f178(x59532),f176(x59532,x59531,x59533)),f176(x59532,f335(f335(f23(a927),x59531),f84(a927)),x59533)) % 186.01/186.02 [6004]E(f335(f335(f158(x60041),x60042),x60043),f147(x60041,x60042,x60043))+P1(f335(f335(f337(x60041),x60042),f335(f179(x60041),x60043))) % 186.01/186.02 [6013]E(x60131,x60132)+~E(f335(f335(f87(a927),f335(a119,x60133)),x60131),f335(f335(f87(a927),f335(a119,x60133)),x60132)) % 186.01/186.02 [6014]~E(x60142,f335(f335(f86(a1),x60141),f335(f107(a1),f335(a119,x60143))))+P1(f335(f335(f244(a1),x60141),x60142)) % 186.01/186.02 [6075]~P31(x60751,x60752,x60753)+P32(a927,x60751,f146(a927,f335(f310(a927,x60752),x60753))) % 186.01/186.02 [6126]~E(x61263,f120(x61261))+E(f335(f335(f335(f190(f928(x61261),f928(x61261)),x61262),f174(x61261)),x61263),f120(x61261)) % 186.01/186.02 [6130]P1(f335(x61301,x61302))+~P1(f335(f335(f337(x61303),x61302),f335(f270(x61303),x61301))) % 186.01/186.02 [6160]E(x61601,x61602)+~E(f335(f335(f317(x61603),x61601),f195(f934(x61603,a922))),f335(f335(f317(x61603),x61602),f195(f934(x61603,a922)))) % 186.01/186.02 [6175]~P110(x61751)+E(f335(f335(f108(f934(x61751,a922)),f335(f290(x61751),x61752)),f335(f310(x61751,x61752),x61753)),f195(f934(x61751,a922))) % 186.01/186.02 [6214]E(f147(x62141,x62142,x62143),x62143)+~P1(f335(f335(f337(x62141),x62142),f335(f179(x62141),x62143))) % 186.01/186.02 [6236]~P79(x62361)+E(f335(f318(x62361,x62361,f85(x62361)),f335(f310(x62361,x62362),x62363)),f313(x62361,f335(f85(x62361),x62363),f335(f85(x62361),x62362))) % 186.01/186.02 [6247]E(f335(f196(f928(x62471)),f177(x62471,x62472,x62473)),f335(f196(f928(x62471)),x62473))+P1(f335(f335(f337(x62471),x62472),f335(f179(x62471),x62473))) % 186.01/186.02 [6300]~P110(x63001)+E(f335(f335(f108(f934(x63001,a922)),f335(f310(x63001,x63002),x63003)),f335(f291(x63001),x63003)),f195(f934(x63001,a922))) % 186.01/186.02 [6320]~P79(x63201)+E(f335(f318(x63201,x63201,f85(x63201)),f314(x63201,x63202,x63203)),f314(x63201,f335(f85(x63201),x63203),f335(f85(x63201),x63202))) % 186.01/186.02 [6321]~P79(x63211)+E(f335(f318(x63211,x63211,f85(x63211)),f311(x63211,x63212,x63213)),f311(x63211,f335(f85(x63211),x63213),f335(f85(x63211),x63212))) % 186.01/186.02 [6385]E(f183(x63851,f335(f335(f158(x63851),x63852),f120(x63851)),x63853),f335(f335(f158(x63851),x63852),f120(x63851)))+~P1(f335(f335(f337(a927),f2(a927)),x63853)) % 186.01/186.02 [6390]P31(x63901,x63902,x63903)+~P32(a927,x63901,f146(a927,f335(f310(a927,x63902),x63903))) % 186.01/186.02 [6393]~P79(x63931)+E(f335(f318(x63931,x63931,f85(x63931)),f313(x63931,x63932,x63933)),f335(f310(x63931,f335(f85(x63931),x63933)),f335(f85(x63931),x63932))) % 186.01/186.02 [6413]~P64(x64131)+E(f51(x64131,f335(f85(x64131),f51(x64131,x64132,x64133)),x64133),f51(x64131,f335(f85(x64131),x64132),x64133)) % 186.01/186.02 [6507]~P1(f335(f67(f933(x65072,x65071)),x65073))+P1(f335(f67(x65071),f335(f292(x65072,x65071),x65073))) % 186.01/186.02 [6508]~P1(f335(f67(f933(x65081,x65082)),x65083))+P1(f335(f67(x65081),f335(f272(x65081,x65082),x65083))) % 186.01/186.02 [6513]~P110(x65131)+E(f335(f335(f108(f934(x65131,a922)),f314(x65131,x65132,x65133)),f335(f291(x65131),x65133)),f195(f934(x65131,a922))) % 186.01/186.02 [6514]~P110(x65141)+E(f335(f335(f108(f934(x65141,a922)),f313(x65141,x65142,x65143)),f335(f312(x65141),x65143)),f195(f934(x65141,a922))) % 186.01/186.02 [6515]~P110(x65151)+E(f335(f335(f108(f934(x65151,a922)),f311(x65151,x65152,x65153)),f335(f312(x65151),x65153)),f195(f934(x65151,a922))) % 186.01/186.02 [6584]E(f335(f335(f171(x65841),x65842),f629(x65842,x65843,x65841)),x65843)+~P1(f335(f335(f337(x65841),x65843),f335(f179(x65841),x65842))) % 186.01/186.02 [6725]E(x67251,f120(x67252))+~E(f335(f335(f335(f190(f928(x67252),f928(x67252)),x67253),f174(x67252)),x67251),f120(x67252)) % 186.01/186.02 [6829]~P1(f335(f67(f933(x68292,x68291)),x68293))+P1(f335(f67(f933(x68291,x68292)),f335(f294(x68292,x68291),x68293))) % 186.01/186.02 [6852]E(x68521,x68522)+~E(f298(a927,f295(a927),x68523,x68521),f335(f335(f317(a927),x68522),f195(f934(a927,a922)))) % 186.01/186.02 [6853]E(x68531,x68532)+~E(f298(a927,f295(a927),x68531,x68532),f335(f335(f317(a927),x68533),f195(f934(a927,a922)))) % 186.01/186.02 [6981]P57(x69811,x69812,x69813)+P1(f335(f335(f337(x69811),f844(x69813,x69812,x69811)),x69812)) % 186.01/186.02 [6982]P57(x69821,x69822,x69823)+P1(f335(f335(f337(x69821),f843(x69823,x69822,x69821)),x69822)) % 186.01/186.02 [6992]P1(f335(f323(x69921,x69922),x69923))+P1(f335(f335(x69922,f453(x69923,x69922,x69921)),x69923)) % 186.01/186.02 [6993]P1(f335(f323(x69931,x69932),x69933))+P1(f335(f335(x69932,f461(x69933,x69932,x69931)),x69933)) % 186.01/186.02 [7024]E(f335(f196(f928(x70241)),f177(x70241,x70242,x70243)),f335(f335(f23(a927),f335(f196(f928(x70241)),x70243)),f84(a927)))+~P1(f335(f335(f337(x70241),x70242),f335(f179(x70241),x70243))) % 186.01/186.02 [7063]P1(f335(f256(x70631,x70632),x70633))+P1(f335(f335(f337(x70631),f577(x70633,x70632,x70631)),x70633)) % 186.01/186.02 [7072]~P1(f335(f67(f933(x70722,x70721)),f335(f294(x70721,x70722),x70723)))+P1(f335(f67(f933(x70721,x70722)),x70723)) % 186.01/186.02 [7127]~P1(f335(f335(f337(x71271),x71272),f335(f179(x71271),f121(x71271,x71273))))+P1(f335(f335(f337(x71271),x71272),f335(f179(x71271),x71273))) % 186.01/186.02 [7160]E(f335(f143(x71601,x71602),x71603),x71603)+P1(f335(f335(f337(x71601),f697(x71603,x71602,x71601)),f335(f179(x71601),x71603))) % 186.01/186.02 [7174]E(f335(f143(x71741,x71742),x71743),f120(x71741))+P1(f335(f335(f337(x71741),f696(x71743,x71742,x71741)),f335(f179(x71741),x71743))) % 186.01/186.02 [7200]P32(x72001,x72002,x72003)+P1(f335(f335(f337(x72001),f781(x72003,x72002,x72001)),f335(f179(x72001),x72003))) % 186.01/186.02 [7201]P32(x72011,x72012,x72013)+P1(f335(f335(f337(x72011),f792(x72013,x72012,x72011)),f335(f179(x72011),x72013))) % 186.01/186.02 [7202]P32(x72021,x72022,x72023)+P1(f335(f335(f337(x72021),f791(x72022,x72023,x72021)),f335(f179(x72021),x72023))) % 186.01/186.02 [7205]E(f184(x72051,x72052,x72053),x72053)+P1(f335(f335(f337(x72051),f740(x72053,x72052,x72051)),f335(f179(x72051),x72053))) % 186.01/186.02 [7280]P1(f335(f167(x72801,x72802),x72803))+P1(f335(f335(f337(x72801),f698(x72803,x72802,x72801)),f335(f179(x72801),x72803))) % 186.01/186.02 [7289]~P34(x72891,x72893,x72892)+P1(f335(f335(f337(x72891),f773(x72892,x72893,x72891)),f335(f179(x72891),x72892))) % 186.01/186.02 [7290]~P36(x72901,x72903,x72902)+P1(f335(f335(f337(x72901),f780(x72902,x72903,x72901)),f335(f179(x72901),x72902))) % 186.01/186.02 [7291]~P36(x72911,x72913,x72912)+P1(f335(f335(f337(x72911),f793(x72912,x72913,x72911)),f335(f179(x72911),x72912))) % 186.01/186.02 [7292]~P34(x72921,x72922,x72923)+P1(f335(f335(f337(x72921),f819(x72922,x72923,x72921)),f335(f179(x72921),x72923))) % 186.01/186.02 [7293]~P34(x72931,x72933,x72932)+P1(f335(f335(f337(x72931),f821(x72932,x72933,x72931)),f335(f179(x72931),x72932))) % 186.01/186.02 [7327]P1(f335(f335(f337(x73271),x73272),f631(x73273,x73272,x73271)))+~P1(f335(f335(f337(x73271),x73272),f43(f934(x73271,a922),x73273))) % 186.01/186.02 [7328]~P76(x73281)+E(f335(f335(f86(x73281),f335(f335(f6(a927,x73281),x73282),f335(f290(a927),x73283))),f335(x73282,x73283)),f335(f335(f6(a927,x73281),x73282),f335(f290(a927),f335(a119,x73283)))) % 186.01/186.02 [7340]P31(x73401,x73402,x73403)+P1(f335(f335(f337(a927),f848(x73403,x73402,x73401)),f335(f310(a927,x73402),x73403))) % 186.01/186.02 [7418]~P34(x74182,x74181,x74183)+P1(f335(x74181,f335(f335(f171(x74182),x74183),f777(x74183,x74181,x74182)))) % 186.01/186.02 [7430]~P1(f335(f335(f337(x74301),x74302),f903(x74302,x74303,x74301)))+P1(f335(f335(f337(x74301),x74302),f44(f934(x74301,a922),x74303))) % 186.01/186.02 [7463]~P76(x74631)+E(f335(f335(f86(x74631),f335(f335(f6(a927,x74631),x74632),f335(f309(a927),x74633))),f335(x74632,f335(a119,x74633))),f335(f335(f6(a927,x74631),x74632),f335(f309(a927),f335(a119,x74633)))) % 186.01/186.02 [7605]P1(f335(f335(f337(f928(x76051)),x76052),f168(x76051,x76053)))+P1(f335(f335(f337(x76051),f682(x76053,x76052,x76051)),f335(f179(x76051),x76052))) % 186.01/186.02 [7619]~P1(f335(f335(f337(f928(x76191)),x76192),f168(x76191,f324(x76191,x76193))))+P1(f335(f335(f337(f928(x76191)),x76192),f324(f928(x76191),f164(x76191,x76193)))) % 186.01/186.02 [7644]~P1(f335(f335(f337(f928(x76441)),x76442),f324(f928(x76441),f164(x76441,x76443))))+P1(f335(f335(f337(f928(x76441)),x76442),f168(x76441,f324(x76441,x76443)))) % 186.01/186.02 [7677]E(f335(f335(f335(f190(f928(x76771),f928(x76771)),x76772),f174(x76771)),x76773),x76773)+~P1(f335(f335(f243(a927),f335(f196(f928(x76771)),x76773)),f84(a927))) % 186.01/186.02 [7710]E(f335(f335(f141(x77101),f778(x77102,x77103,x77101)),f335(f335(f158(x77101),x77103),f779(x77102,x77103,x77101))),x77102)+~P1(f335(f335(f337(x77101),x77103),f335(f179(x77101),x77102))) % 186.01/186.02 [7711]E(f335(f335(f141(x77111),f784(x77112,x77113,x77111)),f335(f335(f158(x77111),x77113),f785(x77112,x77113,x77111))),x77112)+~P1(f335(f335(f337(x77111),x77113),f335(f179(x77111),x77112))) % 186.01/186.02 [7712]E(f335(f335(f141(x77121),f786(x77122,x77123,x77121)),f335(f335(f158(x77121),x77123),f787(x77122,x77123,x77121))),x77122)+~P1(f335(f335(f337(x77121),x77123),f335(f179(x77121),x77122))) % 186.01/186.02 [7733]~P26(x77331,x77332,x77333,f250(f934(x77331,a922)))+P26(f928(x77331),f928(x77332),f335(f161(x77331,x77332),x77333),f250(f934(f928(x77331),a922))) % 186.01/186.02 [7879]E(x78791,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x78792)),x78793)),f335(f264(a927,a927),x78792)))+~P1(f335(f54(x78791,x78793),x78792)) % 186.01/186.02 [7887]P26(x78871,x78872,x78873,f250(f934(x78871,a922)))+~P26(f928(x78871),f928(x78872),f335(f161(x78871,x78872),x78873),f250(f934(f928(x78871),a922))) % 186.01/186.02 [7930]P1(f335(f335(f337(f934(x79301,a922)),f903(x79302,x79303,x79301)),x79303))+P1(f335(f335(f337(x79301),x79302),f44(f934(x79301,a922),x79303))) % 186.01/186.02 [8019]P1(f335(f335(f337(f928(x80191)),x80192),f168(x80191,x80193)))+~P1(f335(f335(f337(x80191),f682(x80193,x80192,x80191)),x80193)) % 186.01/186.02 [8118]P32(x81181,x81182,x81183)+~P1(f335(x81182,f335(f335(f171(x81181),x81183),f783(x81183,x81182,x81181)))) % 186.01/186.02 [8142]E(x81421,x81422)+~E(f335(f335(f7(x81423,f934(x81423,a922),a922),f337(x81423)),x81421),f335(f335(f7(x81423,f934(x81423,a922),a922),f337(x81423)),x81422)) % 186.01/186.02 [8150]~P1(f335(f335(f337(f933(x81501,x81501)),x81503),f271(x81501,x81502)))+P1(f335(f335(f337(x81501),f893(x81502,x81503,x81501)),x81502)) % 186.01/186.02 [8152]~P1(f335(f335(f337(x81521),x81523),f43(f934(x81521,a922),x81522)))+P1(f335(f335(f337(f934(x81521,a922)),f631(x81522,x81523,x81521)),x81522)) % 186.01/186.02 [8272]P26(x82721,x82722,f97(x82722,x82721,f250(f934(x82722,a922)),x82723),f250(f934(x82721,a922)))+~E(f335(f318(x82722,x82721,x82723),f250(f934(x82722,a922))),f250(f934(x82721,a922))) % 186.01/186.02 [8326]~P1(f335(f335(f337(x83261),x83262),f335(f179(x83261),f784(x83263,x83262,x83261))))+~P1(f335(f335(f337(x83261),x83262),f335(f179(x83261),x83263))) % 186.01/186.02 [8327]~P1(f335(f335(f337(x83271),x83272),f335(f179(x83271),f787(x83273,x83272,x83271))))+~P1(f335(f335(f337(x83271),x83272),f335(f179(x83271),x83273))) % 186.01/186.02 [8351]P31(f335(f78(a922,a922,a927,a330),x83511),x83512,x83513)+P34(a927,x83511,f146(a927,f335(f310(a927,x83512),x83513))) % 186.01/186.02 [8513]E(x85131,f120(x85132))+P1(f335(f335(f337(x85132),f335(f259(x85132,f933(a106,a106)),f335(f283(x85132,x85131),x85133))),f335(f179(x85132),x85131))) % 186.01/186.02 [8611]~P71(x86111)+E(f335(f149(x86111,x86111,f335(f7(x86111,x86111,x86111),f86(x86111)),x86112),f335(f175(x86111),x86113)),f335(f149(x86111,x86111,f86(x86111),x86112),x86113)) % 186.01/186.02 [8803]~P26(x88032,x88031,x88033,f250(f934(x88032,a922)))+E(f335(f318(x88031,x88032,f97(x88032,x88031,f250(f934(x88032,a922)),x88033)),f250(f934(x88031,a922))),f250(f934(x88032,a922))) % 186.01/186.02 [8873]~P31(f335(f78(a922,a922,a927,a330),x88731),x88732,x88733)+~P34(a927,x88731,f146(a927,f335(f310(a927,x88732),x88733))) % 186.01/186.02 [9120]~P109(x91201)+E(f335(f179(x91201),f156(x91201,x91201,f5(x91201),x91202,x91203)),f335(f335(f317(x91201),x91202),f335(f179(x91201),x91203))) % 186.01/186.02 [9131]~E(f335(x91313,f335(f97(x91311,x91312,f250(f934(x91311,a922)),x91313),f586(x91313,x91312,x91311))),f586(x91313,x91312,x91311))+E(f335(f318(x91311,x91312,x91313),f250(f934(x91311,a922))),f250(f934(x91312,a922))) % 186.01/186.02 [9133]P1(f335(f335(f244(a927),f2(a927)),f616(x91331,x91332,x91333)))+~P1(f335(f335(f337(f933(x91333,x91333)),x91332),f335(f335(f297(x91333,x91333,x91333),x91331),f315(x91333,x91331)))) % 186.01/186.02 [9411]~P59(x94111,x94112)+~P1(f335(f335(f337(f933(x94111,x94111)),f335(f335(f260(x94111,x94111),x94113),x94113)),f335(f335(f297(x94111,x94111,x94111),x94112),f315(x94111,x94112)))) % 186.01/186.02 [9543]~E(f335(f335(f108(f934(f933(x95431,x95431),a922)),f335(f294(x95431,x95431),x95432)),f315(x95431,x95432)),f195(f934(f933(x95431,x95431),a922)))+~P1(f335(f335(f337(f933(x95431,x95431)),f335(f335(f260(x95431,x95431),x95433),x95433)),f335(f335(f297(x95431,x95431,x95431),x95432),f315(x95431,x95432)))) % 186.01/186.02 [9723]~P1(f335(f67(x97231),x97232))+P1(f335(f335(f243(a927),f335(f41(x97231),f335(f335(f23(f934(x97231,a922)),x97232),f335(f335(f317(x97231),x97233),f195(f934(x97231,a922)))))),f335(f41(x97231),x97232))) % 186.01/186.02 [5297]~E(x52973,f120(x52971))+E(f151(x52971,f335(f335(f158(x52971),x52972),x52973)),x52972) % 186.01/186.02 [5306]~E(x53063,f120(x53061))+E(f121(x53061,f335(f335(f158(x53061),x53062),x53063)),f120(x53061)) % 186.01/186.02 [5336]E(x53361,f120(x53362))+E(f151(x53362,f335(f335(f158(x53362),x53363),x53361)),f151(x53362,x53361)) % 186.01/186.02 [5338]E(x53381,f120(x53382))+E(f151(x53382,f335(f335(f141(x53382),x53383),x53381)),f151(x53382,x53381)) % 186.01/186.02 [5344]~E(x53443,f120(x53441))+E(f121(x53441,f335(f335(f141(x53441),x53442),x53443)),f121(x53441,x53442)) % 186.01/186.02 [5346]~E(x53463,f120(x53461))+E(f151(x53461,f335(f335(f141(x53461),x53462),x53463)),f151(x53461,x53462)) % 186.01/186.02 [5379]E(x53791,f120(x53792))+E(f335(f148(x53792),f335(f335(f141(x53792),x53791),x53793)),f335(f148(x53792),x53791)) % 186.01/186.02 [5407]~E(x54072,f120(x54071))+E(f335(f148(x54071),f335(f335(f141(x54071),x54072),x54073)),f335(f148(x54071),x54073)) % 186.01/186.02 [5459]~P98(x54591)+E(f335(f335(f108(x54591),x54592),f335(f335(f117(x54591),x54592),x54593)),x54592) % 186.01/186.02 [5460]~P98(x54601)+E(f335(f335(f117(x54601),x54602),f335(f335(f108(x54601),x54602),x54603)),x54602) % 186.01/186.02 [5461]~P109(x54611)+E(f335(f335(f241(x54611),x54612),f335(f335(f242(x54611),x54612),x54613)),x54612) % 186.01/186.02 [5462]~P109(x54621)+E(f335(f335(f242(x54621),x54622),f335(f335(f241(x54621),x54622),x54623)),x54622) % 186.01/186.02 [5481]~P63(x54811)+E(f51(x54811,f335(f335(f87(x54811),x54812),x54813),x54813),f2(x54811)) % 186.01/186.02 [5482]~P63(x54821)+E(f51(x54821,f335(f335(f87(x54821),x54822),x54823),x54822),f2(x54821)) % 186.01/186.02 [5554]~P5(x55541)+E(f335(f85(x55541),f335(f335(f23(x55541),x55542),x55543)),f335(f335(f23(x55541),x55543),x55542)) % 186.01/186.02 [5615]E(x56151,f120(x56152))+E(f121(x56152,f335(f335(f158(x56152),x56153),x56151)),f335(f335(f158(x56152),x56153),f121(x56152,x56151))) % 186.01/186.02 [5616]E(x56161,f120(x56162))+E(f121(x56162,f335(f335(f141(x56162),x56163),x56161)),f335(f335(f141(x56162),x56163),f121(x56162,x56161))) % 186.01/186.02 [5619]~P6(x56191)+E(f44(x56191,f335(f335(f317(x56191),x56192),x56193)),f335(f335(f108(x56191),x56192),f44(x56191,x56193))) % 186.01/186.02 [5620]~P6(x56201)+E(f43(x56201,f335(f335(f317(x56201),x56202),x56203)),f335(f335(f117(x56201),x56202),f43(x56201,x56203))) % 186.01/186.02 [5665]~P96(x56651)+E(f335(f335(f87(x56651),x56652),f335(f335(f87(x56651),x56652),x56653)),f335(f335(f87(x56651),x56652),x56653)) % 186.01/186.02 [5667]~P97(x56671)+E(f335(f335(f108(x56671),x56672),f335(f335(f108(x56671),x56672),x56673)),f335(f335(f108(x56671),x56672),x56673)) % 186.01/186.02 [5668]~P98(x56681)+E(f335(f335(f108(x56681),x56682),f335(f335(f108(x56681),x56682),x56683)),f335(f335(f108(x56681),x56682),x56683)) % 186.01/186.02 [5669]~P98(x56691)+E(f335(f335(f117(x56691),x56692),f335(f335(f117(x56691),x56692),x56693)),f335(f335(f117(x56691),x56692),x56693)) % 186.01/186.02 [5671]~P103(x56711)+E(f335(f335(f117(x56711),x56712),f335(f335(f117(x56711),x56712),x56713)),f335(f335(f117(x56711),x56712),x56713)) % 186.01/186.02 [5673]~P109(x56731)+E(f335(f335(f241(x56731),x56732),f335(f335(f241(x56731),x56732),x56733)),f335(f335(f241(x56731),x56732),x56733)) % 186.01/186.02 [5675]~P109(x56751)+E(f335(f335(f242(x56751),x56752),f335(f335(f242(x56751),x56752),x56753)),f335(f335(f242(x56751),x56752),x56753)) % 186.01/186.02 [5682]~P63(x56821)+E(f51(x56821,f335(f335(f86(x56821),x56822),x56823),x56823),f51(x56821,x56822,x56823)) % 186.01/186.02 [5683]~P63(x56831)+E(f51(x56831,f335(f335(f86(x56831),x56832),x56833),x56832),f51(x56831,x56833,x56832)) % 186.01/186.02 [5692]~P112(x56921)+E(f335(f335(f87(x56921),x56922),f335(f85(x56921),x56923)),f335(f85(x56921),f335(f335(f87(x56921),x56922),x56923))) % 186.01/186.02 [5693]~P66(x56931)+E(f335(f335(f299(x56931),x56932),f335(f85(x56931),x56933)),f335(f85(x56931),f335(f335(f299(x56931),x56932),x56933))) % 186.01/186.02 [5694]~P82(x56941)+E(f335(f335(f86(x56941),x56942),f335(f172(x56941),x56943)),f335(f172(x56941),f335(f335(f158(x56941),x56942),x56943))) % 186.01/186.02 [5722]~P112(x57221)+E(f335(f335(f87(x57221),f335(f85(x57221),x57222)),x57223),f335(f335(f87(x57221),x57222),f335(f85(x57221),x57223))) % 186.01/186.02 [5728]~P9(x57281,x57282,x57283)+E(f43(f934(x57281,a922),f335(f335(f66(x57281),x57282),x57283)),x57282) % 186.01/186.02 [5793]~P117(x57931)+E(f335(f335(f87(x57931),x57932),f335(f335(f252(x57931),x57932),x57933)),f335(f335(f252(x57931),x57932),f335(a119,x57933))) % 186.01/186.02 [5794]~P118(x57941)+E(f335(f335(f87(x57941),x57942),f335(f335(f252(x57941),x57942),x57943)),f335(f335(f252(x57941),x57942),f335(a119,x57943))) % 186.01/186.02 [5804]~P4(x58041)+E(f335(f335(f86(x58041),f335(f85(x58041),x58042)),f335(f335(f86(x58041),x58042),x58043)),x58043) % 186.01/186.02 [5827]~P146(x58271)+E(f335(f335(f252(x58271),f335(f107(x58271),x58272)),x58273),f335(f107(x58271),f335(f335(f252(a927),x58272),x58273))) % 186.01/186.02 [5828]~P140(x58281)+E(f335(f335(f252(x58281),f335(f109(x58281),x58282)),x58283),f335(f109(x58281),f335(f335(f252(a1),x58282),x58283))) % 186.01/186.02 [5834]~P87(x58341)+E(f335(f81(x58341),f335(f335(f23(x58341),x58342),x58343)),f335(f81(x58341),f335(f335(f23(x58341),x58343),x58342))) % 186.01/186.02 [5836]~P113(x58361)+E(f335(f335(f87(x58361),f88(x58361,x58362)),f88(x58361,x58363)),f88(x58361,f335(f335(f87(x58361),x58362),x58363))) % 186.01/186.02 [5840]E(x58401,f120(x58402))+E(f335(f335(f141(x58402),f335(f178(x58402),x58401)),x58403),f335(f178(x58402),f335(f335(f141(x58402),x58401),x58403))) % 186.01/186.02 [5845]~E(x58452,f335(a119,f335(f335(f86(a927),x58451),x58453)))+P1(f335(f335(f244(a927),x58451),x58452)) % 186.01/186.02 [5846]~P112(x58461)+E(f335(f335(f87(x58461),f335(f85(x58461),x58462)),x58463),f335(f85(x58461),f335(f335(f87(x58461),x58462),x58463))) % 186.01/186.02 [5847]~P121(x58471)+E(f335(f335(f299(x58471),f335(f85(x58471),x58472)),x58473),f335(f85(x58471),f335(f335(f299(x58471),x58472),x58473))) % 186.01/186.02 [5848]~P113(x58481)+E(f335(f335(f252(x58481),f335(f81(x58481),x58482)),x58483),f335(f81(x58481),f335(f335(f252(x58481),x58482),x58483))) % 186.01/186.02 [5946]E(f827(x59461,x59462,x59463),f833(x59461,x59462,x59463))+E(f335(f335(f108(f934(x59463,a922)),x59462),x59461),f195(f934(x59463,a922))) % 186.01/186.02 [5961]~P76(x59612)+E(f335(f335(f6(x59611,x59612),f335(f16(x59612,x59611),f2(x59612))),x59613),f2(x59612)) % 186.01/186.02 [5962]~P72(x59622)+E(f335(f335(f9(x59621,x59622),f335(f16(x59622,x59621),f84(x59622))),x59623),f84(x59622)) % 186.01/186.02 [5964]~P146(x59641)+E(f335(f335(f87(x59641),f335(f107(x59641),x59642)),f335(f107(x59641),x59643)),f335(f107(x59641),f335(f335(f87(a927),x59642),x59643))) % 186.01/186.02 [5965]~P146(x59651)+E(f335(f335(f86(x59651),f335(f107(x59651),x59652)),f335(f107(x59651),x59653)),f335(f107(x59651),f335(f335(f86(a927),x59652),x59653))) % 186.01/186.02 [5966]~P140(x59661)+E(f335(f335(f23(x59661),f335(f109(x59661),x59662)),f335(f109(x59661),x59663)),f335(f109(x59661),f335(f335(f23(a1),x59662),x59663))) % 186.01/186.02 [5967]~P140(x59671)+E(f335(f335(f87(x59671),f335(f109(x59671),x59672)),f335(f109(x59671),x59673)),f335(f109(x59671),f335(f335(f87(a1),x59672),x59673))) % 186.01/186.02 [5968]~P140(x59681)+E(f335(f335(f86(x59681),f335(f109(x59681),x59682)),f335(f109(x59681),x59683)),f335(f109(x59681),f335(f335(f86(a1),x59682),x59683))) % 186.01/186.02 [5969]~P94(x59691)+E(f335(f335(f23(x59691),f335(f110(x59691),x59692)),f335(f110(x59691),x59693)),f335(f110(x59691),f335(f335(f23(a1),x59692),x59693))) % 186.01/186.02 [5972]~P94(x59721)+E(f335(f335(f87(x59721),f335(f110(x59721),x59722)),f335(f110(x59721),x59723)),f335(f110(x59721),f335(f335(f87(a1),x59722),x59723))) % 186.01/186.02 [5973]~P94(x59731)+E(f335(f335(f86(x59731),f335(f110(x59731),x59732)),f335(f110(x59731),x59733)),f335(f110(x59731),f335(f335(f86(a1),x59732),x59733))) % 186.01/186.02 [6021]~E(x60213,x60212)+P1(f335(f335(f243(f934(x60211,a922)),x60212),x60213)) % 186.01/186.02 [6027]~E(x60272,x60273)+P1(f335(f335(f243(f934(x60271,a922)),x60272),x60273)) % 186.01/186.02 [6032]~P83(x60321)+E(f335(f335(f117(x60321),f335(f85(x60321),x60322)),f335(f85(x60321),x60323)),f335(f85(x60321),f335(f335(f108(x60321),x60322),x60323))) % 186.01/186.02 [6033]~P83(x60331)+E(f335(f335(f108(x60331),f335(f85(x60331),x60332)),f335(f85(x60331),x60333)),f335(f85(x60331),f335(f335(f117(x60331),x60332),x60333))) % 186.01/186.02 [6034]~P4(x60341)+E(f335(f335(f86(x60341),f335(f85(x60341),x60342)),f335(f85(x60341),x60343)),f335(f85(x60341),f335(f335(f86(x60341),x60343),x60342))) % 186.01/186.02 [6035]~P5(x60351)+E(f335(f335(f86(x60351),f335(f85(x60351),x60352)),f335(f85(x60351),x60353)),f335(f85(x60351),f335(f335(f86(x60351),x60352),x60353))) % 186.01/186.02 [6036]~P78(x60361)+E(f335(f335(f242(x60361),f335(f85(x60361),x60362)),f335(f85(x60361),x60363)),f335(f85(x60361),f335(f335(f241(x60361),x60362),x60363))) % 186.01/186.02 [6037]~P78(x60371)+E(f335(f335(f241(x60371),f335(f85(x60371),x60372)),f335(f85(x60371),x60373)),f335(f85(x60371),f335(f335(f242(x60371),x60372),x60373))) % 186.01/186.02 [6038]~P113(x60381)+E(f335(f335(f87(x60381),f335(f81(x60381),x60382)),f335(f81(x60381),x60383)),f335(f81(x60381),f335(f335(f87(x60381),x60382),x60383))) % 186.01/186.02 [6039]~P68(x60391)+E(f335(f335(f299(x60391),f335(f81(x60391),x60392)),f335(f81(x60391),x60393)),f335(f81(x60391),f335(f335(f299(x60391),x60392),x60393))) % 186.01/186.02 [6040]~P82(x60401)+E(f335(f335(f86(x60401),f335(f172(x60401),x60402)),f335(f172(x60401),x60403)),f335(f172(x60401),f335(f335(f141(x60401),x60402),x60403))) % 186.01/186.02 [6041]E(x60411,f195(f934(x60412,a922)))+~E(f335(f335(f117(f934(x60412,a922)),x60413),x60411),f195(f934(x60412,a922))) % 186.01/186.02 [6042]E(x60421,f195(f934(x60422,a922)))+~E(f335(f335(f117(f934(x60422,a922)),x60421),x60423),f195(f934(x60422,a922))) % 186.01/186.02 [6043]~P148(x60431,x60433,x60432)+P1(f335(x60431,f335(f335(f42(a1),x60432),x60433))) % 186.01/186.02 [6099]~P1(f335(f67(x60991),x60993))+P1(f335(f67(x60991),f335(f335(f317(x60991),x60992),x60993))) % 186.01/186.02 [6100]~P1(f335(f144(x61001),x61003))+P1(f335(f144(x61001),f335(f335(f182(x61001),x61002),x61003))) % 186.01/186.02 [6101]~P1(f335(f144(x61011),x61013))+P1(f335(f144(x61011),f335(f335(f145(x61011),x61012),x61013))) % 186.01/186.02 [6131]~P98(x61311)+P1(f335(f335(f243(x61311),x61312),f335(f335(f117(x61311),x61313),x61312))) % 186.01/186.02 [6132]~P103(x61321)+P1(f335(f335(f243(x61321),x61322),f335(f335(f117(x61321),x61323),x61322))) % 186.01/186.02 [6133]~P98(x61331)+P1(f335(f335(f243(x61331),x61332),f335(f335(f117(x61331),x61332),x61333))) % 186.01/186.02 [6134]~P103(x61341)+P1(f335(f335(f243(x61341),x61342),f335(f335(f117(x61341),x61342),x61343))) % 186.01/186.02 [6135]~P109(x61351)+P1(f335(f335(f243(x61351),x61352),f335(f335(f242(x61351),x61353),x61352))) % 186.01/186.02 [6136]~P109(x61361)+P1(f335(f335(f243(x61361),x61362),f335(f335(f242(x61361),x61362),x61363))) % 186.01/186.02 [6150]~E(x61501,f2(a927))+E(f335(f335(f42(a927),f335(f335(f87(a927),x61501),x61502)),f335(f335(f87(a927),x61501),x61503)),f2(a927)) % 186.01/186.02 [6230]~P94(x62301)+E(f335(f335(f23(x62301),f335(f110(x62301),x62302)),f335(f110(x62301),x62303)),f335(f110(x62301),f335(f335(f86(a1),x62302),f335(f85(a1),x62303)))) % 186.01/186.02 [6288]E(x62881,f2(a927))+E(f335(f335(f42(a927),f335(f335(f87(a927),x62881),x62882)),f335(f335(f87(a927),x62881),x62883)),f335(f335(f42(a927),x62882),x62883)) % 186.01/186.02 [6318]E(f159(x63181,f335(f335(f158(x63181),x63182),x63183)),f335(f335(f158(x63181),x63182),f159(x63181,x63183)))+P1(f335(f335(f337(x63181),x63182),f335(f179(x63181),x63183))) % 186.01/186.02 [6354]P148(x63541,x63542,x63543)+~P1(f335(x63541,f335(f335(f42(a1),x63543),x63542))) % 186.01/186.02 [6426]E(x64261,f120(x64262))+E(f335(f335(f158(x64262),f335(f148(x64262),x64261)),f335(f335(f182(x64262),x64263),f335(f178(x64262),x64261))),f335(f335(f182(x64262),f335(a119,x64263)),x64261)) % 186.01/186.02 [6433]E(f335(f335(f23(f934(x64331,a922)),x64332),x64333),x64332)+~E(f335(f335(f108(f934(x64331,a922)),x64332),x64333),f195(f934(x64331,a922))) % 186.01/186.02 [6447]E(f159(x64471,f335(f335(f158(x64471),x64472),x64473)),f159(x64471,x64473))+~P1(f335(f335(f337(x64471),x64472),f335(f179(x64471),x64473))) % 186.01/186.02 [6477]~P1(f335(f335(f243(a927),x64771),x64773))+P1(f335(f335(f243(a927),x64771),f335(f335(f86(a927),x64772),x64773))) % 186.01/186.02 [6479]~P1(f335(f335(f243(a927),x64791),x64792))+P1(f335(f335(f243(a927),x64791),f335(f335(f86(a927),x64792),x64793))) % 186.01/186.02 [6481]~P1(f335(f335(f244(a927),x64811),x64813))+P1(f335(f335(f244(a927),x64811),f335(f335(f86(a927),x64812),x64813))) % 186.01/186.02 [6483]~P1(f335(f335(f244(a927),x64831),x64832))+P1(f335(f335(f244(a927),x64831),f335(f335(f86(a927),x64832),x64833))) % 186.01/186.02 [6521]P1(f335(f67(x65211),x65212))+~P1(f335(f67(x65211),f335(f335(f317(x65211),x65213),x65212))) % 186.01/186.02 [6522]P1(f335(f144(x65221),x65222))+~P1(f335(f144(x65221),f335(f335(f158(x65221),x65223),x65222))) % 186.01/186.02 [6523]P1(f335(f144(x65231),x65232))+~P1(f335(f144(x65231),f335(f335(f141(x65231),x65233),x65232))) % 186.01/186.02 [6524]P1(f335(f144(x65241),x65242))+~P1(f335(f144(x65241),f335(f335(f141(x65241),x65242),x65243))) % 186.01/186.02 [6574]~P118(x65741)+E(f335(f335(f86(x65741),x65742),f335(f335(f87(x65741),x65743),x65742)),f335(f335(f87(x65741),f335(f335(f86(x65741),x65743),f84(x65741))),x65742)) % 186.01/186.02 [6620]~E(x66201,x66202)+~P1(f335(f335(f244(f934(x66203,a922)),x66201),x66202)) % 186.01/186.02 [6665]P1(f335(f335(f337(x66651),x66652),x66653))+P1(f335(f335(f337(x66651),x66652),f335(f85(f934(x66651,a922)),x66653))) % 186.01/186.02 [6671]E(f151(x66711,f335(f335(f145(x66711),x66712),x66713)),f151(x66711,x66713))+~P1(f335(f335(f244(a927),x66712),f335(f196(f928(x66711)),x66713))) % 186.01/186.02 [6672]E(f335(f335(f182(x66721),x66722),f121(x66721,x66723)),f335(f335(f182(x66721),x66722),x66723))+~P1(f335(f335(f244(a927),x66722),f335(f196(f928(x66721)),x66723))) % 186.01/186.02 [6727]E(f335(f335(f335(f190(f928(x67271),f928(x67271)),x67272),f174(x67271)),x67273),x67273)+~E(f51(a927,x67272,f335(f196(f928(x67271)),x67273)),f2(a927)) % 186.01/186.02 [6734]~P9(x67341,x67343,x67342)+E(f335(f335(f297(x67341,x67341,x67341),f335(f294(x67341,x67341),x67342)),x67342),x67342) % 186.01/186.02 [6777]~E(f335(f335(f117(f934(x67771,a922)),x67772),x67773),x67773)+P1(f335(f335(f243(f934(x67771,a922)),x67772),x67773)) % 186.01/186.02 [6782]~P56(x67821,x67821,x67823)+P56(x67821,x67821,f335(f335(f190(f933(x67821,x67821),a922),x67822),x67823)) % 186.01/186.02 [6786]~P1(f335(f335(f337(x67861),x67863),f335(f179(x67861),x67862)))+P1(f335(f335(f244(a927),f2(a927)),f335(f196(f928(x67861)),x67862))) % 186.01/186.02 [6812]~P87(x68121)+E(f335(f81(x68121),f335(f335(f86(x68121),f335(f81(x68121),x68122)),f335(f81(x68121),x68123))),f335(f335(f86(x68121),f335(f81(x68121),x68122)),f335(f81(x68121),x68123))) % 186.01/186.02 [6822]E(f335(f335(f42(a927),f335(f335(f87(a927),x68221),x68222)),f335(f335(f87(a927),x68221),x68223)),f335(f335(f42(a927),x68222),x68223))+~P1(f335(f335(f244(a927),f2(a927)),x68221)) % 186.01/186.02 [6962]~P1(f335(f67(x69621),x69623))+E(f335(f335(f70(x69621,f934(x69621,a922),f317(x69621)),x69622),x69623),f335(f335(f117(f934(x69621,a922)),x69623),x69622)) % 186.01/186.02 [7017]E(f335(f335(f108(f934(x70171,a922)),x70172),x70173),x70173)+~P1(f335(f335(f243(f934(x70171,a922)),x70173),x70172)) % 186.01/186.02 [7018]E(f335(f335(f108(f934(x70181,a922)),x70182),x70183),x70182)+~P1(f335(f335(f243(f934(x70181,a922)),x70182),x70183)) % 186.01/186.02 [7019]E(f335(f335(f117(f934(x70191,a922)),x70192),x70193),x70192)+~P1(f335(f335(f243(f934(x70191,a922)),x70193),x70192)) % 186.01/186.02 [7021]E(f335(f335(f117(f934(x70211,a922)),x70212),x70213),x70213)+~P1(f335(f335(f243(f934(x70211,a922)),x70212),x70213)) % 186.01/186.02 [7070]~P1(f335(f144(x70701),x70702))+E(f335(f335(f23(f934(x70701,a922)),f335(f179(x70701),x70702)),f335(f335(f317(x70701),x70703),f195(f934(x70701,a922)))),f335(f179(x70701),f177(x70701,x70703,x70702))) % 186.01/186.02 [7122]P38(x71221,x71222)+~P38(x71221,f335(f335(f190(f933(x71221,x71221),a922),x71223),x71222)) % 186.01/186.02 [7186]P1(f335(f55(x71861,x71862),f335(a57,x71863)))+~P1(f335(f55(f335(f85(a1),x71861),f335(f85(a1),x71862)),x71863)) % 186.01/186.02 [7191]E(f335(f335(f23(f934(x71911,a922)),f335(f335(f317(x71911),x71912),x71913)),f335(f335(f317(x71911),x71912),f195(f934(x71911,a922)))),x71913)+P1(f335(f335(f337(x71911),x71912),x71913)) % 186.01/186.02 [7214]E(f335(f335(f108(f934(x72141,a922)),f335(f179(x72141),x72142)),f335(f179(x72141),x72143)),f195(f934(x72141,a922)))+~P1(f335(f144(x72141),f335(f335(f141(x72141),x72142),x72143))) % 186.01/186.02 [7229]~P1(f335(f335(f337(x72291),x72292),f335(f179(x72291),x72293)))+~P1(f335(f144(x72291),f335(f335(f158(x72291),x72292),x72293))) % 186.01/186.02 [7299]P32(x72991,x72992,x72993)+P1(f335(f335(f244(a927),f783(x72993,x72992,x72991)),f335(f196(f928(x72991)),x72993))) % 186.01/186.02 [7309]E(f335(f335(f108(f934(x73091,a922)),x73092),x73093),f195(f934(x73091,a922)))+P1(f335(f335(f337(x73091),f827(x73093,x73092,x73091)),x73092)) % 186.01/186.02 [7310]E(f335(f335(f108(f934(x73101,a922)),x73102),x73103),f195(f934(x73101,a922)))+P1(f335(f335(f337(x73101),f833(x73103,x73102,x73101)),x73103)) % 186.01/186.02 [7313]E(f121(x73131,f335(f335(f182(x73131),x73132),x73133)),f335(f335(f182(x73131),f335(f335(f23(a927),x73132),f84(a927))),x73133))+~P1(f335(f335(f243(a927),x73132),f335(f196(f928(x73131)),x73133))) % 186.01/186.02 [7373]~P34(x73733,x73732,x73731)+P1(f335(f335(f244(a927),f777(x73731,x73732,x73733)),f335(f196(f928(x73733)),x73731))) % 186.01/186.02 [7391]P1(f335(f335(f244(a927),f2(a927)),x73911))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x73912),x73911)),f335(f335(f87(a927),x73913),x73911))) % 186.01/186.02 [7392]P1(f335(f335(f244(a927),f2(a927)),x73921))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x73921),x73922)),f335(f335(f87(a927),x73921),x73923))) % 186.01/186.02 [7395]~P1(f335(f335(f337(x73951),x73952),x73953))+~P1(f335(f335(f337(x73951),x73952),f335(f85(f934(x73951,a922)),x73953))) % 186.01/186.02 [7401]~P1(f335(f335(f244(f934(x74011,a922)),x74012),x74013))+P1(f335(f335(f243(f934(x74011,a922)),x74012),x74013)) % 186.01/186.02 [7511]~P1(f335(f335(f243(a927),x75113),x75112))+P1(f335(f335(f243(a927),f335(f335(f23(a927),x75111),x75112)),f335(f335(f23(a927),x75111),x75113))) % 186.01/186.02 [7512]~P1(f335(f335(f243(a927),x75121),x75123))+P1(f335(f335(f243(a927),f335(f335(f23(a927),x75121),x75122)),f335(f335(f23(a927),x75123),x75122))) % 186.01/186.02 [7514]~P1(f335(f335(f243(a927),x75142),x75143))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x75141),x75142)),f335(f335(f87(a927),x75141),x75143))) % 186.01/186.02 [7516]~P1(f335(f335(f243(a927),x75161),x75163))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x75161),x75162)),f335(f335(f87(a927),x75163),x75162))) % 186.01/186.02 [7517]~P1(f335(f335(f243(a927),x75172),x75173))+P1(f335(f335(f243(a927),f335(f335(f86(a927),x75171),x75172)),f335(f335(f86(a927),x75171),x75173))) % 186.01/186.02 [7518]~P1(f335(f335(f243(a927),x75181),x75183))+P1(f335(f335(f243(a927),f335(f335(f86(a927),x75181),x75182)),f335(f335(f86(a927),x75183),x75182))) % 186.01/186.02 [7519]~P1(f335(f335(f243(a927),x75191),x75193))+P1(f335(f335(f243(a927),f335(f335(f42(a927),x75191),x75192)),f335(f335(f42(a927),x75193),x75192))) % 186.01/186.02 [7520]~P1(f335(f335(f243(a1),x75202),x75203))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x75201),x75202)),f335(f335(f86(a1),x75201),x75203))) % 186.01/186.02 [7523]~P1(f335(f335(f244(a927),x75232),x75233))+P1(f335(f335(f244(a927),f335(f335(f86(a927),x75231),x75232)),f335(f335(f86(a927),x75231),x75233))) % 186.01/186.02 [7524]~P1(f335(f335(f244(a927),x75241),x75243))+P1(f335(f335(f244(a927),f335(f335(f86(a927),x75241),x75242)),f335(f335(f86(a927),x75243),x75242))) % 186.01/186.02 [7525]~P1(f335(f335(f244(a1),x75251),x75253))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x75251),x75252)),f335(f335(f86(a1),x75253),x75252))) % 186.01/186.02 [7604]E(x76041,x76042)+~P1(f335(f335(f337(x76043),x76041),f335(f335(f317(x76043),x76042),f195(f934(x76043,a922))))) % 186.01/186.02 [7606]~E(f335(f335(f108(f934(x76061,a922)),x76062),x76063),f195(f934(x76061,a922)))+P1(f335(f335(f243(f934(x76061,a922)),x76062),f335(f85(f934(x76061,a922)),x76063))) % 186.01/186.02 [7611]P1(f335(f335(f337(f934(x76111,a922)),x76112),f335(f316(x76111),x76113)))+~P1(f335(f335(f243(f934(x76111,a922)),x76112),x76113)) % 186.01/186.02 [7661]E(f335(f335(f158(x76611),f335(f335(f171(x76611),x76612),x76613)),f335(f335(f145(x76611),f335(a119,x76613)),x76612)),f335(f335(f145(x76611),x76613),x76612))+~P1(f335(f335(f244(a927),x76613),f335(f196(f928(x76611)),x76612))) % 186.01/186.02 [7687]P1(f335(f335(f337(f933(x76871,x76871)),x76872),f315(x76871,x76873)))+~P1(f335(f335(f337(f933(x76871,x76871)),x76872),x76873)) % 186.01/186.02 [7696]~P1(f335(f335(f337(f934(x76961,a922)),x76962),f335(f316(x76961),x76963)))+P1(f335(f335(f243(f934(x76961,a922)),x76962),x76963)) % 186.01/186.02 [7739]P1(f335(f335(f243(f934(x77391,a922)),x77392),f43(f934(x77391,a922),x77393)))+~P1(f335(f335(f337(f934(x77391,a922)),x77392),x77393)) % 186.01/186.02 [7761]~P140(x77611)+E(f335(f335(f87(x77611),f335(f335(f252(x77611),f335(f85(x77611),f84(x77611))),x77612)),f335(f335(f252(x77611),x77613),x77612)),f335(f335(f252(x77611),f335(f85(x77611),x77613)),x77612)) % 186.01/186.02 [7783]E(f335(f335(f171(x77831),x77832),f335(f335(f23(a927),f335(f196(f928(x77831)),x77832)),f335(a119,x77833))),f335(f335(f171(x77831),f335(f175(x77831),x77832)),x77833))+~P1(f335(f335(f244(a927),x77833),f335(f196(f928(x77831)),x77832))) % 186.01/186.02 [7800]~E(f335(f335(f108(f934(x78001,a922)),f581(x78003,x78002,x78001)),x78003),f195(f934(x78001,a922)))+E(f335(f335(f108(f934(x78001,a922)),f43(f934(x78001,a922),x78002)),x78003),f195(f934(x78001,a922))) % 186.01/186.02 [7862]~P1(f335(f335(f337(x78623),x78622),f335(f179(x78623),x78621)))+P1(f335(f335(f244(a927),f629(x78621,x78622,x78623)),f335(f196(f928(x78623)),x78621))) % 186.01/186.02 [7870]P1(f335(f335(f337(x78701),f335(f335(f171(x78701),x78702),x78703)),f335(f179(x78701),x78702)))+~P1(f335(f335(f244(a927),x78703),f335(f196(f928(x78701)),x78702))) % 186.01/186.02 [7966]~P1(f335(x79662,f741(x79663,x79662,x79661)))+E(f335(f335(f145(x79661),f335(f196(f928(x79661)),f184(x79661,x79662,x79663))),x79663),f120(x79661)) % 186.01/186.02 [7979]P1(f335(f335(f243(f934(f928(x79791),a922)),f168(x79791,x79792)),f168(x79791,x79793)))+~P1(f335(f335(f243(f934(x79791,a922)),x79792),x79793)) % 186.01/186.02 [7980]P1(f335(f335(f243(f934(f928(x79801),a922)),f167(x79801,x79802)),f167(x79801,x79803)))+~P1(f335(f335(f243(f934(x79801,a922)),x79802),x79803)) % 186.01/186.02 [8006]E(f335(f335(f108(f934(x80061,a922)),f43(f934(x80061,a922),x80062)),x80063),f195(f934(x80061,a922)))+P1(f335(f335(f337(f934(x80061,a922)),f581(x80063,x80062,x80061)),x80062)) % 186.01/186.02 [8008]~P1(f335(f335(f337(f934(x80081,a922)),x80083),x80082))+P1(f335(f335(f243(f934(x80081,a922)),f44(f934(x80081,a922),x80082)),x80083)) % 186.01/186.02 [8010]E(f335(f335(f108(f934(x80101,a922)),x80102),x80103),f195(f934(x80101,a922)))+~P1(f335(f335(f243(f934(x80101,a922)),x80102),f335(f85(f934(x80101,a922)),x80103))) % 186.01/186.02 [8056]E(f335(f335(f23(a927),f335(f335(f86(a927),f335(f172(a927),x80561)),x80562)),f335(f335(f171(a927),x80561),x80563)),f335(f172(a927),f335(f335(f166(a927,x80561),x80563),x80562)))+~P1(f335(f335(f244(a927),x80563),f335(f196(f928(a927)),x80561))) % 186.01/186.02 [8107]P1(f335(f335(f243(a927),x81071),x81072))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x81073),x81071)),f335(f335(f86(a927),x81073),x81072))) % 186.01/186.02 [8110]P1(f335(f335(f244(a927),x81101),x81102))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),x81103),x81101)),f335(f335(f86(a927),x81103),x81102))) % 186.01/186.02 [8111]P1(f335(f335(f244(a927),x81111),x81112))+~P1(f335(f335(f244(a927),f335(f335(f87(a927),x81113),x81111)),f335(f335(f87(a927),x81113),x81112))) % 186.01/186.02 [8112]P1(f335(f335(f244(a927),x81121),x81122))+~P1(f335(f335(f244(a927),f335(f335(f87(a927),x81121),x81123)),f335(f335(f87(a927),x81122),x81123))) % 186.01/186.02 [8140]P1(f335(f335(f244(a927),f2(a927)),x81401))+~P1(f335(f335(f244(a927),f335(f335(f87(a927),x81402),x81401)),f335(f335(f87(a927),x81403),x81401))) % 186.01/186.02 [8141]P1(f335(f335(f244(a927),f2(a927)),x81411))+~P1(f335(f335(f244(a927),f335(f335(f87(a927),x81411),x81412)),f335(f335(f87(a927),x81411),x81413))) % 186.01/186.02 [8215]E(f255(x82151,x82152,x82153),x82152)+~P1(f335(f335(f243(f934(x82151,a922)),x82153),f335(f335(f317(x82151),x82152),f195(f934(x82151,a922))))) % 186.01/186.02 [8265]~P1(f335(f144(x82651),x82653))+E(f335(f143(x82651,f335(f335(f8(a922,a922,x82651),a330),f335(a332,x82652))),x82653),f177(x82651,x82652,x82653)) % 186.01/186.02 [8290]E(f335(f335(f145(x82901),f335(f196(f928(x82901)),f184(x82901,x82902,x82903))),x82903),f120(x82901))+P1(f335(f335(f337(x82901),f741(x82903,x82902,x82901)),f335(f179(x82901),x82903))) % 186.01/186.02 [8294]E(f335(f335(f141(x82941),f335(f335(f182(x82941),x82942),x82943)),f335(f335(f158(x82941),f335(f335(f171(x82941),x82943),x82942)),f120(x82941))),f335(f335(f182(x82941),f335(a119,x82942)),x82943))+~P1(f335(f335(f244(a927),x82942),f335(f196(f928(x82941)),x82943))) % 186.01/186.02 [8356]E(f335(f143(x83561,f335(f335(f8(a922,a922,x83561),a330),f335(a332,x83562))),x83563),x83563)+P1(f335(f335(f337(x83561),x83562),f335(f179(x83561),x83563))) % 186.01/186.02 [8362]P1(f335(f335(f243(f934(f934(x83621,a922),a922)),f256(x83621,x83622)),f256(x83621,x83623)))+~P1(f335(f335(f243(f934(x83621,a922)),x83622),x83623)) % 186.01/186.02 [8401]~P1(f335(f144(x84011),x84013))+P1(f335(f144(x84011),f335(f335(f335(f190(f928(x84011),f928(x84011)),x84012),f174(x84011)),x84013))) % 186.01/186.02 [8407]~P1(f335(f335(f244(a927),x84072),x84073))+P1(f335(f335(f244(a927),f335(f335(f87(a927),f335(a119,x84071)),x84072)),f335(f335(f87(a927),f335(a119,x84071)),x84073))) % 186.01/186.02 [8427]P1(f335(f335(f243(f934(f934(x84271,a922),a922)),f335(f316(x84271),x84272)),f335(f316(x84271),x84273)))+~P1(f335(f335(f243(f934(x84271,a922)),x84272),x84273)) % 186.01/186.02 [8497]~E(f335(f318(x84971,x84972,x84973),f250(f934(x84971,a922))),f250(f934(x84972,a922)))+E(f335(f78(x84971,x84972,x84972,x84973),f97(x84971,x84972,f250(f934(x84971,a922)),x84973)),f25(x84972)) % 186.01/186.02 [8591]~P1(f335(f335(f243(f934(x85911,a922)),x85913),x85912))+P1(f335(f335(f243(f934(x85911,a922)),f335(f85(f934(x85911,a922)),x85912)),f335(f85(f934(x85911,a922)),x85913))) % 186.01/186.02 [8625]E(f335(f318(a927,a927,f335(f335(f7(a927,a927,a927),f23(a927)),x86251)),f335(f310(a927,x86252),x86253)),f335(f310(a927,f335(f335(f23(a927),x86252),x86251)),f335(f335(f23(a927),x86253),x86251)))+~P1(f335(f335(f244(a927),x86251),x86253)) % 186.01/186.02 [8651]~P82(x86511)+E(f335(f335(f86(x86511),x86512),f335(f149(x86511,x86511,f86(x86511),f2(x86511)),x86513)),f335(f149(x86511,x86511,f86(x86511),x86512),x86513)) % 186.01/186.02 [8727]~P87(x87271)+P1(f335(f335(f243(x87271),f335(f81(x87271),f335(f335(f23(x87271),x87272),x87273))),f335(f335(f86(x87271),f335(f81(x87271),x87272)),f335(f81(x87271),x87273)))) % 186.01/186.02 [8728]~P87(x87281)+P1(f335(f335(f243(x87281),f335(f81(x87281),f335(f335(f86(x87281),x87282),x87283))),f335(f335(f86(x87281),f335(f81(x87281),x87282)),f335(f81(x87281),x87283)))) % 186.01/186.02 [8739]E(f335(f335(f86(a1),f335(f335(f87(a1),x87391),f51(a1,f335(f335(f42(a1),x87392),x87391),x87393))),f51(a1,x87392,x87391)),f51(a1,x87392,f335(f335(f87(a1),x87391),x87393)))+~P1(f335(f335(f244(a1),f2(a1)),x87393)) % 186.01/186.02 [8745]E(f335(f335(f141(x87451),f335(f335(f182(x87451),x87452),x87453)),f335(f335(f158(x87451),f335(f148(x87451),f335(f335(f145(x87451),x87452),x87453))),f120(x87451))),f335(f335(f182(x87451),f335(a119,x87452)),x87453))+~P1(f335(f335(f244(a927),x87452),f335(f196(f928(x87451)),x87453))) % 186.01/186.02 [8765]E(f335(f276(x87651,f335(f335(f161(x87651,f933(a106,x87651)),f335(f260(a106,x87651),f84(a106))),x87652)),f335(a3,x87653)),f335(f335(f171(x87651),x87652),x87653))+~P1(f335(f335(f244(a927),x87653),f335(f196(f928(x87651)),x87652))) % 186.01/186.02 [8833]P1(f335(f335(f337(f933(x88331,x88331)),x88332),f335(f335(f297(x88331,x88331,x88331),x88333),f315(x88331,x88333))))+~P1(f335(f335(f337(f933(x88331,x88331)),x88332),x88333)) % 186.01/186.02 [8844]E(f335(f318(x88441,x88442,x88443),f250(f934(x88441,a922))),f250(f934(x88442,a922)))+~E(f335(f78(x88441,x88442,x88442,x88443),f97(x88441,x88442,f250(f934(x88441,a922)),x88443)),f25(x88442)) % 186.01/186.02 [8853]P1(f335(f335(f243(a927),x88531),x88532))+~P1(f335(f335(f243(a927),f335(f335(f87(a927),f335(a119,x88533)),x88531)),f335(f335(f87(a927),f335(a119,x88533)),x88532))) % 186.01/186.02 [8869]P1(f335(f335(f243(f934(x88691,a922)),x88692),x88693))+~P1(f335(f335(f243(f934(x88691,a922)),f335(f85(f934(x88691,a922)),x88693)),f335(f85(f934(x88691,a922)),x88692))) % 186.01/186.02 [8892]P1(f335(f144(x88921),x88922))+~P1(f335(f144(x88921),f335(f335(f335(f190(f928(x88921),f928(x88921)),x88923),f174(x88921)),x88922))) % 186.01/186.02 [8965]E(f335(f293(x89651,x89651,f315(x89651,x89652)),x89653),x89653)+~P1(f335(f335(f243(f934(x89651,a922)),f335(f293(x89651,x89651,x89652),x89653)),x89653)) % 186.01/186.02 [9013]~P109(x90131)+P14(x90131,f335(f143(x90131,f335(f335(f7(x90131,x90131,a922),a332),f335(x90132,x90133))),x90133)) % 186.01/186.02 [9020]~P1(f335(f335(f243(a927),x90201),x90202))+P1(f335(f335(f243(a927),x90201),f335(f149(a927,a927,f86(a927),x90202),x90203))) % 186.01/186.02 [9106]~P1(f335(f335(f337(f933(x91061,x91061)),x91062),f315(x91061,x91063)))+P1(f335(f335(f337(f933(x91061,x91061)),x91062),f335(f335(f190(f933(x91061,x91061),a922),f615(x91063,x91062,x91061)),x91063))) % 186.01/186.02 [9191]~P82(x91911)+E(f335(f335(f86(x91911),x91912),f335(f149(x91911,x91911,f335(f7(x91911,x91911,x91911),f86(x91911)),f2(x91911)),f335(f175(x91911),x91913))),f335(f149(x91911,x91911,f86(x91911),x91912),x91913)) % 186.01/186.02 [9308]~P27(x93082,x93081,x93083,f250(f934(x93082,a922)),f250(f934(x93081,a922)))+E(f97(x93081,x93082,f250(f934(x93081,a922)),f97(x93082,x93081,f250(f934(x93082,a922)),x93083)),x93083) % 186.01/186.02 [9459]P56(x94591,x94592,x94593)+P1(f335(f335(f337(f933(x94591,x94592)),f335(f335(f260(x94591,x94592),f625(x94593,x94592,x94591)),f601(x94593,x94592,x94591))),x94593)) % 186.01/186.02 [9460]P56(x94601,x94602,x94603)+P1(f335(f335(f337(f933(x94601,x94602)),f335(f335(f260(x94601,x94602),f625(x94603,x94602,x94601)),f600(x94603,x94602,x94601))),x94603)) % 186.01/186.02 [9528]~P1(f335(f335(f337(f933(x95281,x95281)),x95282),f335(f335(f297(x95281,x95281,x95281),x95283),f315(x95281,x95283))))+P1(f335(f335(f337(f933(x95281,x95281)),x95282),f335(f335(f190(f933(x95281,x95281),a922),f616(x95283,x95282,x95281)),x95283))) % 186.01/186.02 [9529]~P1(f335(x95291,f335(f335(f171(x95292),x95293),f335(f196(f928(x95292)),f184(x95292,x95291,x95293)))))+~P1(f335(f335(f244(a927),f335(f196(f928(x95292)),f184(x95292,x95291,x95293))),f335(f196(f928(x95292)),x95293))) % 186.01/186.02 [9618]~P1(f335(f335(f243(f934(x96181,a922)),x96182),x96183))+P1(f335(f335(f243(f934(x96181,a922)),f335(f335(f7(x96181,f934(x96181,a922),a922),f337(x96181)),x96182)),f335(f335(f7(x96181,f934(x96181,a922),a922),f337(x96181)),x96183))) % 186.01/186.02 [9675]~P1(f335(f335(f337(f933(f934(x96751,a922),f934(x96751,a922))),f335(f335(f260(f934(x96751,a922),f934(x96751,a922)),x96752),x96753)),f322(x96751)))+P1(f335(f335(f244(f934(x96751,a922)),x96752),x96753)) % 186.01/186.02 [9699]P57(x96991,x96992,x96993)+~P1(f335(f335(f337(f933(x96991,x96991)),f335(f335(f260(x96991,x96991),f844(x96993,x96992,x96991)),f843(x96993,x96992,x96991))),x96993)) % 186.01/186.02 [9700]P57(x97001,x97002,x97003)+~P1(f335(f335(f337(f933(x97001,x97001)),f335(f335(f260(x97001,x97001),f843(x97003,x97002,x97001)),f844(x97003,x97002,x97001))),x97003)) % 186.01/186.02 [9737]~P1(f335(f335(f337(f933(f928(x97371),f928(x97371))),f335(f335(f260(f928(x97371),f928(x97371)),x97372),x97372)),f154(x97371,x97373)))+P1(f335(f335(f337(f933(x97371,x97371)),f335(f335(f260(x97371,x97371),f681(x97372,x97373,x97371)),f681(x97372,x97373,x97371))),x97373)) % 186.01/186.02 [9787]P1(f335(f335(f243(f934(x97871,a922)),x97872),x97873))+~P1(f335(f335(f243(f934(x97871,a922)),f335(f335(f7(x97871,f934(x97871,a922),a922),f337(x97871)),x97872)),f335(f335(f7(x97871,f934(x97871,a922),a922),f337(x97871)),x97873))) % 186.01/186.02 [9868]E(f335(f335(f23(a927),f335(f335(f6(a927,a927),x98681),f335(f290(a927),x98682))),f335(f335(f6(a927,a927),x98683),f335(f290(a927),x98682))),f335(f335(f6(a927,a927),f335(f335(f18(a927,a927,a927),f335(f335(f8(a927,f934(a927,a927),a927),f23(a927)),x98681)),x98683)),f335(f290(a927),x98682)))+~P1(f335(f335(f243(a927),f335(x98683,f491(x98682,x98681,x98683))),f335(x98681,f491(x98682,x98681,x98683)))) % 186.01/186.02 [5882]~P4(x58821)+E(f335(f335(f23(x58821),f335(f335(f86(x58821),x58822),x58823)),x58823),x58822) % 186.01/186.02 [5883]~P4(x58831)+E(f335(f335(f86(x58831),f335(f335(f23(x58831),x58832),x58833)),x58833),x58832) % 186.01/186.02 [6108]~P4(x61081)+E(f335(f335(f86(x61081),x61082),f335(f335(f86(x61081),f335(f85(x61081),x61082)),x61083)),x61083) % 186.01/186.02 [6191]~P81(x61911)+E(f335(f335(f87(x61911),f335(f335(f252(x61911),x61912),x61913)),x61912),f335(f335(f252(x61911),x61912),f335(a119,x61913))) % 186.01/186.02 [6192]~P118(x61921)+E(f335(f335(f87(x61921),f335(f335(f252(x61921),x61922),x61923)),x61922),f335(f335(f252(x61921),x61922),f335(a119,x61923))) % 186.01/186.02 [6410]~P113(x64101)+E(f335(f81(x64101),f335(f335(f252(x64101),f335(f85(x64101),x64102)),x64103)),f335(f81(x64101),f335(f335(f252(x64101),x64102),x64103))) % 186.01/186.02 [6453]~P81(x64531)+E(f335(f335(f87(x64531),f335(f335(f252(x64531),x64532),x64533)),x64532),f335(f335(f87(x64531),x64532),f335(f335(f252(x64531),x64532),x64533))) % 186.01/186.02 [6512]E(f335(f335(f23(a106),f335(f335(f86(a106),x65121),x65122)),x65123),f282(x65121,x65122,x65123))+~P1(f335(f335(f244(a106),x65122),x65123)) % 186.01/186.02 [6535]~E(f335(f335(f145(x65351),x65353),x65352),f120(x65351))+P1(f335(f335(f243(a927),f335(f196(f928(x65351)),x65352)),x65353)) % 186.01/186.02 [6670]E(f335(f335(f87(a927),f335(f110(a927),x66701)),f335(f335(f87(a927),f335(f110(a927),x66702)),x66703)),f2(a927))+~P1(f335(f335(f244(a1),x66701),a89)) % 186.01/186.02 [6686]~P66(x66861)+E(f335(f335(f252(x66861),f335(f335(f299(x66861),f84(x66861)),x66862)),x66863),f335(f335(f299(x66861),f84(x66861)),f335(f335(f252(x66861),x66862),x66863))) % 186.01/186.02 [6763]E(f335(f335(f23(a927),f335(f335(f86(a927),x67631),x67632)),x67633),f335(f335(f23(a927),x67631),f335(f335(f23(a927),x67633),x67632)))+~P1(f335(f335(f243(a927),x67632),x67633)) % 186.01/186.02 [6765]E(f335(f335(f23(a927),f335(f335(f86(a927),x67651),x67652)),x67653),f335(f335(f86(a927),x67651),f335(f335(f23(a927),x67652),x67653)))+~P1(f335(f335(f243(a927),x67653),x67652)) % 186.01/186.02 [6803]~P97(x68031)+P1(f335(f335(f243(x68031),f335(f335(f108(x68031),x68032),x68033)),x68033)) % 186.01/186.02 [6804]~P98(x68041)+P1(f335(f335(f243(x68041),f335(f335(f108(x68041),x68042),x68043)),x68043)) % 186.01/186.02 [6805]~P97(x68051)+P1(f335(f335(f243(x68051),f335(f335(f108(x68051),x68052),x68053)),x68052)) % 186.01/186.02 [6806]~P98(x68061)+P1(f335(f335(f243(x68061),f335(f335(f108(x68061),x68062),x68063)),x68062)) % 186.01/186.02 [6807]~P109(x68071)+P1(f335(f335(f243(x68071),f335(f335(f241(x68071),x68072),x68073)),x68073)) % 186.01/186.02 [6808]~P109(x68081)+P1(f335(f335(f243(x68081),f335(f335(f241(x68081),x68082),x68083)),x68082)) % 186.01/186.02 [6821]E(f335(f335(f42(a1),f335(f335(f42(a1),x68211),x68212)),x68213),f335(f335(f42(a1),x68211),f335(f335(f87(a1),x68212),x68213)))+~P1(f335(f335(f244(a1),f2(a1)),x68213)) % 186.01/186.02 [6873]~P118(x68731)+E(f335(f335(f86(x68731),f335(f335(f87(x68731),x68732),x68733)),x68733),f335(f335(f87(x68731),f335(f335(f86(x68731),x68732),f84(x68731))),x68733)) % 186.01/186.02 [6874]~P94(x68741)+E(f335(f335(f87(x68741),f335(f85(x68741),f335(f110(x68741),x68742))),x68743),f335(f335(f87(x68741),f335(f110(x68741),f335(f85(a1),x68742))),x68743)) % 186.01/186.02 [6946]~P82(x69461)+E(f335(f172(x69461),f335(f335(f161(x69462,x69461),f335(f16(x69461,x69462),f2(x69461))),x69463)),f2(x69461)) % 186.01/186.02 [6963]E(f335(f335(f86(a927),f335(f110(a927),x69631)),f335(f335(f86(a927),f335(f110(a927),x69632)),x69633)),f335(f335(f86(a927),f335(f110(a927),x69632)),x69633))+~P1(f335(a200,f335(f110(a1),x69631))) % 186.01/186.02 [6977]~P6(x69771)+E(f44(x69771,f335(f335(f317(x69771),x69772),f335(f335(f317(x69771),x69773),f195(f934(x69771,a922))))),f335(f335(f108(x69771),x69772),x69773)) % 186.01/186.02 [6978]~P6(x69781)+E(f43(x69781,f335(f335(f317(x69781),x69782),f335(f335(f317(x69781),x69783),f195(f934(x69781,a922))))),f335(f335(f117(x69781),x69782),x69783)) % 186.01/186.02 [7000]E(f335(f335(f182(x70001),x70002),x70003),x70003)+~P1(f335(f335(f243(a927),f335(f196(f928(x70001)),x70003)),x70002)) % 186.01/186.02 [7012]E(f335(f335(f145(x70121),x70122),x70123),f120(x70121))+~P1(f335(f335(f243(a927),f335(f196(f928(x70121)),x70123)),x70122)) % 186.01/186.02 [7023]E(f335(f335(f86(a927),f335(f335(f23(a927),x70231),x70232)),x70233),f335(f335(f23(a927),f335(f335(f86(a927),x70231),x70233)),x70232))+~P1(f335(f335(f243(a927),x70232),x70231)) % 186.01/186.02 [7037]~P1(f335(f335(f244(a927),x70371),x70373))+P1(f335(f335(f244(a927),f335(f335(f23(a927),x70371),x70372)),x70373)) % 186.01/186.02 [7064]~P109(x70641)+E(f177(x70641,x70642,f335(f335(f155(x70641,x70641,f5(x70641)),x70642),x70643)),x70643) % 186.01/186.02 [7150]E(f335(f335(f23(a927),f335(f335(f86(a927),x71501),x71502)),f335(a119,x71503)),f335(f335(f23(a927),x71501),f335(a119,f335(f335(f23(a927),x71503),x71502))))+~P1(f335(f335(f243(a927),x71502),x71503)) % 186.01/186.02 [7151]~P113(x71511)+P1(f335(f335(f243(x71511),f2(x71511)),f335(f335(f252(x71511),f335(f81(x71511),x71512)),x71513))) % 186.01/186.02 [7198]P25(x71981,x71982,x71983)+~P1(f335(f335(f243(f934(f926(x71981),a922)),x71983),x71982)) % 186.01/186.02 [7240]~P1(f335(f67(x72401),x72402))+P1(f335(f67(x72401),f335(f335(f23(f934(x72401,a922)),x72402),x72403))) % 186.01/186.02 [7241]~P1(f335(f67(x72411),x72413))+P1(f335(f67(x72411),f335(f335(f108(f934(x72411,a922)),x72412),x72413))) % 186.01/186.02 [7242]~P1(f335(f67(x72421),x72422))+P1(f335(f67(x72421),f335(f335(f108(f934(x72421,a922)),x72422),x72423))) % 186.01/186.02 [7381]~P38(x73811,x73813)+P38(x73811,f335(f335(f108(f934(f933(x73811,x73811),a922)),x73812),x73813)) % 186.01/186.02 [7382]~P38(x73821,x73822)+P38(x73821,f335(f335(f108(f934(f933(x73821,x73821),a922)),x73822),x73823)) % 186.01/186.02 [7507]~P98(x75071)+E(f13(x75071,f335(f179(x75071),f335(f335(f158(x75071),x75072),x75073))),f335(f149(x75071,x75071,f117(x75071),x75072),x75073)) % 186.01/186.02 [7508]~P98(x75081)+E(f10(x75081,f335(f179(x75081),f335(f335(f158(x75081),x75082),x75083))),f335(f149(x75081,x75081,f108(x75081),x75082),x75083)) % 186.01/186.02 [7509]~P109(x75091)+E(f14(x75091,f335(f179(x75091),f335(f335(f158(x75091),x75092),x75093))),f335(f149(x75091,x75091,f242(x75091),x75092),x75093)) % 186.01/186.02 [7510]~P109(x75101)+E(f15(x75101,f335(f179(x75101),f335(f335(f158(x75101),x75102),x75103))),f335(f149(x75101,x75101,f241(x75101),x75102),x75103)) % 186.01/186.02 [7573]~P1(f335(f67(x75731),x75732))+P1(f335(f335(f243(a927),f335(f41(x75731),x75732)),f335(f41(x75731),f335(f335(f317(x75731),x75733),x75732)))) % 186.01/186.02 [7580]E(f335(f335(f117(f934(a927,a922)),f335(f310(a927,x75801),x75802)),f335(f310(a927,x75802),f335(f335(f86(a927),x75802),x75803))),f335(f310(a927,x75801),f335(f335(f86(a927),x75802),x75803)))+~P1(f335(f335(f243(a927),x75801),x75802)) % 186.01/186.02 [7589]P1(f335(f335(f243(a927),x75891),x75892))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x75893),x75891)),x75892)) % 186.01/186.02 [7590]P1(f335(f335(f243(a927),x75901),x75902))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x75901),x75903)),x75902)) % 186.01/186.02 [7591]P1(f335(f335(f244(a927),x75911),x75912))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),x75911),x75913)),x75912)) % 186.01/186.02 [7628]~P109(x76281)+E(f11(x76281,f242(x76281),f335(f179(x76281),f335(f335(f158(x76281),x76282),x76283))),f335(f149(x76281,x76281,f242(x76281),x76282),x76283)) % 186.01/186.02 [7629]~P109(x76291)+E(f12(x76291,f241(x76291),f335(f179(x76291),f335(f335(f158(x76291),x76292),x76293))),f335(f149(x76291,x76291,f241(x76291),x76292),x76293)) % 186.01/186.02 [7633]~E(x76332,f195(f934(f933(x76331,x76331),a922)))+P1(f335(f335(f243(f934(f933(x76331,x76331),a922)),x76332),x76333)) % 186.01/186.02 [7734]E(f335(f335(f117(f934(x77341,a922)),x77342),f335(f335(f23(f934(x77341,a922)),x77343),x77342)),x77343)+~P1(f335(f335(f243(f934(x77341,a922)),x77342),x77343)) % 186.01/186.02 [7735]~P1(f335(f335(f243(a927),x77351),f335(f335(f86(a927),x77353),x77352)))+P1(f335(f335(f243(a927),f335(f335(f23(a927),x77351),x77352)),x77353)) % 186.01/186.02 [7736]~P1(f335(f335(f244(a927),x77361),f335(f335(f23(a927),x77363),x77362)))+P1(f335(f335(f244(a927),f335(f335(f86(a927),x77361),x77362)),x77363)) % 186.01/186.02 [7790]E(x77901,f120(x77902))+E(f335(f148(x77902),f335(f335(f335(f190(f928(x77902),f928(x77902)),x77903),f174(x77902)),x77901)),f335(f335(f171(x77902),x77901),f51(a927,x77903,f335(f196(f928(x77902)),x77901)))) % 186.01/186.02 [7799]E(f335(f335(f317(x77991),x77992),f335(f335(f23(f934(x77991,a922)),x77993),f335(f335(f317(x77991),x77992),f195(f934(x77991,a922))))),x77993)+~P1(f335(f335(f337(x77991),x77992),x77993)) % 186.01/186.02 [7957]P1(f335(f335(f243(a927),x79571),f335(f335(f86(a927),x79572),x79573)))+~P1(f335(f335(f243(a927),f335(f335(f23(a927),x79571),x79573)),x79572)) % 186.01/186.02 [7958]P1(f335(f335(f244(a927),x79581),f335(f335(f23(a927),x79582),x79583)))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),x79581),x79583)),x79582)) % 186.01/186.02 [7983]P1(f335(f67(x79831),x79832))+~P1(f335(f67(x79831),f335(f335(f117(f934(x79831,a922)),x79833),x79832))) % 186.01/186.02 [7984]P1(f335(f67(x79841),x79842))+~P1(f335(f67(x79841),f335(f335(f117(f934(x79841,a922)),x79842),x79843))) % 186.01/186.02 [8055]~P46(x80551,x80553)+P1(f335(f335(f337(f933(x80551,x80551)),f335(f335(f260(x80551,x80551),x80552),x80552)),x80553)) % 186.01/186.02 [8188]E(f335(f335(f171(a927),f146(a927,f335(f310(a927,x81881),x81882))),x81883),f335(f335(f86(a927),x81881),x81883))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),x81881),x81883)),x81882)) % 186.01/186.02 [8254]E(f335(f335(f182(a927),x82541),f146(a927,f335(f310(a927,x82542),x82543))),f146(a927,f335(f310(a927,x82542),f335(f335(f86(a927),x82542),x82541))))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x82542),x82541)),x82543)) % 186.01/186.02 [8311]~P94(x83111)+E(f335(f335(f252(x83111),x83112),f335(f110(a927),f335(f335(f86(a1),x83113),x83113))),f335(f335(f92(x83111,x83111),f335(f335(f252(x83111),x83112),f335(f110(a927),x83113))),f335(f335(f18(x83111,x83111,x83111),f87(x83111)),f5(x83111)))) % 186.01/186.02 [8572]E(f335(f335(f141(x85721),f335(f335(f182(x85721),x85722),x85723)),f335(f335(f158(x85721),f335(f335(f171(x85721),x85723),x85722)),f335(f335(f145(x85721),f335(a119,x85722)),x85723))),x85723)+~P1(f335(f335(f244(a927),x85722),f335(f196(f928(x85721)),x85723))) % 186.01/186.02 [8579]P1(f335(f335(f243(f934(x85791,a922)),f323(x85791,x85792)),f323(x85791,x85793)))+~P1(f335(f335(f243(f934(x85791,f934(x85791,a922))),x85793),x85792)) % 186.01/186.02 [8580]~P57(x85801,x85802,x85803)+P57(x85801,x85802,f335(f335(f23(f934(f933(x85801,x85801),a922)),x85803),f315(x85801,f195(f934(f933(x85801,x85801),a922))))) % 186.01/186.02 [8599]P1(f335(f335(f243(f934(x85991,a922)),f324(x85991,x85992)),f324(x85991,x85993)))+~P1(f335(f335(f243(f934(f933(x85991,x85991),a922)),x85993),x85992)) % 186.01/186.02 [8605]~P1(f335(f335(f244(f934(x86051,a922)),x86053),x86052))+P1(f335(f335(f337(x86051),f572(x86052,x86053,x86051)),f335(f335(f23(f934(x86051,a922)),x86052),x86053))) % 186.01/186.02 [8607]~P126(x86071)+P1(f335(f335(f243(x86071),f2(x86071)),f335(f335(f86(x86071),f335(f335(f87(x86071),x86072),x86072)),f335(f335(f87(x86071),x86073),x86073)))) % 186.01/186.02 [8640]P1(f335(f335(f243(f934(x86401,a922)),f335(f289(x86401),x86402)),f335(f289(x86401),x86403)))+~P1(f335(f335(f243(f934(f933(x86401,x86401),a922)),x86402),x86403)) % 186.01/186.02 [8669]~P55(x86691,x86692)+~P1(f335(f335(f337(f933(x86691,x86691)),f335(f335(f260(x86691,x86691),x86693),x86693)),x86692)) % 186.01/186.02 [8671]~P38(x86711,x86712)+~P1(f335(f335(f337(f933(x86711,x86711)),f335(f335(f260(x86711,x86711),x86713),x86713)),x86712)) % 186.01/186.02 [8729]P1(f335(f335(f243(f934(x87291,a922)),f44(f934(x87291,a922),x87292)),f44(f934(x87291,a922),x87293)))+~P1(f335(f335(f243(f934(f934(x87291,a922),a922)),x87293),x87292)) % 186.01/186.02 [8730]P1(f335(f335(f243(f934(x87301,a922)),f43(f934(x87301,a922),x87302)),f43(f934(x87301,a922),x87303)))+~P1(f335(f335(f243(f934(f934(x87301,a922),a922)),x87302),x87303)) % 186.01/186.02 [8784]~P9(x87841,x87843,x87842)+P1(f335(f335(f243(f934(f933(x87841,x87841),a922)),x87842),f335(f335(f262(x87841,x87841),x87843),f335(f16(f934(x87841,a922),x87841),x87843)))) % 186.01/186.02 [8785]~P54(x87851,x87853,x87852)+P1(f335(f335(f243(f934(f933(x87851,x87851),a922)),x87852),f335(f335(f262(x87851,x87851),x87853),f335(f16(f934(x87851,a922),x87851),x87853)))) % 186.01/186.02 [8834]~P87(x88341)+P1(f335(f335(f243(x88341),f335(f335(f23(x88341),f335(f81(x88341),x88342)),f335(f81(x88341),x88343))),f335(f81(x88341),f335(f335(f23(x88341),x88343),x88342)))) % 186.01/186.02 [8835]~P87(x88351)+P1(f335(f335(f243(x88351),f335(f335(f23(x88351),f335(f81(x88351),x88352)),f335(f81(x88351),x88353))),f335(f81(x88351),f335(f335(f23(x88351),x88352),x88353)))) % 186.01/186.02 [8867]P1(f335(f335(f243(f934(f933(x88671,x88671),a922)),f315(x88671,x88672)),f315(x88671,x88673)))+~P1(f335(f335(f243(f934(f933(x88671,x88671),a922)),x88672),x88673)) % 186.01/186.02 [8978]~P26(x89782,x89781,x89783,f250(f934(x89782,a922)))+E(f335(f78(x89781,x89782,x89782,f97(x89782,x89781,f250(f934(x89782,a922)),x89783)),x89783),f25(x89782)) % 186.01/186.02 [9038]P57(x90381,x90382,x90383)+~P57(x90381,x90382,f335(f335(f23(f934(f933(x90381,x90381),a922)),x90383),f315(x90381,f195(f934(f933(x90381,x90381),a922))))) % 186.01/186.02 [9058]P1(f335(f335(f243(f934(f933(f928(x90581),f928(x90581)),a922)),f164(x90581,x90582)),f164(x90581,x90583)))+~P1(f335(f335(f243(f934(f933(x90581,x90581),a922)),x90582),x90583)) % 186.01/186.02 [9059]P1(f335(f335(f243(f934(f933(f928(x90591),f928(x90591)),a922)),f165(x90591,x90592)),f165(x90591,x90593)))+~P1(f335(f335(f243(f934(f933(x90591,x90591),a922)),x90592),x90593)) % 186.01/186.02 [9080]~P54(x90801,x90803,x90802)+P1(f335(f335(f243(f934(f933(x90801,x90801),a922)),x90802),f335(f335(f297(x90801,x90801,x90801),f335(f294(x90801,x90801),x90802)),x90802))) % 186.01/186.02 [9134]~P1(f335(f144(x91341),x91342))+E(f335(f143(x91341,f335(f335(f7(x91341,f934(x91341,a922),a922),f337(x91341)),f335(f179(x91341),f183(x91341,x91342,x91343)))),x91342),f183(x91341,x91342,x91343)) % 186.01/186.02 [9189]E(x91891,x91892)+~P1(f335(f335(f337(f933(x91893,x91893)),f335(f335(f260(x91893,x91893),x91891),x91892)),f315(x91893,f195(f934(f933(x91893,x91893),a922))))) % 186.01/186.02 [9271]P1(f335(f335(f337(x92711),x92712),f324(x92711,x92713)))+P1(f335(f335(f337(f933(x92711,x92711)),f335(f335(f260(x92711,x92711),f558(x92713,x92712,x92711)),x92712)),x92713)) % 186.01/186.02 [9272]P1(f335(f335(f337(x92721),x92722),f324(x92721,x92723)))+P1(f335(f335(f337(f933(x92721,x92721)),f335(f335(f260(x92721,x92721),f603(x92723,x92722,x92721)),x92722)),x92723)) % 186.01/186.02 [9273]P1(f335(f335(f337(x92731),x92732),f324(x92731,x92733)))+P1(f335(f335(f337(f933(x92731,x92731)),f335(f335(f260(x92731,x92731),f606(x92733,x92732,x92731)),x92732)),x92733)) % 186.01/186.02 [9309]P26(x93091,x93092,x93093,f250(f934(x93091,a922)))+~E(f335(f78(x93092,x93091,x93091,f97(x93091,x93092,f250(f934(x93091,a922)),x93093)),x93093),f25(x93091)) % 186.01/186.02 [9363]~P1(f335(f335(f337(f928(x93631)),x93633),f168(x93631,x93632)))+P1(f335(f167(x93631,f335(f335(f7(x93631,f934(x93631,a922),a922),f337(x93631)),x93632)),x93633)) % 186.01/186.02 [9386]P1(f335(x93863,x93862))+E(f335(f270(x93861),f335(f335(f18(x93861,a922,a922),f335(f335(f8(a922,f934(a922,a922),x93861),a333),f335(a332,x93862))),x93863)),f195(f934(x93861,a922))) % 186.01/186.02 [9402]~P87(x94021)+P1(f335(f335(f243(x94021),f335(f81(x94021),f335(f335(f23(x94021),f335(f81(x94021),x94022)),f335(f81(x94021),x94023)))),f335(f81(x94021),f335(f335(f23(x94021),x94022),x94023)))) % 186.01/186.02 [9416]~P1(f335(x94163,x94162))+E(f335(f270(x94161),f335(f335(f18(x94161,a922,a922),f335(f335(f8(a922,f934(a922,a922),x94161),a333),f335(a332,x94162))),x94163)),f335(f335(f317(x94161),x94162),f195(f934(x94161,a922)))) % 186.01/186.02 [9423]~P1(f335(f335(f337(f934(x94231,a922)),x94233),f335(f316(x94231),x94232)))+P1(f335(f256(x94231,f335(f335(f7(x94231,f934(x94231,a922),a922),f337(x94231)),x94232)),x94233)) % 186.01/186.02 [9458]P38(x94581,x94582)+P1(f335(f335(f337(f933(x94581,x94581)),f335(f335(f260(x94581,x94581),f335(f386(x94582,x94581),f335(a119,x94583))),f335(f386(x94582,x94581),x94583))),x94582)) % 186.01/186.02 [9597]P1(f335(f335(f337(f928(x95971)),x95972),f168(x95971,x95973)))+~P1(f335(f167(x95971,f335(f335(f7(x95971,f934(x95971,a922),a922),f337(x95971)),x95973)),x95972)) % 186.01/186.02 [9610]P1(f335(f335(f337(f934(x96101,a922)),x96102),f335(f316(x96101),x96103)))+~P1(f335(f256(x96101,f335(f335(f7(x96101,f934(x96101,a922),a922),f337(x96101)),x96103)),x96102)) % 186.01/186.02 [9670]P1(f335(f335(f337(x96701),f335(f276(x96701,x96702),x96703)),f335(f179(x96701),f335(f335(f161(f933(a106,x96701),x96701),f264(a106,x96701)),x96702))))+~P1(f335(f335(f244(a106),x96703),f335(f172(a106),f335(f335(f161(f933(a106,x96701),a106),f259(a106,x96701)),x96702)))) % 186.01/186.02 [9716]P1(f335(f335(f243(f934(f933(f928(x97161),f928(x97161)),a922)),f165(x97161,x97162)),f335(f335(f262(f928(x97161),f928(x97161)),f168(x97161,x97163)),f335(f16(f934(f928(x97161),a922),f928(x97161)),f168(x97161,x97163)))))+~P1(f335(f335(f243(f934(f933(x97161,x97161),a922)),x97162),f335(f335(f262(x97161,x97161),x97163),f335(f16(f934(x97161,a922),x97161),x97163)))) % 186.01/186.02 [9740]P1(f335(f335(f337(x97401),f335(f259(x97401,f933(a106,a106)),f335(f274(x97401,x97402),x97403))),f335(f179(x97401),f335(f335(f161(f933(a106,x97401),x97401),f264(a106,x97401)),x97402))))+~P1(f335(f335(f244(a106),f2(a106)),f335(f172(a106),f335(f335(f161(f933(a106,x97401),a106),f259(a106,x97401)),x97402)))) % 186.01/186.02 [9755]~P1(f335(f335(f243(f934(f933(x97551,x97551),a922)),x97552),f335(f335(f262(x97551,x97551),x97553),f335(f16(f934(x97551,a922),x97551),x97553))))+P1(f335(f335(f243(f934(f933(x97551,x97551),a922)),f335(f335(f297(x97551,x97551,x97551),x97552),f315(x97551,x97552))),f335(f335(f262(x97551,x97551),x97553),f335(f16(f934(x97551,a922),x97551),x97553)))) % 186.01/186.02 [10057]~P38(x100571,x100572)+~P1(f335(f335(f337(f933(x100571,x100571)),f335(f335(f260(x100571,x100571),f335(x100573,f335(a119,f387(x100572,x100571,x100573)))),f335(x100573,f387(x100572,x100571,x100573)))),x100572)) % 186.01/186.02 [10058]~P38(x100581,x100582)+~P1(f335(f335(f337(f933(x100581,x100581)),f335(f335(f260(x100581,x100581),f335(x100583,f335(a119,f644(x100583,x100582,x100581)))),f335(x100583,f644(x100583,x100582,x100581)))),x100582)) % 186.01/186.02 [10318]P1(f335(f335(f243(f934(f933(f934(x103181,a922),f934(x103181,a922)),a922)),f335(f335(f297(f934(x103181,a922),f934(x103181,a922),f934(x103181,a922)),f326(x103181,x103182)),f335(f335(f117(f934(f933(f934(x103181,a922),f934(x103181,a922)),a922)),f326(x103181,x103183)),f335(f335(f317(f933(f934(x103181,a922),f934(x103181,a922))),f335(f335(f260(f934(x103181,a922),f934(x103181,a922)),f195(f934(x103181,a922))),f195(f934(x103181,a922)))),f195(f934(f933(f934(x103181,a922),f934(x103181,a922)),a922)))))),f326(x103181,x103182)))+~P1(f335(f335(f243(f934(f933(x103181,x103181),a922)),f335(f335(f297(x103181,x103181,x103181),x103182),x103183)),x103182)) % 186.01/186.02 [10319]P1(f335(f335(f243(f934(f933(f934(x103191,a922),f934(x103191,a922)),a922)),f335(f335(f297(f934(x103191,a922),f934(x103191,a922),f934(x103191,a922)),f327(x103191,x103192)),f335(f335(f117(f934(f933(f934(x103191,a922),f934(x103191,a922)),a922)),f327(x103191,x103193)),f335(f335(f317(f933(f934(x103191,a922),f934(x103191,a922))),f335(f335(f260(f934(x103191,a922),f934(x103191,a922)),f195(f934(x103191,a922))),f195(f934(x103191,a922)))),f195(f934(f933(f934(x103191,a922),f934(x103191,a922)),a922)))))),f327(x103191,x103192)))+~P1(f335(f335(f243(f934(f933(x103191,x103191),a922)),f335(f335(f297(x103191,x103191,x103191),x103192),x103193)),x103192)) % 186.01/186.02 [7506]~P1(f335(f335(f243(a927),x75062),x75061))+E(f335(f335(f23(a927),f335(a119,f335(f335(f23(a927),x75061),x75062))),x75063),f335(f335(f23(a927),f335(a119,x75061)),f335(f335(f86(a927),x75062),x75063))) % 186.01/186.02 [7545]~P63(x75451)+E(f335(f335(f86(x75451),f51(x75451,x75452,x75453)),f335(f335(f87(x75451),f335(f335(f42(x75451),x75452),x75453)),x75453)),x75452) % 186.01/186.02 [7740]E(f335(f335(f87(a927),f335(f110(a927),x77401)),f335(f335(f87(a927),f335(f110(a927),x77402)),x77403)),f335(f335(f87(a927),f335(f110(a927),f335(f335(f87(a1),x77401),x77402))),x77403))+P1(f335(f335(f244(a1),x77401),a89)) % 186.01/186.02 [8197]~P1(f335(f335(f243(a927),x81973),x81972))+P1(f335(f335(f243(a927),x81971),f335(f335(f23(a927),f335(f335(f86(a927),x81972),x81971)),x81973))) % 186.01/186.02 [8392]~P1(f335(f335(f243(a927),x83921),x83922))+E(f335(f335(f141(a927),f146(a927,f335(f310(a927,x83921),x83922))),f146(a927,f335(f310(a927,x83922),f335(f335(f86(a927),x83922),x83923)))),f146(a927,f335(f310(a927,x83921),f335(f335(f86(a927),x83922),x83923)))) % 186.01/186.02 [8648]~P1(f335(f67(x86481),x86482))+E(f335(a119,f335(f41(x86481),f335(f335(f23(f934(x86481,a922)),x86482),f335(f335(f317(x86481),x86483),f195(f934(x86481,a922)))))),f335(f41(x86481),f335(f335(f317(x86481),x86483),x86482))) % 186.01/186.02 [8687]~P1(f335(f67(x86871),x86872))+E(f335(f335(f86(a927),f84(a927)),f335(f41(x86871),f335(f335(f23(f934(x86871,a922)),x86872),f335(f335(f317(x86871),x86873),f195(f934(x86871,a922)))))),f335(f41(x86871),f335(f335(f317(x86871),x86873),x86872))) % 186.01/186.02 [8876]E(f335(f335(f23(a927),f335(f41(x88761),x88762)),f335(f41(x88761),f335(f335(f108(f934(x88761,a922)),x88762),x88763))),f335(f41(x88761),f335(f335(f23(f934(x88761,a922)),x88762),x88763)))+~P1(f335(f67(x88761),f335(f335(f108(f934(x88761,a922)),x88762),x88763))) % 186.01/186.02 [9129]~P7(f335(x91292,f456(x91292,x91293,x91291)))+E(f335(f107(a1),f335(f335(f6(x91291,a927),f335(f335(f8(a1,a927,x91291),a111),x91292)),x91293)),f335(f335(f6(x91291,a1),x91292),x91293)) % 186.01/186.02 [9130]~P7(f335(x91302,f480(x91302,x91303,x91301)))+E(f335(f107(a1),f335(f335(f9(x91301,a927),f335(f335(f8(a1,a927,x91301),a111),x91302)),x91303)),f335(f335(f9(x91301,a1),x91302),x91303)) % 186.01/186.02 [9172]~P1(f335(f67(x91721),x91723))+P1(f335(f335(f243(a927),f335(f335(f23(a927),f335(f41(x91721),x91722)),f335(f41(x91721),x91723))),f335(f41(x91721),f335(f335(f23(f934(x91721,a922)),x91722),x91723)))) % 186.01/186.02 [9199]P1(f335(f335(f337(x91991),f456(x91992,x91993,x91991)),x91993))+E(f335(f107(a1),f335(f335(f6(x91991,a927),f335(f335(f8(a1,a927,x91991),a111),x91992)),x91993)),f335(f335(f6(x91991,a1),x91992),x91993)) % 186.01/186.02 [9200]P1(f335(f335(f337(x92001),f480(x92002,x92003,x92001)),x92003))+E(f335(f107(a1),f335(f335(f9(x92001,a927),f335(f335(f8(a1,a927,x92001),a111),x92002)),x92003)),f335(f335(f9(x92001,a1),x92002),x92003)) % 186.01/186.02 [9263]E(f91(x92631,f335(f335(f7(x92631,f934(x92631,a922),a922),f337(x92631)),f335(f335(f23(f934(x92631,a922)),x92632),f335(f335(f317(x92631),x92633),f195(f934(x92631,a922)))))),f255(x92631,x92633,x92632))+P1(f335(f335(f243(f934(x92631,a922)),x92632),f335(f335(f317(x92631),x92633),f195(f934(x92631,a922))))) % 186.01/186.02 [9611]E(f335(f335(f161(f928(x96111),x96111),f335(f335(f7(f928(x96111),a927,x96111),f171(x96111)),x96112)),f335(f143(f928(x96111),f335(f335(f8(a927,a922,f928(x96111)),f335(f244(a927),x96112)),f196(f928(x96111)))),x96113)),f335(f335(f171(f928(x96111)),f186(x96111,x96113)),x96112))+~P1(f335(f335(f244(a927),x96112),f335(f196(f928(f928(x96111))),f186(x96111,x96113)))) % 186.01/186.02 [9690]E(f335(f143(x96901,x96902),x96903),f184(x96901,x96902,x96903))+P1(f335(f335(f337(x96901),f745(x96903,x96902,x96901)),f335(f179(x96901),f335(f335(f145(x96901),f335(f196(f928(x96901)),f184(x96901,x96902,x96903))),x96903)))) % 186.01/186.02 [9828]E(f335(f335(f145(x98281),f335(f196(f928(x98281)),f184(x98281,x98282,x98283))),x98283),f120(x98281))+~P1(f335(x98282,f335(f148(x98281),f335(f335(f145(x98281),f335(f196(f928(x98281)),f184(x98281,x98282,x98283))),x98283)))) % 186.01/186.02 [9921]~P1(f335(f335(f337(f933(x99211,x99211)),x99212),f315(x99211,x99213)))+P1(f335(f335(f337(f933(x99211,x99211)),x99212),f335(f335(f45(a927,f934(f933(x99211,x99211),a922)),f250(f934(a927,a922))),f335(f335(f7(a927,f934(f933(x99211,x99211),a922),f934(f933(x99211,x99211),a922)),f190(f933(x99211,x99211),a922)),x99213)))) % 186.01/186.02 [9983]~P1(f335(f335(f243(f934(x99831,a922)),f335(f335(f45(a927,f934(x99831,a922)),f335(f310(a927,f2(a927)),f457(x99833,x99832,x99831))),x99832)),x99833))+P1(f335(f335(f243(f934(x99831,a922)),f335(f335(f45(a927,f934(x99831,a922)),f250(f934(a927,a922))),x99832)),x99833)) % 186.01/186.02 [10029]~P1(f335(f335(f244(a1),f2(a1)),x100293))+P1(f335(f335(f244(a1),x100291),f335(f335(f86(a1),x100292),f335(f335(f87(a1),f335(f335(f86(a1),f335(f81(a1),f335(f335(f23(a1),x100292),x100291))),f84(a1))),x100293)))) % 186.01/186.02 [10043]~P38(x100431,f335(f335(f117(f934(f933(x100431,x100431),a922)),x100432),x100433))+P38(x100431,f335(f335(f117(f934(f933(x100431,x100431),a922)),f335(f335(f117(f934(f933(x100431,x100431),a922)),f335(f335(f297(x100431,x100431,x100431),x100432),x100432)),f335(f335(f297(x100431,x100431,x100431),x100433),x100432))),x100433)) % 186.01/186.02 [10120]P38(x101201,f335(f335(f117(f934(f933(x101201,x101201),a922)),x101202),x101203))+~P38(x101201,f335(f335(f117(f934(f933(x101201,x101201),a922)),f335(f335(f117(f934(f933(x101201,x101201),a922)),f335(f335(f297(x101201,x101201,x101201),x101202),x101202)),f335(f335(f297(x101201,x101201,x101201),x101203),x101202))),x101203)) % 186.01/186.02 [9693]~P140(x96931)+E(f335(f109(x96931),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x96932),x96933)),f195(f934(f933(a927,a927),a922)))))),f335(f335(f23(x96931),f335(f107(x96931),x96932)),f335(f107(x96931),x96933))) % 186.01/186.02 [9775]P1(f335(x97753,x97752))+E(f335(f270(x97751),f335(f335(f18(x97751,a922,a922),f335(f335(f8(a922,f934(a922,a922),x97751),a333),f335(f335(f7(x97751,x97751,a922),a332),x97752))),x97753)),f195(f934(x97751,a922))) % 186.01/186.02 [9777]~P1(f335(x97773,x97772))+E(f335(f270(x97771),f335(f335(f18(x97771,a922,a922),f335(f335(f8(a922,f934(a922,a922),x97771),a333),f335(f335(f7(x97771,x97771,a922),a332),x97772))),x97773)),f335(f335(f317(x97771),x97772),f195(f934(x97771,a922)))) % 186.01/186.02 [10009]E(x100091,x100092)+P1(f335(f335(f251(x100093,x100093,f335(f335(f8(f934(x100093,a922),f934(x100093,a922),x100093),f335(f8(a922,a922,x100093),a330)),a332)),x100091),x100092)) % 186.01/186.02 [10099]~E(x100991,x100992)+~P1(f335(f335(f251(x100993,x100993,f335(f335(f8(f934(x100993,a922),f934(x100993,a922),x100993),f335(f8(a922,a922,x100993),a330)),a332)),x100991),x100992)) % 186.01/186.02 [10112]~P1(f335(f67(x101121),x101123))+E(f335(f335(f70(x101121,f934(x101121,a922),f335(f335(f8(f934(x101121,a922),f934(f934(x101121,a922),f934(x101121,a922)),x101121),f335(f7(f934(x101121,a922),f934(x101121,a922),f934(x101121,a922)),f23(f934(x101121,a922)))),f335(f335(f7(x101121,f934(x101121,a922),f934(x101121,a922)),f317(x101121)),f195(f934(x101121,a922))))),x101122),x101123),f335(f335(f23(f934(x101121,a922)),x101122),x101123)) % 186.01/186.02 [10142]~P1(f335(f335(f244(a1),f2(a1)),x101423))+P1(f335(f335(f244(a1),f335(f335(f23(a1),x101421),f335(f335(f87(a1),f335(f335(f86(a1),f335(f81(a1),f335(f335(f23(a1),x101421),x101422))),f84(a1))),x101423))),x101422)) % 186.01/186.02 [10407]~P1(f335(f335(f337(x104071),x104073),f324(x104071,x104072)))+P1(f335(f323(x104071,f335(f335(f7(x104071,f934(f933(x104071,x104071),a922),f934(x104071,a922)),f335(f335(f8(f934(x104071,f934(f934(f933(x104071,x104071),a922),a922)),f934(f934(f933(x104071,x104071),a922),f934(x104071,a922)),x104071),f7(x104071,f934(f933(x104071,x104071),a922),a922)),f335(f335(f8(f934(x104071,f933(x104071,x104071)),f934(x104071,f934(f934(f933(x104071,x104071),a922),a922)),x104071),f335(f8(f933(x104071,x104071),f934(f934(f933(x104071,x104071),a922),a922),x104071),f337(f933(x104071,x104071)))),f260(x104071,x104071)))),x104072)),x104073)) % 186.01/186.02 [10422]P1(f335(f335(f337(x104221),x104222),f324(x104221,x104223)))+~P1(f335(f323(x104221,f335(f335(f7(x104221,f934(f933(x104221,x104221),a922),f934(x104221,a922)),f335(f335(f8(f934(x104221,f934(f934(f933(x104221,x104221),a922),a922)),f934(f934(f933(x104221,x104221),a922),f934(x104221,a922)),x104221),f7(x104221,f934(f933(x104221,x104221),a922),a922)),f335(f335(f8(f934(x104221,f933(x104221,x104221)),f934(x104221,f934(f934(f933(x104221,x104221),a922),a922)),x104221),f335(f8(f933(x104221,x104221),f934(f934(f933(x104221,x104221),a922),a922),x104221),f337(f933(x104221,x104221)))),f260(x104221,x104221)))),x104223)),x104222)) % 186.01/186.02 [9981]~P1(f335(f67(x99811),f335(f270(x99811),x99813)))+P1(f335(f67(x99811),f335(f270(x99811),f335(f335(f18(x99811,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99811),a333),x99812)),x99813)))) % 186.01/186.02 [9982]~P1(f335(f67(x99821),f335(f270(x99821),x99822)))+P1(f335(f67(x99821),f335(f270(x99821),f335(f335(f18(x99821,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99821),a333),x99822)),x99823)))) % 186.01/186.02 [10078]P1(f335(f67(x100781),f335(f270(x100781),x100782)))+~P1(f335(f67(x100781),f335(f270(x100781),f335(f335(f18(x100781,a922,a922),f335(f335(f8(a922,f934(a922,a922),x100781),a334),x100783)),x100782)))) % 186.01/186.02 [10079]P1(f335(f67(x100791),f335(f270(x100791),x100792)))+~P1(f335(f67(x100791),f335(f270(x100791),f335(f335(f18(x100791,a922,a922),f335(f335(f8(a922,f934(a922,a922),x100791),a334),x100792)),x100793)))) % 186.01/186.02 [10383]~P1(f335(f67(x103831),x103832))+P1(f335(f67(f928(x103831)),f335(f270(f928(x103831)),f335(f335(f18(f928(x103831),a922,a922),f335(f335(f8(a922,f934(a922,a922),f928(x103831)),a333),f335(f335(f7(f928(x103831),f934(x103831,a922),a922),f335(f335(f8(f934(x103831,a922),f934(f934(x103831,a922),a922),f928(x103831)),f243(f934(x103831,a922))),f179(x103831))),x103832))),f335(f335(f7(f928(x103831),a927,a922),f335(f335(f8(a927,f934(a927,a922),f928(x103831)),a332),f196(f928(x103831)))),x103833))))) % 186.01/186.02 [10384]~P1(f335(f67(x103841),x103842))+P1(f335(f67(f928(x103841)),f335(f270(f928(x103841)),f335(f335(f18(f928(x103841),a922,a922),f335(f335(f8(a922,f934(a922,a922),f928(x103841)),a333),f335(f335(f7(f928(x103841),f934(x103841,a922),a922),f335(f335(f8(f934(x103841,a922),f934(f934(x103841,a922),a922),f928(x103841)),f243(f934(x103841,a922))),f179(x103841))),x103842))),f335(f335(f7(f928(x103841),a927,a922),f335(f335(f8(a927,f934(a927,a922),f928(x103841)),f243(a927)),f196(f928(x103841)))),x103843))))) % 186.01/186.02 [10092]~P118(x100921)+E(f335(f335(f252(x100921),x100922),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x100923)),f335(f335(f87(x100921),f335(f335(f252(x100921),x100922),x100923)),f335(f335(f252(x100921),x100922),x100923))) % 186.01/186.02 [10123]~P81(x101231)+E(f335(f335(f252(x101231),f335(f335(f252(x101231),x101232),x101233)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f252(x101231),x101232),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101233))) % 186.01/186.02 [10182]~P140(x101821)+E(f335(f335(f252(x101821),f335(f85(x101821),x101822)),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101823)),f335(f335(f252(x101821),x101822),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101823))) % 186.01/186.02 [10328]~P113(x103281)+P1(f335(f335(f243(x103281),f2(x103281)),f335(f335(f86(x103281),f335(f335(f252(x103281),x103282),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103281),x103283),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))) % 186.01/186.02 [10192]~P118(x101921)+E(f335(f335(f252(x101921),x101922),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101923))),f335(f335(f87(x101921),x101922),f335(f335(f87(x101921),f335(f335(f252(x101921),x101922),x101923)),f335(f335(f252(x101921),x101922),x101923)))) % 186.01/186.02 [10242]~P81(x102421)+E(f335(f335(f87(x102421),x102422),f335(f335(f252(x102421),f335(f335(f252(x102421),x102422),x102423)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x102421),x102422),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x102423)))) % 186.01/186.02 [10283]~P113(x102831)+P1(f335(f335(f243(x102831),f2(x102831)),f335(f335(f252(x102831),x102832),f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x102833)))) % 186.01/186.02 [10359]~P94(x103591)+E(f335(f335(f23(x103591),f335(f335(f86(x103591),f335(f335(f252(x103591),x103592),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103591),x103593),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f335(f335(f87(x103591),f335(f335(f87(x103591),f335(f110(x103591),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103592)),x103593)),f335(f335(f252(x103591),f335(f335(f23(x103591),x103592),x103593)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [10360]~P94(x103601)+E(f335(f335(f86(x103601),f335(f335(f86(x103601),f335(f335(f252(x103601),x103602),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103601),x103603),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f335(f335(f87(x103601),f335(f335(f87(x103601),f335(f110(x103601),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103602)),x103603)),f335(f335(f252(x103601),f335(f335(f86(x103601),x103602),x103603)),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.02 [4917]E(x49171,x49172)+~E(f32(x49173,x49171),f32(x49174,x49172)) % 186.01/186.02 [4918]E(x49181,x49182)+~E(f32(x49181,x49183),f32(x49182,x49184)) % 186.01/186.02 [4919]E(x49191,x49192)+~E(f31(x49193,x49191),f31(x49194,x49192)) % 186.01/186.02 [4920]E(x49201,x49202)+~E(f31(x49201,x49203),f31(x49202,x49204)) % 186.01/186.02 [4921]E(x49211,x49212)+~E(f27(x49213,x49211),f27(x49214,x49212)) % 186.01/186.02 [4922]E(x49221,x49222)+~E(f27(x49221,x49223),f27(x49222,x49224)) % 186.01/186.02 [8000]P26(x80001,x80002,x80003,x80004)+~E(f438(x80004,x80003,x80002,x80001),f449(x80004,x80003,x80002,x80001)) % 186.01/186.02 [8288]P35(x82881,x82882,x82883,x82884,f120(x82882))+~E(x82884,f120(x82881)) % 186.01/186.02 [8289]P35(x82891,x82892,x82893,f120(x82891),x82894)+~E(x82894,f120(x82892)) % 186.01/186.02 [8824]~P35(x88242,x88243,x88244,x88241,f120(x88243))+E(x88241,f120(x88242)) % 186.01/186.02 [8825]~P35(x88253,x88252,x88254,f120(x88253),x88251)+E(x88251,f120(x88252)) % 186.01/186.02 [5302]~P18(x53023,x53021,x53024)+E(f335(f335(x53021,x53022),x53022),x53022) % 186.01/186.02 [5552]P1(f335(x55522,x55524))+E(f335(f143(x55521,x55522),f176(x55521,x55523,x55524)),f120(x55521)) % 186.01/186.02 [5589]~E(x55894,f195(f934(x55891,a922)))+E(f335(f318(x55891,x55892,x55893),x55894),f195(f934(x55892,a922))) % 186.01/186.02 [5832]~P1(f335(x58322,x58324))+E(f335(f143(x58321,x58322),f176(x58321,x58323,x58324)),f176(x58321,x58323,x58324)) % 186.01/186.02 [5861]~E(f335(f318(x58612,x58613,x58614),x58611),f195(f934(x58613,a922)))+E(x58611,f195(f934(x58612,a922))) % 186.01/186.02 [6048]~P8(x60481,x60483)+E(f279(x60481,x60482,f278(x60481,x60483),x60484),x60484) % 186.01/186.02 [6151]~P109(x61512)+E(f335(f335(f155(x61511,x61512,x61513),x61514),f120(x61511)),f335(f335(f158(x61511),x61514),f120(x61511))) % 186.01/186.02 [6506]~E(x65061,f195(f934(x65062,a922)))+~P1(f335(f68(x65062,x65063,x65061),x65064)) % 186.01/186.02 [6528]~P60(x65281,x65283,x65284,x65282)+P1(f335(f67(x65281),x65282)) % 186.01/186.02 [6530]~P60(x65301,x65303,x65302,x65304)+P1(f335(f67(x65301),x65302)) % 186.01/186.02 [6537]~P60(x65372,x65373,x65374,x65371)+~E(x65371,f195(f934(x65372,a922))) % 186.01/186.02 [6569]~P110(x65691)+E(f335(f335(f108(f934(x65691,a922)),f335(f310(x65691,x65692),x65693)),f311(x65691,x65693,x65694)),f195(f934(x65691,a922))) % 186.01/186.02 [6595]~P1(f335(f335(x65953,x65954),x65952))+P1(f335(f335(f337(x65951),x65952),f303(x65951,x65953,x65954))) % 186.01/186.02 [6596]~P1(f335(f335(x65963,x65964),x65962))+P1(f335(f335(f337(x65961),x65962),f302(x65961,x65963,x65964))) % 186.01/186.02 [6597]~P1(f335(f335(x65973,x65972),x65974))+P1(f335(f335(f337(x65971),x65972),f306(x65971,x65973,x65974))) % 186.01/186.02 [6598]~P1(f335(f335(x65983,x65982),x65984))+P1(f335(f335(f337(x65981),x65982),f304(x65981,x65983,x65984))) % 186.01/186.02 [6661]~P50(x66614,x66611,x66612,x66613)+P1(f335(f335(x66611,x66612),x66613)) % 186.01/186.02 [6738]~P110(x67381)+E(f335(f335(f108(f934(x67381,a922)),f314(x67381,x67382,x67383)),f311(x67381,x67383,x67384)),f195(f934(x67381,a922))) % 186.01/186.02 [6739]~P110(x67391)+E(f335(f335(f108(f934(x67391,a922)),f313(x67391,x67392,x67393)),f314(x67391,x67393,x67394)),f195(f934(x67391,a922))) % 186.01/186.02 [6740]~P110(x67401)+E(f335(f335(f108(f934(x67401,a922)),f313(x67401,x67402,x67403)),f313(x67401,x67403,x67404)),f195(f934(x67401,a922))) % 186.01/186.02 [6741]~P110(x67411)+E(f335(f335(f108(f934(x67411,a922)),f311(x67411,x67412,x67413)),f314(x67411,x67413,x67414)),f195(f934(x67411,a922))) % 186.01/186.02 [6742]~P110(x67421)+E(f335(f335(f108(f934(x67421,a922)),f311(x67421,x67422,x67423)),f313(x67421,x67423,x67424)),f195(f934(x67421,a922))) % 186.01/186.02 [6780]P1(f335(f335(x67801,x67802),f890(x67802,x67801)))+~P1(f335(f257(x67803,x67804,x67801),x67802)) % 186.01/186.02 [6784]~P50(x67841,x67842,x67843,x67844)+~P1(f335(f335(x67842,x67844),x67843)) % 186.01/186.02 [6860]~P109(x68602)+E(f335(f179(x68601),f157(x68601,x68602,x68603,x68604)),f335(f179(x68601),x68604)) % 186.01/186.02 [6910]~P146(x69101)+E(f197(x69101,x69102,f335(a119,x69103),x69104),f197(x69101,x69102,x69103,f335(x69102,x69104))) % 186.01/186.02 [6972]~P1(f335(f335(f337(x69724),x69723),f303(x69724,x69721,x69722)))+P1(f335(f335(x69721,x69722),x69723)) % 186.01/186.02 [6973]~P1(f335(f335(f337(x69734),x69733),f302(x69734,x69731,x69732)))+P1(f335(f335(x69731,x69732),x69733)) % 186.01/186.02 [6974]~P1(f335(f335(f337(x69744),x69742),f306(x69744,x69741,x69743)))+P1(f335(f335(x69741,x69742),x69743)) % 186.01/186.02 [6975]~P1(f335(f335(f337(x69754),x69752),f304(x69754,x69751,x69753)))+P1(f335(f335(x69751,x69752),x69753)) % 186.01/186.02 [7049]E(f335(f41(f935(x70491,x70492)),f321(x70491,x70492,x70493,x70494)),f2(a927))+P1(f335(f67(x70492),x70494)) % 186.01/186.02 [7050]E(f335(f41(f935(x70501,x70502)),f321(x70501,x70502,x70503,x70504)),f2(a927))+P1(f335(f67(x70501),x70503)) % 186.01/186.02 [7248]~P15(x72484,x72481,x72482)+E(f335(f78(x72481,x72481,x72481,f335(x72482,x72483)),f335(x72482,x72483)),f335(x72482,x72483)) % 186.01/186.02 [7488]E(f285(x74881,x74882,x74883,x74884),f335(f260(f934(a106,f934(a922,f931(f929(x74881)))),f933(a106,a106)),f47(x74881)))+~P1(f335(f335(f243(a106),x74883),f2(a106))) % 186.01/186.02 [8119]~E(x81192,x81193)+P1(f335(f335(f337(f933(x81191,x81191)),f335(f335(f260(x81191,x81191),x81192),x81193)),f315(x81191,x81194))) % 186.01/186.02 [8148]~P26(x81481,x81482,x81483,f250(f934(x81481,a922)))+E(f335(f83(x81481,x81482,f250(f934(x81481,a922)),x81483),f335(x81483,x81484)),x81484) % 186.01/186.02 [8149]~P26(x81491,x81492,x81493,f250(f934(x81491,a922)))+E(f335(f97(x81491,x81492,f250(f934(x81491,a922)),x81493),f335(x81493,x81494)),x81494) % 186.01/186.02 [8237]~P1(f335(f335(f337(f928(x82371)),f335(f335(f158(x82371),x82374),x82372)),f168(x82371,x82373)))+P1(f335(f335(f337(f928(x82371)),x82372),f168(x82371,x82373))) % 186.01/186.02 [8238]~P1(f335(f335(f337(f928(x82381)),f335(f335(f141(x82381),x82384),x82382)),f168(x82381,x82383)))+P1(f335(f335(f337(f928(x82381)),x82382),f168(x82381,x82383))) % 186.01/186.02 [8239]~P1(f335(f335(f337(f928(x82391)),f335(f335(f141(x82391),x82392),x82394)),f168(x82391,x82393)))+P1(f335(f335(f337(f928(x82391)),x82392),f168(x82391,x82393))) % 186.01/186.02 [8250]~P109(x82501)+P14(x82501,f335(f335(f161(x82502,x82501),x82503),f157(x82502,x82501,x82503,x82504))) % 186.01/186.02 [8350]P26(x83504,x83503,x83501,x83502)+E(f335(x83501,f438(x83502,x83501,x83503,x83504)),f335(x83501,f449(x83502,x83501,x83503,x83504))) % 186.01/186.02 [8457]~P26(x84572,x84571,x84574,x84573)+P26(x84571,x84572,f83(x84572,x84571,x84573,x84574),f335(f318(x84572,x84571,x84574),x84573)) % 186.01/186.02 [8597]P38(f933(x85972,x85974),f288(x85972,x85974,x85971,x85973))+P1(f335(x85971,f915(x85972,x85973,x85974,x85971))) % 186.01/186.02 [8712]E(x87121,x87122)+~P1(f335(f335(f337(f933(x87123,x87123)),f335(f335(f260(x87123,x87123),x87121),x87122)),f271(x87123,x87124))) % 186.01/186.02 [8776]~P1(f335(f67(f935(x87763,x87761)),f321(x87763,x87761,x87764,x87762)))+P1(f335(f67(x87761),x87762)) % 186.01/186.02 [8777]~P1(f335(f67(f935(x87771,x87773)),f321(x87771,x87773,x87772,x87774)))+P1(f335(f67(x87771),x87772)) % 186.01/186.02 [8786]~P26(x87861,x87862,x87863,x87864)+P27(x87861,x87862,x87863,x87864,f335(f318(x87861,x87862,x87863),x87864)) % 186.01/186.02 [8787]P12(x87871,x87872,x87873,x87874)+~E(f335(x87874,f894(x87872,x87874,x87873,x87871)),f335(x87874,f895(x87872,x87874,x87873,x87871))) % 186.01/186.02 [8877]~P27(x88772,x88773,x88774,x88771,f195(f934(x88773,a922)))+E(x88771,f195(f934(x88772,a922))) % 186.01/186.02 [8878]~P27(x88783,x88782,x88784,f195(f934(x88783,a922)),x88781)+E(x88781,f195(f934(x88782,a922))) % 186.01/186.02 [8970]P38(f933(x89701,x89702),f288(x89701,x89702,x89703,x89704))+~P38(x89702,f335(x89704,f915(x89701,x89704,x89702,x89703))) % 186.01/186.02 [9533]E(f335(f335(f166(x95331,x95332),f692(x95333,x95334,x95332,x95331)),f693(x95333,x95334,x95332,x95331)),x95334)+~P1(f335(f335(f337(f933(f928(x95331),f928(x95331))),f335(f335(f260(f928(x95331),f928(x95331)),x95332),x95334)),f164(x95331,x95333))) % 186.01/186.02 [9538]~P1(f335(f335(f337(f933(f928(x95381),f928(x95381))),f335(f335(f260(f928(x95381),f928(x95381)),x95382),x95383)),f152(x95381,x95384)))+P1(f335(f335(f337(f933(f928(x95381),f928(x95381))),f335(f335(f260(f928(x95381),f928(x95381)),x95382),x95383)),f154(x95381,x95384))) % 186.01/186.02 [9647]P1(f335(f67(x96471),x96472))+~P1(f335(f335(f337(f933(f934(x96471,a922),f934(x96471,a922))),f335(f335(f260(f934(x96471,a922),f934(x96471,a922)),x96473),x96472)),f327(x96471,x96474))) % 186.01/186.02 [9648]P1(f335(f67(x96481),x96482))+~P1(f335(f335(f337(f933(f934(x96481,a922),f934(x96481,a922))),f335(f335(f260(f934(x96481,a922),f934(x96481,a922)),x96482),x96483)),f327(x96481,x96484))) % 186.01/186.02 [9651]~E(x96511,f195(f934(x96512,a922)))+~P1(f335(f335(f337(f933(f934(x96512,a922),f934(x96512,a922))),f335(f335(f260(f934(x96512,a922),f934(x96512,a922)),x96513),x96511)),f327(x96512,x96514))) % 186.01/186.02 [10294]P12(x102941,x102942,x102943,x102944)+~P1(f335(f335(f265(x102941,x102941,a922),f335(f335(f7(x102941,f934(x102941,x102942),f934(x102941,a922)),f335(f335(f8(f934(x102942,a922),f934(f934(x102941,x102942),f934(x102941,a922)),x102941),f8(x102942,a922,x102941)),f335(f335(f8(x102942,f934(x102942,a922),x102941),a332),x102944))),x102944)),f578(x102944,x102943,x102942,x102941))) % 186.01/186.02 [5201]~E(x52012,f120(x52011))+E(f335(f335(f166(x52011,x52012),x52013),x52014),f120(x52011)) % 186.01/186.02 [5202]~E(x52024,f120(x52021))+E(f335(f335(f161(x52021,x52022),x52023),x52024),f120(x52022)) % 186.01/186.02 [5435]E(x54351,f120(x54352))+~E(f335(f335(f161(x54352,x54353),x54354),x54351),f120(x54353)) % 186.01/186.02 [5436]E(x54361,f120(x54362))+~E(f335(f335(f166(x54362,x54361),x54363),x54364),f120(x54362)) % 186.01/186.02 [5473]E(x54731,x54732)+~E(f335(f335(f141(x54733),x54734),x54731),f335(f335(f141(x54733),x54734),x54732)) % 186.01/186.02 [5474]E(x54741,x54742)+~E(f335(f335(f141(x54743),x54741),x54744),f335(f335(f141(x54743),x54742),x54744)) % 186.01/186.02 [5625]P1(f335(x56253,x56252))+E(f177(x56251,x56252,f335(f143(x56251,x56253),x56254)),f335(f143(x56251,x56253),x56254)) % 186.01/186.02 [5627]~P1(f335(x56272,x56273))+P34(x56271,x56272,f335(f335(f158(x56271),x56273),x56274)) % 186.01/186.02 [5636]E(x56361,x56362)+~E(f146(a927,f335(f310(a927,x56361),x56363)),f335(f335(f158(a927),x56362),x56364)) % 186.01/186.02 [5685]~P38(x56852,x56853)+P38(x56851,f335(f335(f296(x56852,x56851),x56853),x56854)) % 186.01/186.02 [5686]~P28(x56862,x56863)+P28(x56861,f335(f335(f79(x56862,x56861),x56863),x56864)) % 186.01/186.02 [5687]~P39(x56872,x56873)+P39(x56871,f335(f335(f296(x56872,x56871),x56873),x56874)) % 186.01/186.02 [5688]~P53(x56882,x56883)+P53(x56881,f335(f335(f296(x56882,x56881),x56883),x56884)) % 186.01/186.02 [5816]~P34(x58161,x58162,x58164)+P34(x58161,x58162,f335(f335(f158(x58161),x58163),x58164)) % 186.01/186.02 [5817]~P34(x58171,x58172,x58174)+P34(x58171,x58172,f335(f335(f141(x58171),x58173),x58174)) % 186.01/186.02 [5818]~P34(x58181,x58182,x58183)+P34(x58181,x58182,f335(f335(f141(x58181),x58183),x58184)) % 186.01/186.02 [5904]~E(x59041,f120(x59042))+~E(f335(f335(f141(x59042),x59043),f335(f335(f158(x59042),x59044),f120(x59042))),x59041) % 186.01/186.02 [5929]~P32(x59293,x59291,f335(f335(f158(x59293),x59292),x59294))+P1(f335(x59291,x59292)) % 186.01/186.02 [5939]E(f121(x59391,x59392),x59393)+~E(f335(f335(f141(x59391),x59393),f335(f335(f158(x59391),x59394),f120(x59391))),x59392) % 186.01/186.02 [5940]E(f151(x59401,x59402),x59403)+~E(f335(f335(f141(x59401),x59404),f335(f335(f158(x59401),x59403),f120(x59401))),x59402) % 186.01/186.02 [6050]~E(f146(a927,f335(f310(a927,x60501),x60502)),f335(f335(f158(a927),x60503),x60504))+P1(f335(f335(f244(a927),x60501),x60502)) % 186.01/186.02 [6059]P32(x60591,x60592,x60593)+~P32(x60591,x60592,f335(f335(f158(x60591),x60594),x60593)) % 186.01/186.02 [6060]P32(x60601,x60602,x60603)+~P32(x60601,x60602,f335(f335(f141(x60601),x60604),x60603)) % 186.01/186.02 [6061]P32(x60611,x60612,x60613)+~P32(x60611,x60612,f335(f335(f141(x60611),x60613),x60614)) % 186.01/186.02 [6254]E(x62541,f335(f335(f141(x62542),f335(f175(x62542),x62543)),f335(f335(f158(x62542),x62544),f120(x62542))))+~E(f335(f175(x62542),x62541),f335(f335(f158(x62542),x62544),x62543)) % 186.01/186.02 [6428]~P110(x64281)+E(f335(f335(f108(f934(x64281,a922)),f335(f310(x64281,x64282),x64283)),f335(f310(x64281,x64283),x64284)),f195(f934(x64281,a922))) % 186.01/186.02 [6439]E(f335(f335(f171(x64391),f176(x64391,x64392,x64393)),x64394),x64393)+~P1(f335(f335(f244(a927),x64394),x64392)) % 186.01/186.02 [6466]~P76(x64661)+E(f335(f172(x64661),f335(f335(f161(a1,x64661),x64662),f185(x64663,x64664))),f335(f335(f6(a1,x64661),x64662),f335(f179(a1),f185(x64663,x64664)))) % 186.01/186.02 [6467]~P76(x64671)+E(f335(f335(f6(a1,x64671),x64672),f335(f179(a1),f185(x64673,x64674))),f335(f172(x64671),f335(f335(f161(a1,x64671),x64672),f185(x64673,x64674)))) % 186.01/186.02 [6608]~E(x66082,f335(f335(f141(x66081),f335(f175(x66081),x66084)),f335(f335(f158(x66081),x66083),f120(x66081))))+E(f335(f175(x66081),x66082),f335(f335(f158(x66081),x66083),x66084)) % 186.01/186.02 [6624]~P20(x66242,x66243,x66244,x66241)+E(f335(x66241,f195(f934(x66242,a922))),f25(x66243)) % 186.01/186.02 [6650]~P110(x66501)+E(f335(f335(f108(f934(x66501,a922)),f314(x66501,x66502,x66503)),f335(f310(x66501,x66503),x66504)),f195(f934(x66501,a922))) % 186.01/186.02 [6861]E(x68611,f195(f934(x68612,a922)))+~E(f321(x68613,x68612,x68614,x68611),f195(f934(f935(x68613,x68612),a922))) % 186.01/186.02 [6862]E(x68621,f195(f934(x68622,a922)))+~E(f321(x68622,x68623,x68621,x68624),f195(f934(f935(x68622,x68623),a922))) % 186.01/186.02 [6931]~P109(x69312)+E(f335(f196(f928(x69311)),f157(x69311,x69312,x69313,x69314)),f335(f196(f928(x69311)),x69314)) % 186.01/186.02 [6942]~P1(f335(f258(x69423,x69424,x69421),x69422))+P1(f335(f335(x69421,f891(x69422,x69421)),x69422)) % 186.01/186.02 [6983]~P1(f335(f67(x69832),x69834))+P1(f335(f67(x69831),f335(f318(x69832,x69831,x69833),x69834))) % 186.01/186.02 [7210]~P26(x72102,x72101,x72103,x72104)+E(f335(f41(x72101),f335(f318(x72102,x72101,x72103),x72104)),f335(f41(x72102),x72104)) % 186.01/186.02 [7228]E(f335(f318(x72281,x72282,x72283),f335(f319(x72281,x72282,x72283),x72284)),x72284)+~E(f335(f318(x72281,x72282,x72283),f250(f934(x72281,a922))),f250(f934(x72282,a922))) % 186.01/186.02 [7642]~P26(x76421,x76422,x76423,f250(f934(x76421,a922)))+E(f335(f319(x76421,x76422,x76423),f335(f318(x76421,x76422,x76423),x76424)),x76424) % 186.01/186.02 [7918]E(x79181,x79182)+~P1(f335(f335(f337(x79183),x79181),f335(f179(x79183),f176(x79183,x79184,x79182)))) % 186.01/186.02 [7927]~E(x79271,f2(a927))+~P1(f335(f335(f337(x79272),x79273),f335(f179(x79272),f176(x79272,x79271,x79274)))) % 186.01/186.02 [7960]P1(f335(x79601,x79602))+~P1(f335(f335(f337(x79603),x79602),f335(f179(x79603),f184(x79603,x79601,x79604)))) % 186.01/186.02 [8066]~P1(f335(f335(f337(f928(x80661)),f335(f335(f158(x80661),x80662),x80664)),f168(x80661,x80663)))+P1(f335(f335(f337(x80661),x80662),x80663)) % 186.01/186.02 [8194]~P1(f335(f335(f337(x81941),x81942),f335(f179(x81941),f183(x81941,x81943,x81944))))+P1(f335(f335(f337(x81941),x81942),f335(f179(x81941),x81943))) % 186.01/186.02 [8195]~P1(f335(f335(f337(x81951),x81952),f335(f179(x81951),f177(x81951,x81954,x81953))))+P1(f335(f335(f337(x81951),x81952),f335(f179(x81951),x81953))) % 186.01/186.02 [8196]~P1(f335(f335(f337(x81961),x81962),f335(f179(x81961),f184(x81961,x81964,x81963))))+P1(f335(f335(f337(x81961),x81962),f335(f179(x81961),x81963))) % 186.01/186.02 [8206]E(f335(f196(f928(x82061)),x82062),x82063)+~P1(f335(f335(f337(f928(x82061)),x82062),f335(f179(f928(x82061)),f61(x82061,x82063,x82064)))) % 186.01/186.02 [8301]P1(f335(x83013,x83012))+E(f335(f143(x83011,f335(f335(f8(a922,a922,x83011),a330),f335(a332,x83012))),f335(f143(x83011,x83013),x83014)),f335(f143(x83011,x83013),x83014)) % 186.01/186.02 [8408]E(f335(f335(f171(x84081),f184(x84081,x84082,x84083)),x84084),f335(f335(f171(x84081),x84083),x84084))+~P1(f335(f335(f244(a927),x84084),f335(f196(f928(x84081)),f184(x84081,x84082,x84083)))) % 186.01/186.02 [8495]~P76(x84951)+E(f335(f335(f6(a927,x84951),f335(f335(f8(a927,x84951,a927),x84952),a119)),f335(f310(a927,x84953),x84954)),f335(f335(f6(a927,x84951),x84952),f335(f310(a927,f335(a119,x84953)),f335(a119,x84954)))) % 186.01/186.02 [8505]~P76(x85051)+E(f335(f335(f6(a927,x85051),f335(f335(f8(a927,x85051,a927),x85052),a119)),f311(a927,x85053,x85054)),f335(f335(f6(a927,x85051),x85052),f311(a927,f335(a119,x85053),f335(a119,x85054)))) % 186.01/186.02 [8633]~P26(x86331,x86333,x86334,f250(f934(x86331,a922)))+P26(x86331,f934(x86332,x86333),f335(f335(f8(x86333,f934(x86332,x86333),x86331),f16(x86333,x86332)),x86334),f250(f934(x86331,a922))) % 186.01/186.02 [8718]~P26(x87182,x87181,x87184,x87183)+E(f335(f318(x87181,x87182,f83(x87182,x87181,x87183,x87184)),f335(f318(x87182,x87181,x87184),x87183)),x87183) % 186.01/186.02 [8778]~P1(f335(f335(f337(f933(x87781,x87781)),f335(f335(f260(x87781,x87781),x87782),x87784)),f271(x87781,x87783)))+P1(f335(f335(f337(x87781),x87782),x87783)) % 186.01/186.02 [8901]~P26(x89012,x89011,x89013,f250(f934(x89012,a922)))+E(f335(f318(x89011,x89012,f97(x89012,x89011,f250(f934(x89012,a922)),x89013)),f335(f318(x89012,x89011,x89013),x89014)),x89014) % 186.01/186.02 [8976]~P27(x89761,x89762,x89763,x89764,f250(f934(x89762,a922)))+E(f335(f318(x89761,x89762,x89763),f250(f934(x89761,a922))),f250(f934(x89762,a922))) % 186.01/186.02 [9009]~E(f335(f335(f6(x90091,a927),x90094),x90093),f335(a119,x90092))+P1(f335(f335(f337(x90091),f594(x90092,x90093,x90094,x90091)),x90093)) % 186.01/186.02 [9030]~E(f335(f335(f6(x90304,a927),x90301),x90303),f335(a119,x90302))+P1(f335(f335(f244(a927),f2(a927)),f335(x90301,f594(x90302,x90303,x90301,x90304)))) % 186.01/186.02 [9041]~P1(f335(f67(x90412),x90414))+P1(f335(f335(f243(a927),f335(f41(x90411),f335(f318(x90412,x90411,x90413),x90414))),f335(f41(x90412),x90414))) % 186.01/186.02 [9042]E(f335(f335(f260(x90421,x90422),f664(x90423,x90424,x90422,x90421)),f665(x90423,x90424,x90422,x90421)),x90424)+~P1(f335(f335(f337(f933(x90421,x90422)),x90424),f335(f294(x90422,x90421),x90423))) % 186.01/186.02 [9050]P26(x90501,x90502,x90503,x90504)+P1(f335(f335(f337(x90501),f438(x90504,x90503,x90502,x90501)),x90504)) % 186.01/186.02 [9051]P26(x90511,x90512,x90513,x90514)+P1(f335(f335(f337(x90511),f449(x90514,x90513,x90512,x90511)),x90514)) % 186.01/186.02 [9119]P12(x91191,x91192,x91193,x91194)+P1(f335(f335(f337(f933(x91191,x91191)),f578(x91194,x91193,x91192,x91191)),x91193)) % 186.01/186.02 [9177]P1(f335(x91771,x91772))+~P1(f335(x91771,f335(f335(f260(x91773,x91774),f368(x91774,x91773,x91771)),f369(x91774,x91773,x91771)))) % 186.01/186.02 [9194]E(f335(f196(f928(x91941)),x91942),f335(f196(f928(x91941)),x91943))+~P1(f335(f335(f337(f933(f928(x91941),f928(x91941))),f335(f335(f260(f928(x91941),f928(x91941)),x91942),x91943)),f152(x91941,x91944))) % 186.01/186.02 [9195]E(f335(f196(f928(x91951)),x91952),f335(f196(f928(x91951)),x91953))+~P1(f335(f335(f337(f933(f928(x91951),f928(x91951))),f335(f335(f260(f928(x91951),f928(x91951)),x91952),x91953)),f164(x91951,x91954))) % 186.01/186.02 [9198]E(f335(f196(f928(x91981)),x91982),f335(f196(f928(x91981)),x91983))+~P1(f335(f335(f337(f933(f928(x91981),f928(x91981))),f335(f335(f260(f928(x91981),f928(x91981)),x91982),x91983)),f165(x91981,x91984))) % 186.01/186.02 [9267]P1(f335(f335(f243(a927),f162(x92671,x92672,x92673)),f162(x92671,x92674,x92673)))+P1(f335(f335(f337(x92671),f691(x92674,x92672,x92673,x92671)),f335(f179(x92671),x92673))) % 186.01/186.02 [9270]E(f335(f196(f928(x92701)),x92702),f335(f196(f928(x92701)),x92703))+~P1(f335(f335(f337(f933(f928(x92701),f928(x92701))),f335(f335(f260(f928(x92701),f928(x92701)),x92702),x92703)),f315(f928(x92701),f164(x92701,x92704)))) % 186.01/186.02 [9504]~P26(x95041,x95042,x95043,x95044)+~P1(f335(f335(f244(a927),f335(f41(x95042),f335(f318(x95041,x95042,x95043),x95044))),f335(f41(x95041),x95044))) % 186.01/186.02 [9551]~P1(f335(f335(f337(f933(f928(x95511),f928(x95511))),f335(f335(f260(f928(x95511),f928(x95511)),x95512),x95513)),f164(x95511,x95514)))+P1(f335(f335(f337(f933(f928(x95511),f928(x95511))),f335(f335(f260(f928(x95511),f928(x95511)),x95512),x95513)),f165(x95511,f315(x95511,x95514)))) % 186.01/186.02 [9555]~P1(f335(f335(f337(f933(f928(x95551),f928(x95551))),f335(f335(f260(f928(x95551),f928(x95551)),x95552),x95553)),f165(x95551,x95554)))+P1(f335(f335(f337(f933(f928(x95551),f928(x95551))),f335(f335(f260(f928(x95551),f928(x95551)),x95552),x95553)),f315(f928(x95551),f164(x95551,x95554)))) % 186.01/186.02 [9571]P1(f335(f335(f337(f933(x95711,x95711)),f335(f335(f260(x95711,x95711),x95712),x95713)),f315(x95711,x95714)))+~P1(f335(f335(f337(f933(x95711,x95711)),f335(f335(f260(x95711,x95711),x95712),x95713)),f335(f335(f297(x95711,x95711,x95711),x95714),f315(x95711,x95714)))) % 186.01/186.02 [9756]E(f335(f335(f141(x97561),f710(x97562,x97563,x97564,x97561)),f335(f335(f158(x97561),f708(x97562,x97563,x97564,x97561)),f711(x97562,x97563,x97564,x97561))),x97564)+~P1(f335(f335(f337(f933(f928(x97561),f928(x97561))),f335(f335(f260(f928(x97561),f928(x97561)),x97564),x97563)),f164(x97561,x97562))) % 186.01/186.02 [9757]E(f335(f335(f141(x97571),f710(x97572,x97573,x97574,x97571)),f335(f335(f158(x97571),f709(x97572,x97573,x97574,x97571)),f711(x97572,x97573,x97574,x97571))),x97573)+~P1(f335(f335(f337(f933(f928(x97571),f928(x97571))),f335(f335(f260(f928(x97571),f928(x97571)),x97574),x97573)),f164(x97571,x97572))) % 186.01/186.02 [9835]P1(f335(f335(f337(f933(x98351,x98351)),f335(f335(f260(x98351,x98351),x98352),f642(x98353,x98354,x98352,x98351))),f315(x98351,x98353)))+~P1(f335(f335(f337(f933(x98351,x98351)),f335(f335(f260(x98351,x98351),x98352),x98354)),f335(f335(f297(x98351,x98351,x98351),x98353),f315(x98351,x98353)))) % 186.01/186.02 [9904]P1(f335(f335(f243(a927),f162(x99041,x99042,x99043)),f162(x99041,x99044,x99043)))+~P1(f335(f335(f244(a927),f335(x99042,f691(x99044,x99042,x99043,x99041))),f335(x99044,f691(x99044,x99042,x99043,x99041)))) % 186.01/186.02 [9977]P1(f335(f335(f337(f933(x99771,x99771)),f335(f335(f260(x99771,x99771),f636(x99772,x99773,x99774,x99771)),x99773)),f315(x99771,x99772)))+~P1(f335(f335(f337(f933(x99771,x99771)),f335(f335(f260(x99771,x99771),x99774),x99773)),f335(f335(f297(x99771,x99771,x99771),x99772),f315(x99771,x99772)))) % 186.01/186.02 [5454]~E(x54542,x54543)+E(f177(x54541,x54542,f335(f335(f158(x54541),x54543),x54544)),x54544) % 186.01/186.02 [5582]P1(f335(x55822,x55823))+E(f184(x55821,x55822,f335(f335(f158(x55821),x55823),x55824)),f120(x55821)) % 186.01/186.02 [5648]~P84(x56482)+E(f335(f335(f85(f934(x56481,x56482)),x56483),x56484),f335(f85(x56482),f335(x56483,x56484))) % 186.01/186.02 [5661]~E(x56612,f2(a927))+E(f335(f335(f145(x56611),x56612),f335(f335(f158(x56611),x56613),x56614)),f335(f335(f158(x56611),x56613),x56614)) % 186.01/186.02 [5662]P1(f335(x56622,x56623))+E(f335(f143(x56621,x56622),f335(f335(f158(x56621),x56623),x56624)),f335(f143(x56621,x56622),x56624)) % 186.01/186.02 [5799]~E(x57992,x57994)+P1(f335(f335(f335(f317(x57991),x57992),x57993),x57994)) % 186.01/186.02 [5807]E(x58071,f120(x58072))+E(f151(x58073,f335(f335(f161(x58072,x58073),x58074),x58071)),f335(x58074,f151(x58072,x58071))) % 186.01/186.02 [5821]~E(x58211,f69(x58212,x58214))+E(f335(x58211,f335(f335(f317(x58212),x58213),f195(f934(x58212,a922)))),x58213) % 186.01/186.02 [5856]E(x58561,f120(x58562))+E(f335(f148(x58563),f335(f335(f161(x58562,x58563),x58564),x58561)),f335(x58564,f335(f148(x58562),x58561))) % 186.01/186.02 [5959]~P1(f335(x59593,x59594))+P1(f335(f335(f335(f317(x59591),x59592),x59593),x59594)) % 186.01/186.02 [6078]~P19(x60782,x60784,x60781)+E(f335(x60781,f335(f335(f317(x60782),x60783),f195(f934(x60782,a922)))),x60783) % 186.01/186.02 [6104]~E(x61042,x61043)+P1(f335(f335(f337(x61041),x61042),f335(f335(f317(x61041),x61043),x61044))) % 186.01/186.02 [6109]~P118(x61091)+E(f335(f335(f87(x61091),x61092),f335(f335(f87(x61091),x61093),x61094)),f335(f335(f87(x61091),x61093),f335(f335(f87(x61091),x61092),x61094))) % 186.01/186.02 [6111]~P97(x61111)+E(f335(f335(f108(x61111),x61112),f335(f335(f108(x61111),x61113),x61114)),f335(f335(f108(x61111),x61113),f335(f335(f108(x61111),x61112),x61114))) % 186.01/186.02 [6112]~P98(x61121)+E(f335(f335(f108(x61121),x61122),f335(f335(f108(x61121),x61123),x61124)),f335(f335(f108(x61121),x61123),f335(f335(f108(x61121),x61122),x61124))) % 186.01/186.02 [6113]~P98(x61131)+E(f335(f335(f117(x61131),x61132),f335(f335(f117(x61131),x61133),x61134)),f335(f335(f117(x61131),x61133),f335(f335(f117(x61131),x61132),x61134))) % 186.01/186.02 [6115]~P103(x61151)+E(f335(f335(f117(x61151),x61152),f335(f335(f117(x61151),x61153),x61154)),f335(f335(f117(x61151),x61153),f335(f335(f117(x61151),x61152),x61154))) % 186.01/186.02 [6116]~P118(x61161)+E(f335(f335(f86(x61161),x61162),f335(f335(f86(x61161),x61163),x61164)),f335(f335(f86(x61161),x61163),f335(f335(f86(x61161),x61162),x61164))) % 186.01/186.02 [6118]~P109(x61181)+E(f335(f335(f241(x61181),x61182),f335(f335(f241(x61181),x61183),x61184)),f335(f335(f241(x61181),x61183),f335(f335(f241(x61181),x61182),x61184))) % 186.01/186.02 [6120]~P109(x61201)+E(f335(f335(f242(x61201),x61202),f335(f335(f242(x61201),x61203),x61204)),f335(f335(f242(x61201),x61203),f335(f335(f242(x61201),x61202),x61204))) % 186.01/186.02 [6125]E(x61251,x61252)+E(f177(x61253,x61251,f335(f335(f158(x61253),x61252),x61254)),f335(f335(f158(x61253),x61252),f177(x61253,x61251,x61254))) % 186.01/186.02 [6138]~P1(f335(x61382,x61383))+E(f335(f143(x61381,x61382),f335(f335(f158(x61381),x61383),x61384)),f335(f335(f158(x61381),x61383),f335(f143(x61381,x61382),x61384))) % 186.01/186.02 [6274]~P1(f335(x62742,x62743))+E(f184(x62741,x62742,f335(f335(f158(x62741),x62743),x62744)),f335(f335(f158(x62741),x62743),f184(x62741,x62742,x62744))) % 186.01/186.02 [6338]E(x63381,f195(f934(x63382,a922)))+E(f335(f335(f45(x63382,f934(x63383,a922)),x63381),f335(f16(f934(x63383,a922),x63382),x63384)),x63384) % 186.01/186.02 [6339]E(x63391,f195(f934(x63392,a922)))+E(f335(f335(f46(x63392,f934(x63393,a922)),x63391),f335(f16(f934(x63393,a922),x63392),x63394)),x63394) % 186.01/186.02 [6348]~E(x63484,f195(f934(x63482,a922)))+E(f335(f335(f262(x63481,x63482),x63483),f335(f16(f934(x63482,a922),x63481),x63484)),f195(f934(f933(x63481,x63482),a922))) % 186.01/186.02 [6349]~E(x63493,f195(f934(x63491,a922)))+E(f335(f335(f262(x63491,x63492),x63493),f335(f16(f934(x63492,a922),x63491),x63494)),f195(f934(f933(x63491,x63492),a922))) % 186.01/186.02 [6401]E(x64011,f2(a927))+E(f335(f335(f145(x64012),x64011),f335(f335(f158(x64012),x64013),x64014)),f335(f335(f145(x64012),f335(f335(f23(a927),x64011),f84(a927))),x64014)) % 186.01/186.02 [6422]E(x64221,f195(f934(x64222,a922)))+E(f335(f318(x64222,x64223,f335(f16(x64223,x64222),x64224)),x64221),f335(f335(f317(x64223),x64224),f195(f934(x64223,a922)))) % 186.01/186.02 [6425]E(f335(f319(x64251,x64252,f335(f16(x64252,x64251),x64253)),x64254),f195(f934(x64251,a922)))+P1(f335(f335(f337(x64252),x64253),x64254)) % 186.01/186.02 [6490]~E(x64903,f195(f934(x64901,a922)))+E(f335(f335(f45(x64901,f934(x64902,a922)),x64903),f335(f16(f934(x64902,a922),x64901),x64904)),f195(f934(x64902,a922))) % 186.01/186.02 [6491]~E(x64913,f195(f934(x64911,a922)))+E(f335(f335(f46(x64911,f934(x64912,a922)),x64913),f335(f16(f934(x64912,a922),x64911),x64914)),f250(f934(x64912,a922))) % 186.01/186.02 [6493]~P63(x64931)+E(f51(x64931,f335(f335(f87(x64931),x64932),x64933),f335(f335(f87(x64931),x64932),x64934)),f335(f335(f87(x64931),x64932),f51(x64931,x64933,x64934))) % 186.01/186.02 [6660]E(f335(f319(x66601,x66602,f335(f16(x66602,x66601),x66603)),x66604),f250(f934(x66601,a922)))+~P1(f335(f335(f337(x66602),x66603),x66604)) % 186.01/186.02 [6684]~P1(f335(f335(f337(x66841),x66842),x66844))+P1(f335(f335(f337(x66841),x66842),f335(f335(f317(x66841),x66843),x66844))) % 186.01/186.02 [6689]P1(f335(x66891,x66892))+~P1(f335(f167(x66893,x66891),f335(f335(f158(x66893),x66892),x66894))) % 186.01/186.02 [6698]~E(x66983,f335(f335(f23(a927),f335(f196(f928(x66981)),x66982)),f84(a927)))+E(f121(x66981,f335(f335(f166(x66981,x66982),x66983),x66984)),f121(x66981,x66982)) % 186.01/186.02 [6716]~P109(x67161)+E(f335(f335(f108(f934(x67161,a922)),f335(f309(x67161),x67162)),f311(x67161,x67163,x67164)),f311(x67161,x67163,f335(f335(f241(x67161),x67162),x67164))) % 186.01/186.02 [6717]~P109(x67171)+E(f335(f335(f108(f934(x67171,a922)),f335(f291(x67171),x67172)),f311(x67171,x67173,x67174)),f311(x67171,f335(f335(f242(x67171),x67172),x67173),x67174)) % 186.01/186.02 [6733]E(f335(f335(f108(f934(x67331,a922)),x67332),f335(f335(f317(x67331),x67333),x67334)),f335(f335(f108(f934(x67331,a922)),x67332),x67334))+P1(f335(f335(f337(x67331),x67333),x67332)) % 186.01/186.02 [6745]E(f177(x67451,x67452,f335(f335(f141(x67451),x67453),x67454)),f335(f335(f141(x67451),x67453),f177(x67451,x67452,x67454)))+P1(f335(f335(f337(x67451),x67452),f335(f179(x67451),x67453))) % 186.01/186.02 [6750]~P81(x67501)+E(f335(f335(f87(x67501),f335(f335(f252(x67501),x67502),x67503)),f335(f335(f252(x67501),x67502),x67504)),f335(f335(f252(x67501),x67502),f335(f335(f86(a927),x67503),x67504))) % 186.01/186.02 [6751]~P118(x67511)+E(f335(f335(f87(x67511),f335(f335(f252(x67511),x67512),x67513)),f335(f335(f252(x67511),x67512),x67514)),f335(f335(f252(x67511),x67512),f335(f335(f86(a927),x67513),x67514))) % 186.01/186.02 [6789]~P118(x67891)+E(f335(f335(f86(x67891),f335(f335(f87(x67891),x67892),x67893)),f335(f335(f87(x67891),x67892),x67894)),f335(f335(f87(x67891),x67892),f335(f335(f86(x67891),x67893),x67894))) % 186.01/186.02 [6790]~P102(x67901)+E(f335(f335(f117(x67901),f335(f335(f108(x67901),x67902),x67903)),f335(f335(f108(x67901),x67902),x67904)),f335(f335(f108(x67901),x67902),f335(f335(f117(x67901),x67903),x67904))) % 186.01/186.02 [6791]~P102(x67911)+E(f335(f335(f108(x67911),f335(f335(f117(x67911),x67912),x67913)),f335(f335(f117(x67911),x67912),x67914)),f335(f335(f117(x67911),x67912),f335(f335(f108(x67911),x67913),x67914))) % 186.01/186.02 [6792]~P109(x67921)+E(f335(f335(f242(x67921),f335(f335(f241(x67921),x67922),x67923)),f335(f335(f241(x67921),x67922),x67924)),f335(f335(f241(x67921),x67922),f335(f335(f242(x67921),x67923),x67924))) % 186.01/186.02 [6793]~P109(x67931)+E(f335(f335(f241(x67931),f335(f335(f242(x67931),x67932),x67933)),f335(f335(f242(x67931),x67932),x67934)),f335(f335(f242(x67931),x67932),f335(f335(f241(x67931),x67933),x67934))) % 186.01/186.02 [6824]~P63(x68241)+E(f51(x68241,f335(f335(f87(x68241),x68242),x68243),f335(f335(f87(x68241),x68244),x68243)),f335(f335(f87(x68241),f51(x68241,x68242,x68244)),x68243)) % 186.01/186.02 [6827]~E(f335(f196(f928(x68271)),x68273),f335(f196(f928(x68272)),x68274))+E(f335(f335(f161(f933(x68271,x68272),x68272),f264(x68271,x68272)),f335(f335(f188(x68271,x68272),x68273),x68274)),x68274) % 186.01/186.02 [6828]~E(f335(f196(f928(x68281)),x68283),f335(f196(f928(x68282)),x68284))+E(f335(f335(f161(f933(x68281,x68282),x68281),f259(x68281,x68282)),f335(f335(f188(x68281,x68282),x68283),x68284)),x68283) % 186.01/186.02 [6833]P1(f335(f167(x68331,x68332),x68333))+~P1(f335(f167(x68331,x68332),f335(f335(f158(x68331),x68334),x68333))) % 186.01/186.02 [6834]P1(f335(f167(x68341,x68342),x68343))+~P1(f335(f167(x68341,x68342),f335(f335(f141(x68341),x68344),x68343))) % 186.01/186.02 [6835]P1(f335(f167(x68351,x68352),x68353))+~P1(f335(f167(x68351,x68352),f335(f335(f141(x68351),x68353),x68354))) % 186.01/186.02 [6840]~P64(x68401)+E(f51(x68401,f335(f335(f23(x68401),x68402),f51(x68401,x68403,x68404)),x68404),f51(x68401,f335(f335(f23(x68401),x68402),x68403),x68404)) % 186.01/186.02 [6841]~P63(x68411)+E(f51(x68411,f335(f335(f87(x68411),x68412),f51(x68411,x68413,x68414)),x68414),f51(x68411,f335(f335(f87(x68411),x68412),x68413),x68414)) % 186.01/186.02 [6843]~P63(x68431)+E(f51(x68431,f335(f335(f86(x68431),x68432),f51(x68431,x68433,x68434)),x68434),f51(x68431,f335(f335(f86(x68431),x68432),x68433),x68434)) % 186.01/186.02 [6924]~P109(x69241)+E(f335(f335(f108(f934(x69241,a922)),f311(x69241,x69242,x69243)),f335(f309(x69241),x69244)),f311(x69241,x69242,f335(f335(f241(x69241),x69243),x69244))) % 186.01/186.02 [6925]~P109(x69251)+E(f335(f335(f108(f934(x69251,a922)),f311(x69251,x69252,x69253)),f335(f291(x69251),x69254)),f311(x69251,f335(f335(f242(x69251),x69252),x69254),x69253)) % 186.01/186.02 [6928]~E(f335(f196(f928(x69281)),x69283),f335(f196(f928(x69282)),x69284))+E(f335(f335(f188(x69281,x69282),f335(f175(x69281),x69283)),f335(f175(x69282),x69284)),f335(f175(f933(x69281,x69282)),f335(f335(f188(x69281,x69282),x69283),x69284))) % 186.01/186.02 [6939]E(x69391,f335(f335(f23(a927),f335(f196(f928(x69392)),x69393)),f84(a927)))+E(f121(x69392,f335(f335(f166(x69392,x69393),x69391),x69394)),f335(f335(f166(x69392,f121(x69392,x69393)),x69391),x69394)) % 186.01/186.02 [6953]~P1(f335(f144(x69532),x69534))+P1(f335(f144(f933(x69531,x69532)),f335(f335(f188(x69531,x69532),x69533),x69534))) % 186.01/186.02 [6954]~P1(f335(f144(x69541),x69543))+P1(f335(f144(f933(x69541,x69542)),f335(f335(f188(x69541,x69542),x69543),x69544))) % 186.01/186.02 [7213]E(f335(f335(f42(a927),x72131),x72132),x72133)+~P1(f335(f54(x72131,x72132),f335(f335(f260(a927,a927),x72133),x72134))) % 186.01/186.02 [7236]E(f51(a927,x72361,x72362),x72363)+~P1(f335(f54(x72361,x72362),f335(f335(f260(a927,a927),x72364),x72363))) % 186.01/186.02 [7239]P1(f335(f144(x72391),x72392))+~P1(f335(f144(x72393),f335(f335(f161(x72391,x72393),x72394),x72392))) % 186.01/186.02 [7322]E(f177(x73221,x73222,f335(f335(f141(x73221),x73223),x73224)),f335(f335(f141(x73221),f177(x73221,x73222,x73223)),x73224))+~P1(f335(f335(f337(x73221),x73222),f335(f179(x73221),x73223))) % 186.01/186.02 [7413]~P64(x74131)+E(f51(x74131,f335(f335(f23(x74131),f51(x74131,x74132,x74133)),x74134),x74133),f51(x74131,f335(f335(f23(x74131),x74132),x74134),x74133)) % 186.01/186.02 [7416]~P63(x74161)+E(f51(x74161,f335(f335(f87(x74161),f51(x74161,x74162,x74163)),x74164),x74163),f51(x74161,f335(f335(f87(x74161),x74162),x74164),x74163)) % 186.01/186.02 [7417]~P63(x74171)+E(f51(x74171,f335(f335(f86(x74171),f51(x74171,x74172,x74173)),x74174),x74173),f51(x74171,f335(f335(f86(x74171),x74172),x74174),x74173)) % 186.01/186.02 [7613]~E(x76131,f335(f335(f158(x76132),x76133),x76134))+~P1(f335(f335(f243(a927),f335(f196(f928(x76132)),x76131)),f335(f196(f928(x76132)),x76134))) % 186.01/186.02 [7812]P26(x78121,x78122,x78123,f335(f179(x78121),x78124))+~P1(f335(f144(x78122),f335(f335(f161(x78121,x78122),x78123),x78124))) % 186.01/186.02 [7885]~P1(f335(f335(f243(f934(x78851,a922)),x78852),x78854))+P1(f335(f335(f243(f934(x78851,a922)),x78852),f335(f335(f317(x78851),x78853),x78854))) % 186.01/186.02 [7919]~P64(x79191)+E(f51(x79191,f335(f335(f23(x79191),f51(x79191,x79192,x79193)),f51(x79191,x79194,x79193)),x79193),f51(x79191,f335(f335(f23(x79191),x79192),x79194),x79193)) % 186.01/186.02 [7920]~P63(x79201)+E(f51(x79201,f335(f335(f87(x79201),f51(x79201,x79202,x79203)),f51(x79201,x79204,x79203)),x79203),f51(x79201,f335(f335(f87(x79201),x79202),x79204),x79203)) % 186.01/186.02 [7921]~P63(x79211)+E(f51(x79211,f335(f335(f86(x79211),f51(x79211,x79212,x79213)),f51(x79211,x79214,x79213)),x79213),f51(x79211,f335(f335(f86(x79211),x79212),x79214),x79213)) % 186.01/186.02 [8023]~E(f335(x80234,f695(x80234,x80233,x80231,x80232)),f195(f934(x80232,a922)))+E(f335(f335(f45(x80231,f934(x80232,a922)),x80233),x80234),f195(f934(x80232,a922))) % 186.01/186.02 [8024]~E(f335(x80244,f632(x80244,x80243,x80241,x80242)),f250(f934(x80242,a922)))+E(f335(f335(f46(x80241,f934(x80242,a922)),x80243),x80244),f250(f934(x80242,a922))) % 186.01/186.02 [8025]~E(f335(x80254,f700(x80254,x80253,x80252,x80251)),f195(f934(x80252,a922)))+E(f335(f335(f45(x80251,f934(x80252,a922)),x80253),x80254),f195(f934(x80252,a922))) % 186.01/186.02 [8026]~E(f335(x80264,f633(x80264,x80263,x80262,x80261)),f250(f934(x80262,a922)))+E(f335(f335(f46(x80261,f934(x80262,a922)),x80263),x80264),f250(f934(x80262,a922))) % 186.01/186.02 [8409]P1(f335(x84091,x84092))+~P1(f335(f335(f337(x84093),x84092),f335(f335(f108(f934(x84093,a922)),x84094),f335(f270(x84093),x84091)))) % 186.01/186.02 [8446]~P1(f335(f335(f243(f934(x84461,a922)),x84463),x84464))+P1(f335(f335(f243(f934(x84461,a922)),f335(f335(f317(x84461),x84462),x84463)),f335(f335(f317(x84461),x84462),x84464))) % 186.01/186.02 [8456]E(f335(x84561,f538(x84561,x84562,x84563)),x84563)+~P1(f335(f335(f337(x84564),x84563),f335(f318(x84562,x84564,x84561),f250(f934(x84562,a922))))) % 186.01/186.02 [8626]P1(f335(x86262,x86263))+E(f335(f335(f145(x86261),f335(f196(f928(x86261)),f184(x86261,x86262,f335(f335(f158(x86261),x86263),x86264)))),f335(f335(f158(x86261),x86263),x86264)),f335(f335(f158(x86261),x86263),x86264)) % 186.01/186.02 [8732]~P1(f335(f335(f244(a927),f335(x87324,x87322)),f335(x87324,x87323)))+P1(f335(f335(f337(f933(x87321,x87321)),f335(f335(f260(x87321,x87321),x87322),x87323)),f335(f335(f296(a927,x87321),a248),x87324))) % 186.01/186.02 [8828]~P1(f335(x88282,f763(x88284,x88282,x88283,x88281)))+E(f184(x88281,x88282,f335(f335(f141(x88281),x88283),x88284)),f335(f335(f141(x88281),x88283),f184(x88281,x88282,x88284))) % 186.01/186.02 [8905]P26(f928(x89051),f928(x89052),f335(f161(x89051,x89052),x89053),x89054)+~P26(x89051,x89052,x89053,f43(f934(x89051,a922),f335(f318(f928(x89051),f934(x89051,a922),f179(x89051)),x89054))) % 186.01/186.02 [8980]~P1(f335(x89802,x89803))+E(f335(f335(f145(x89801),f335(f196(f928(x89801)),f184(x89801,x89802,f335(f335(f158(x89801),x89803),x89804)))),f335(f335(f158(x89801),x89803),x89804)),f335(f335(f145(x89801),f335(f196(f928(x89801)),f184(x89801,x89802,x89804))),x89804)) % 186.01/186.02 [9021]~E(x90212,x90213)+E(f335(f143(x90211,f335(f335(f8(a922,a922,x90211),a330),f335(a332,x90212))),f335(f335(f158(x90211),x90213),x90214)),f335(f143(x90211,f335(f335(f8(a922,a922,x90211),a330),f335(a332,x90212))),x90214)) % 186.01/186.02 [9031]E(f335(f335(f45(x90311,f934(x90312,a922)),x90313),x90314),f195(f934(x90312,a922)))+P1(f335(f335(f337(x90311),f695(x90314,x90313,x90311,x90312)),x90313)) % 186.01/186.02 [9032]E(f335(f335(f46(x90321,f934(x90322,a922)),x90323),x90324),f250(f934(x90322,a922)))+P1(f335(f335(f337(x90321),f632(x90324,x90323,x90321,x90322)),x90323)) % 186.01/186.02 [9033]E(f335(f335(f45(x90331,f934(x90332,a922)),x90333),x90334),f195(f934(x90332,a922)))+P1(f335(f335(f337(x90331),f700(x90334,x90333,x90332,x90331)),x90333)) % 186.01/186.02 [9034]E(f335(f335(f46(x90341,f934(x90342,a922)),x90343),x90344),f250(f934(x90342,a922)))+P1(f335(f335(f337(x90341),f633(x90344,x90343,x90342,x90341)),x90343)) % 186.01/186.02 [9072]P1(f335(f335(f244(a927),f335(x90721,x90722)),f335(x90721,x90723)))+~P1(f335(f335(f337(f933(x90724,x90724)),f335(f335(f260(x90724,x90724),x90722),x90723)),f335(f335(f296(a927,x90724),a248),x90721))) % 186.01/186.02 [9098]E(f184(x90981,x90982,f335(f335(f141(x90981),x90983),x90984)),f335(f335(f141(x90981),x90983),f184(x90981,x90982,x90984)))+P1(f335(f335(f337(x90981),f763(x90984,x90982,x90983,x90981)),f335(f179(x90981),x90983))) % 186.01/186.02 [9153]~P27(x91531,x91532,x91533,f250(f934(x91531,a922)),f250(f934(x91532,a922)))+E(f335(f318(x91531,x91532,x91533),f335(f85(f934(x91531,a922)),x91534)),f335(f85(f934(x91532,a922)),f335(f318(x91531,x91532,x91533),x91534))) % 186.01/186.02 [9256]P1(f335(f335(f337(x92561),f595(x92562,x92563,x92564,x92561)),x92563))+~P1(f335(f335(f337(f934(x92561,a922)),x92564),f335(f335(f66(x92561),x92563),x92562))) % 186.01/186.02 [9259]E(x92591,x92592)+~P1(f335(f335(f337(f933(x92593,x92593)),f335(f335(f260(x92593,x92593),x92591),x92592)),f335(f335(f190(f933(x92593,x92593),a922),f2(a927)),x92594))) % 186.01/186.02 [9341]E(f335(f293(x93411,x93411,x93412),f335(f335(f317(x93411),f595(x93412,x93413,x93414,x93411)),f195(f934(x93411,a922)))),x93414)+~P1(f335(f335(f337(f934(x93411,a922)),x93414),f335(f335(f66(x93411),x93413),x93412))) % 186.01/186.02 [9346]~P1(f335(f335(f337(f933(x93461,x93461)),f335(f335(f260(x93461,x93461),x93463),x93462)),f315(x93461,x93464)))+P1(f335(f335(f337(f933(x93461,x93461)),f335(f335(f260(x93461,x93461),x93462),x93463)),f315(x93461,f335(f294(x93461,x93461),x93464)))) % 186.01/186.02 [9359]~P63(x93591)+E(f335(f335(f86(x93591),f335(f335(f86(x93591),f335(f335(f87(x93591),x93592),f335(f335(f42(x93591),x93593),x93592))),f51(x93591,x93593,x93592))),x93594),f335(f335(f86(x93591),x93593),x93594)) % 186.01/186.02 [9370]~P1(f335(f335(f337(x93701),x93703),x93704))+P1(f335(f335(f337(f934(x93701,a922)),f335(f293(x93701,x93701,x93702),f335(f335(f317(x93701),x93703),f195(f934(x93701,a922))))),f335(f335(f66(x93701),x93704),x93702))) % 186.01/186.02 [9382]P1(f335(f335(f337(f933(x93821,x93821)),f335(f335(f260(x93821,x93821),x93822),x93823)),f315(x93821,x93824)))+~P1(f335(f335(f337(f933(x93821,x93821)),f335(f335(f260(x93821,x93821),x93823),x93822)),f315(x93821,f335(f294(x93821,x93821),x93824)))) % 186.01/186.02 [9465]E(f335(f335(f166(x94651,f335(f175(x94651),x94652)),f335(f335(f23(a927),f335(f335(f23(a927),f335(f196(f928(x94651)),x94652)),x94653)),f84(a927))),x94654),f335(f175(x94651),f335(f335(f166(x94651,x94652),x94653),x94654)))+~P1(f335(f335(f244(a927),x94653),f335(f196(f928(x94651)),x94652))) % 186.01/186.02 [9468]~P1(f335(x94682,f758(x94684,x94682,x94683,x94681)))+E(f335(f335(f145(x94681),f335(f196(f928(x94681)),f184(x94681,x94682,f335(f335(f141(x94681),x94683),x94684)))),f335(f335(f141(x94681),x94683),x94684)),f335(f335(f145(x94681),f335(f196(f928(x94681)),f184(x94681,x94682,x94684))),x94684)) % 186.01/186.02 [9512]~P26(x95122,x95121,x95123,f250(f934(x95122,a922)))+P1(f335(f335(f243(f934(x95121,a922)),f335(f318(x95122,x95121,x95123),f335(f85(f934(x95122,a922)),x95124))),f335(f85(f934(x95121,a922)),f335(f318(x95122,x95121,x95123),x95124)))) % 186.01/186.02 [9524]~P6(x95241)+E(f335(f149(x95241,x95242,f335(f7(x95242,x95241,x95241),f335(f335(f8(x95241,f934(x95241,x95241),x95242),f117(x95241)),x95243)),f195(x95241)),x95244),f335(f335(f45(x95242,x95241),f335(f179(x95242),x95244)),x95243)) % 186.01/186.02 [9525]~P6(x95251)+E(f335(f149(x95251,x95252,f335(f7(x95252,x95251,x95251),f335(f335(f8(x95251,f934(x95251,x95251),x95252),f108(x95251)),x95253)),f250(x95251)),x95254),f335(f335(f46(x95252,x95251),f335(f179(x95252),x95254)),x95253)) % 186.01/186.02 [9535]E(f335(f335(f145(x95351),f335(f196(f928(x95351)),f184(x95351,x95352,f335(f335(f141(x95351),x95353),x95354)))),f335(f335(f141(x95351),x95353),x95354)),f335(f335(f145(x95351),f335(f196(f928(x95351)),f184(x95351,x95352,x95354))),x95354))+P1(f335(f335(f337(x95351),f758(x95354,x95352,x95353,x95351)),f335(f179(x95351),x95353))) % 186.01/186.02 [9605]~P1(f335(f335(f337(f933(f928(x96054),f928(x96054))),f335(f335(f260(f928(x96054),f928(x96054)),x96053),x96052)),f164(x96054,x96051)))+P1(f335(f335(f244(a927),f692(x96051,x96052,x96053,x96054)),f335(f196(f928(x96054)),x96053))) % 186.01/186.02 [9606]~P63(x96061)+E(f335(f335(f86(x96061),f335(f335(f86(x96061),f335(f335(f87(x96061),f335(f335(f42(x96061),x96062),x96063)),x96063)),f51(x96061,x96062,x96063))),x96064),f335(f335(f86(x96061),x96062),x96064)) % 186.01/186.03 [9633]~P1(f335(f335(f337(f933(f928(x96331),f928(x96331))),f335(f335(f260(f928(x96331),f928(x96331)),x96332),x96333)),f335(f294(f928(x96331),f928(x96331)),f164(x96331,x96334))))+P1(f335(f335(f337(f933(f928(x96331),f928(x96331))),f335(f335(f260(f928(x96331),f928(x96331)),x96332),x96333)),f164(x96331,f335(f294(x96331,x96331),x96334)))) % 186.01/186.03 [9634]P1(f335(f335(f337(f933(f928(x96341),f928(x96341))),f335(f335(f260(f928(x96341),f928(x96341)),x96342),x96343)),f335(f294(f928(x96341),f928(x96341)),f164(x96341,x96344))))+~P1(f335(f335(f337(f933(f928(x96341),f928(x96341))),f335(f335(f260(f928(x96341),f928(x96341)),x96342),x96343)),f164(x96341,f335(f294(x96341,x96341),x96344)))) % 186.01/186.03 [9673]~P1(f335(f335(f337(x96731),x96733),f335(f272(x96731,x96732),x96734)))+P1(f335(f335(f337(f933(x96731,x96732)),f335(f335(f260(x96731,x96732),x96733),f898(x96734,x96732,x96733,x96731))),x96734)) % 186.01/186.03 [9674]~P1(f335(f335(f337(x96741),x96743),f335(f272(x96741,x96742),x96744)))+P1(f335(f335(f337(f933(x96741,x96742)),f335(f335(f260(x96741,x96742),x96743),f899(x96744,x96742,x96743,x96741))),x96744)) % 186.01/186.03 [9830]~P1(f335(f335(f337(f933(x98301,x98301)),f335(f335(f260(x98301,x98301),x98302),x98304)),f335(f335(f297(x98301,x98301,x98301),x98303),f315(x98301,x98303))))+P1(f335(f335(f337(f933(x98301,x98301)),f335(f335(f260(x98301,x98301),x98302),f636(x98303,x98304,x98302,x98301))),x98303)) % 186.01/186.03 [9991]P12(x99911,x99912,x99913,x99914)+P1(f335(f335(f337(f933(x99911,x99911)),f335(f335(f260(x99911,x99911),f895(x99912,x99914,x99913,x99911)),f894(x99912,x99914,x99913,x99911))),x99913)) % 186.01/186.03 [9998]~P1(f335(f335(f337(f933(x99982,x99981)),x99984),f335(f294(x99981,x99982),x99983)))+P1(f335(f335(f337(f933(x99981,x99982)),f335(f335(f260(x99981,x99982),f665(x99983,x99984,x99981,x99982)),f664(x99983,x99984,x99981,x99982))),x99983)) % 186.01/186.03 [10022]~P1(f335(f335(f337(f933(f928(x100221),f928(x100221))),f335(f335(f260(f928(x100221),f928(x100221)),x100224),x100223)),f164(x100221,x100222)))+P1(f335(f335(f337(f933(x100221,x100221)),f335(f335(f260(x100221,x100221),f708(x100222,x100223,x100224,x100221)),f709(x100222,x100223,x100224,x100221))),x100222)) % 186.01/186.03 [10114]~P1(f335(f335(f337(f933(f928(x101141),f928(x101141))),f335(f335(f260(f928(x101141),f928(x101141)),x101142),x101144)),f164(x101141,x101143)))+P1(f335(f335(f337(f933(x101141,x101141)),f335(f335(f260(x101141,x101141),f335(f335(f171(x101141),x101142),f692(x101143,x101144,x101142,x101141))),f693(x101143,x101144,x101142,x101141))),x101143)) % 186.01/186.03 [10134]~P1(f335(f67(x101342),x101344))+E(f335(f335(f335(f71(f934(x101341,a922),x101342,f117(f934(x101341,a922))),f335(f335(f7(x101342,f934(x101341,a922),f934(x101341,a922)),f335(f335(f8(x101341,f934(f934(x101341,a922),f934(x101341,a922)),x101342),f317(x101341)),x101343)),f195(f934(x101341,a922)))),f195(f934(x101341,a922))),x101344),f335(f318(x101342,x101341,x101343),x101344)) % 186.01/186.03 [10247]~P26(x102471,x102472,x102473,f250(f934(x102471,a922)))+P1(f335(f335(f243(f934(x102471,a922)),f335(f319(x102471,x102472,x102473),f335(f335(f317(x102472),x102474),f195(f934(x102472,a922))))),f335(f335(f317(x102471),f91(x102471,f335(f335(f7(x102471,x102472,a922),f335(f335(f8(x102472,f934(x102472,a922),x102471),a332),x102473)),x102474))),f195(f934(x102471,a922))))) % 186.01/186.03 [5867]~E(f335(f335(f141(x58671),x58672),x58674),x58673)+E(f335(f335(f182(x58671),f335(f196(f928(x58671)),x58672)),x58673),x58672) % 186.01/186.03 [5868]~E(f335(f335(f141(x58682),x58683),x58681),x58684)+E(x58681,f335(f335(f145(x58682),f335(f196(f928(x58682)),x58683)),x58684)) % 186.01/186.03 [5879]~E(x58794,f2(a927))+E(f335(f335(f171(x58791),f335(f335(f158(x58791),x58792),x58793)),x58794),x58792) % 186.01/186.03 [6414]~P118(x64141)+E(f335(f335(f252(x64141),f335(f335(f252(x64141),x64142),x64143)),x64144),f335(f335(f252(x64141),x64142),f335(f335(f87(a927),x64143),x64144))) % 186.01/186.03 [6415]~P81(x64151)+E(f335(f335(f252(x64151),f335(f335(f252(x64151),x64152),x64153)),x64154),f335(f335(f252(x64151),x64152),f335(f335(f87(a927),x64153),x64154))) % 186.01/186.03 [6423]E(x64231,f2(a927))+E(f335(f335(f171(x64232),f335(f335(f158(x64232),x64233),x64234)),x64231),f335(f335(f171(x64232),x64234),f335(f335(f23(a927),x64231),f84(a927)))) % 186.01/186.03 [6449]~P121(x64491)+E(f335(f335(f299(x64491),f335(f335(f87(x64491),x64492),x64493)),x64494),f335(f335(f87(x64491),x64492),f335(f335(f299(x64491),x64493),x64494))) % 186.01/186.03 [6451]~P70(x64511)+E(f335(f335(f87(x64511),f335(f335(f87(x64511),x64512),x64513)),x64514),f335(f335(f87(x64511),x64512),f335(f335(f87(x64511),x64513),x64514))) % 186.01/186.03 [6452]~P118(x64521)+E(f335(f335(f87(x64521),f335(f335(f87(x64521),x64522),x64523)),x64524),f335(f335(f87(x64521),x64522),f335(f335(f87(x64521),x64523),x64524))) % 186.01/186.03 [6455]~P97(x64551)+E(f335(f335(f108(x64551),f335(f335(f108(x64551),x64552),x64553)),x64554),f335(f335(f108(x64551),x64552),f335(f335(f108(x64551),x64553),x64554))) % 186.01/186.03 [6456]~P98(x64561)+E(f335(f335(f108(x64561),f335(f335(f108(x64561),x64562),x64563)),x64564),f335(f335(f108(x64561),x64562),f335(f335(f108(x64561),x64563),x64564))) % 186.01/186.03 [6457]~P98(x64571)+E(f335(f335(f117(x64571),f335(f335(f117(x64571),x64572),x64573)),x64574),f335(f335(f117(x64571),x64572),f335(f335(f117(x64571),x64573),x64574))) % 186.01/186.03 [6459]~P103(x64591)+E(f335(f335(f117(x64591),f335(f335(f117(x64591),x64592),x64593)),x64594),f335(f335(f117(x64591),x64592),f335(f335(f117(x64591),x64593),x64594))) % 186.01/186.03 [6460]~P118(x64601)+E(f335(f335(f86(x64601),f335(f335(f86(x64601),x64602),x64603)),x64604),f335(f335(f86(x64601),x64602),f335(f335(f86(x64601),x64603),x64604))) % 186.01/186.03 [6461]~P71(x64611)+E(f335(f335(f86(x64611),f335(f335(f86(x64611),x64612),x64613)),x64614),f335(f335(f86(x64611),x64612),f335(f335(f86(x64611),x64613),x64614))) % 186.01/186.03 [6463]~P109(x64631)+E(f335(f335(f241(x64631),f335(f335(f241(x64631),x64632),x64633)),x64634),f335(f335(f241(x64631),x64632),f335(f335(f241(x64631),x64633),x64634))) % 186.01/186.03 [6465]~P109(x64651)+E(f335(f335(f242(x64651),f335(f335(f242(x64651),x64652),x64653)),x64654),f335(f335(f242(x64651),x64652),f335(f335(f242(x64651),x64653),x64654))) % 186.01/186.03 [6474]~P63(x64741)+E(f51(x64741,f335(f335(f86(x64741),x64742),f335(f335(f87(x64741),x64743),x64744)),x64744),f51(x64741,x64742,x64744)) % 186.01/186.03 [6475]~P63(x64751)+E(f51(x64751,f335(f335(f86(x64751),x64752),f335(f335(f87(x64751),x64753),x64754)),x64753),f51(x64751,x64752,x64753)) % 186.01/186.03 [6609]E(f335(f335(f171(x66091),f335(f335(f182(x66091),x66092),x66093)),x66094),f335(f335(f171(x66091),x66093),x66094))+~P1(f335(f335(f244(a927),x66094),x66092)) % 186.01/186.03 [6785]~E(x67852,x67854)+P1(f335(f335(f179(x67851),f335(f335(f158(x67851),x67852),x67853)),x67854)) % 186.01/186.03 [6787]~P118(x67871)+E(f335(f335(f87(x67871),f335(f335(f87(x67871),x67872),x67873)),x67874),f335(f335(f87(x67871),f335(f335(f87(x67871),x67872),x67874)),x67873)) % 186.01/186.03 [6788]~P118(x67881)+E(f335(f335(f86(x67881),f335(f335(f86(x67881),x67882),x67883)),x67884),f335(f335(f86(x67881),f335(f335(f86(x67881),x67882),x67884)),x67883)) % 186.01/186.03 [6846]~P146(x68462)+E(f335(f335(f6(x68461,x68462),f335(f16(x68462,x68461),x68463)),x68464),f335(f335(f87(x68462),f335(f107(x68462),f335(f41(x68461),x68464))),x68463)) % 186.01/186.03 [7015]E(f335(f335(f108(f934(x70151,a922)),f335(f335(f317(x70151),x70152),x70153)),x70154),f335(f335(f108(f934(x70151,a922)),x70153),x70154))+P1(f335(f335(f337(x70151),x70152),x70154)) % 186.01/186.03 [7082]~P79(x70821)+E(f335(f335(f241(x70821),f335(f335(f23(x70821),x70822),x70823)),f335(f335(f23(x70821),x70824),x70823)),f335(f335(f23(x70821),f335(f335(f241(x70821),x70822),x70824)),x70823)) % 186.01/186.03 [7083]~P79(x70831)+E(f335(f335(f242(x70831),f335(f335(f23(x70831),x70832),x70833)),f335(f335(f23(x70831),x70834),x70833)),f335(f335(f23(x70831),f335(f335(f242(x70831),x70832),x70834)),x70833)) % 186.01/186.03 [7085]~P119(x70851)+E(f335(f335(f86(x70851),f335(f335(f87(x70851),x70852),x70853)),f335(f335(f87(x70851),x70854),x70853)),f335(f335(f87(x70851),f335(f335(f86(x70851),x70852),x70854)),x70853)) % 186.01/186.03 [7086]~P102(x70861)+E(f335(f335(f117(x70861),f335(f335(f108(x70861),x70862),x70863)),f335(f335(f108(x70861),x70864),x70863)),f335(f335(f108(x70861),f335(f335(f117(x70861),x70862),x70864)),x70863)) % 186.01/186.03 [7087]~P102(x70871)+E(f335(f335(f108(x70871),f335(f335(f117(x70871),x70872),x70873)),f335(f335(f117(x70871),x70874),x70873)),f335(f335(f117(x70871),f335(f335(f108(x70871),x70872),x70874)),x70873)) % 186.01/186.03 [7088]~P85(x70881)+E(f335(f335(f241(x70881),f335(f335(f86(x70881),x70882),x70883)),f335(f335(f86(x70881),x70884),x70883)),f335(f335(f86(x70881),f335(f335(f241(x70881),x70882),x70884)),x70883)) % 186.01/186.03 [7089]~P85(x70891)+E(f335(f335(f242(x70891),f335(f335(f86(x70891),x70892),x70893)),f335(f335(f86(x70891),x70894),x70893)),f335(f335(f86(x70891),f335(f335(f242(x70891),x70892),x70894)),x70893)) % 186.01/186.03 [7090]~P109(x70901)+E(f335(f335(f242(x70901),f335(f335(f241(x70901),x70902),x70903)),f335(f335(f241(x70901),x70904),x70903)),f335(f335(f241(x70901),f335(f335(f242(x70901),x70902),x70904)),x70903)) % 186.01/186.03 [7091]~P109(x70911)+E(f335(f335(f241(x70911),f335(f335(f242(x70911),x70912),x70913)),f335(f335(f242(x70911),x70914),x70913)),f335(f335(f242(x70911),f335(f335(f241(x70911),x70912),x70914)),x70913)) % 186.01/186.03 [7092]~P72(x70921)+E(f335(f335(f87(x70921),f335(f335(f252(x70921),x70922),x70923)),f335(f335(f252(x70921),x70924),x70923)),f335(f335(f252(x70921),f335(f335(f87(x70921),x70922),x70924)),x70923)) % 186.01/186.03 [7093]~P118(x70931)+E(f335(f335(f87(x70931),f335(f335(f252(x70931),x70932),x70933)),f335(f335(f252(x70931),x70934),x70933)),f335(f335(f252(x70931),f335(f335(f87(x70931),x70932),x70934)),x70933)) % 186.01/186.03 [7094]~P66(x70941)+E(f335(f335(f299(x70941),f335(f335(f252(x70941),x70942),x70943)),f335(f335(f252(x70941),x70944),x70943)),f335(f335(f252(x70941),f335(f335(f299(x70941),x70942),x70944)),x70943)) % 186.01/186.03 [7095]~P121(x70951)+E(f335(f335(f23(x70951),f335(f335(f299(x70951),x70952),x70953)),f335(f335(f299(x70951),x70954),x70953)),f335(f335(f299(x70951),f335(f335(f23(x70951),x70952),x70954)),x70953)) % 186.01/186.03 [7096]~P121(x70961)+E(f335(f335(f86(x70961),f335(f335(f299(x70961),x70962),x70963)),f335(f335(f299(x70961),x70964),x70963)),f335(f335(f299(x70961),f335(f335(f86(x70961),x70962),x70964)),x70963)) % 186.01/186.03 [7097]~P118(x70971)+E(f335(f335(f86(x70971),f335(f335(f87(x70971),x70972),x70973)),f335(f335(f87(x70971),x70974),x70973)),f335(f335(f87(x70971),f335(f335(f86(x70971),x70972),x70974)),x70973)) % 186.01/186.03 [7128]E(f335(f335(f166(x71281,x71282),x71283),x71284),x71282)+~P1(f335(f335(f243(a927),f335(f196(f928(x71281)),x71282)),x71283)) % 186.01/186.03 [7153]~P1(f335(x71533,x71534))+P1(f335(f335(f335(f117(f934(x71531,a922)),x71532),x71533),x71534)) % 186.01/186.03 [7155]~P1(f335(x71552,x71554))+P1(f335(f335(f335(f117(f934(x71551,a922)),x71552),x71553),x71554)) % 186.01/186.03 [7173]E(f335(f335(f171(x71731),f335(f335(f141(x71731),x71732),x71733)),x71734),f335(f335(f171(x71731),x71732),x71734))+~P1(f335(f335(f244(a927),x71734),f335(f196(f928(x71731)),x71732))) % 186.01/186.03 [7184]E(f335(f335(f23(f934(x71841,a922)),f335(f335(f317(x71841),x71842),x71843)),x71844),f335(f335(f23(f934(x71841,a922)),x71843),x71844))+~P1(f335(f335(f337(x71841),x71842),x71844)) % 186.01/186.03 [7226]~E(f146(a927,f335(f310(a927,x72261),x72262)),f335(f335(f158(a927),x72264),x72263))+E(f146(a927,f335(f310(a927,f335(f335(f86(a927),x72261),f84(a927))),x72262)),x72263) % 186.01/186.03 [7247]~P1(f335(f335(f179(x72471),x72473),x72474))+P1(f335(f335(f179(x72471),f335(f335(f158(x72471),x72472),x72473)),x72474)) % 186.01/186.03 [7297]E(x72971,f2(a927))+E(f335(f335(f158(x72972),x72973),f335(f335(f182(x72972),f335(f335(f23(a927),x72971),f84(a927))),x72974)),f335(f335(f182(x72972),x72971),f335(f335(f158(x72972),x72973),x72974))) % 186.01/186.03 [7397]E(f335(f335(f171(x73971),x73972),f335(f335(f23(a927),x73973),f335(f196(f928(x73971)),x73974))),f335(f335(f171(x73971),f335(f335(f141(x73971),x73974),x73972)),x73973))+P1(f335(f335(f244(a927),x73973),f335(f196(f928(x73971)),x73974))) % 186.01/186.03 [7426]E(f335(f335(f108(f934(x74261,a922)),x74262),f335(f335(f317(x74261),x74263),x74264)),f335(f335(f317(x74261),x74263),f335(f335(f108(f934(x74261,a922)),x74262),x74264)))+~P1(f335(f335(f337(x74261),x74263),x74262)) % 186.01/186.03 [7464]E(f335(f335(f171(x74641),f335(f335(f166(x74641,x74642),x74643),x74644)),x74643),x74644)+~P1(f335(f335(f244(a927),x74643),f335(f196(f928(x74641)),x74642))) % 186.01/186.03 [7486]E(x74861,f195(f934(x74862,a922)))+E(f335(f318(f933(x74863,x74862),x74863,f259(x74863,x74862)),f335(f335(f262(x74863,x74862),x74864),f335(f16(f934(x74862,a922),x74863),x74861))),x74864) % 186.01/186.03 [7487]E(x74871,f195(f934(x74872,a922)))+E(f335(f318(f933(x74872,x74873),x74873,f264(x74872,x74873)),f335(f335(f262(x74872,x74873),x74871),f335(f16(f934(x74873,a922),x74872),x74874))),x74874) % 186.01/186.03 [7564]E(f335(f335(f23(f934(x75641,a922)),f335(f335(f317(x75641),x75642),x75643)),x75644),f335(f335(f317(x75641),x75642),f335(f335(f23(f934(x75641,a922)),x75643),x75644)))+P1(f335(f335(f337(x75641),x75642),x75644)) % 186.01/186.03 [7599]~E(x75994,f195(f934(x75992,a922)))+E(f335(f318(f933(x75991,x75992),x75991,f259(x75991,x75992)),f335(f335(f262(x75991,x75992),x75993),f335(f16(f934(x75992,a922),x75991),x75994))),f195(f934(x75991,a922))) % 186.01/186.03 [7600]~E(x76003,f195(f934(x76001,a922)))+E(f335(f318(f933(x76001,x76002),x76002,f264(x76001,x76002)),f335(f335(f262(x76001,x76002),x76003),f335(f16(f934(x76002,a922),x76001),x76004))),f195(f934(x76002,a922))) % 186.01/186.03 [7651]~P1(f335(f335(f337(x76511),x76512),x76514))+P1(f335(f335(f337(x76511),x76512),f335(f335(f117(f934(x76511,a922)),x76513),x76514))) % 186.01/186.03 [7654]~P1(f335(f335(f337(x76541),x76542),x76543))+P1(f335(f335(f337(x76541),x76542),f335(f335(f117(f934(x76541,a922)),x76543),x76544))) % 186.01/186.03 [7672]E(f335(f335(f108(f934(x76721,a922)),f335(f335(f317(x76721),x76722),x76723)),x76724),f335(f335(f317(x76721),x76722),f335(f335(f108(f934(x76721,a922)),x76723),x76724)))+~P1(f335(f335(f337(x76721),x76722),x76724)) % 186.01/186.03 [7941]P1(f335(x79411,x79412))+~P1(f335(f335(f335(f108(f934(x79413,a922)),x79414),x79411),x79412)) % 186.01/186.03 [7942]P1(f335(x79421,x79422))+~P1(f335(f335(f335(f108(f934(x79423,a922)),x79421),x79424),x79422)) % 186.01/186.03 [7943]E(f335(f335(f6(x79431,a927),x79432),f335(f335(f23(f934(x79431,a922)),x79433),f335(f335(f317(x79431),x79434),f195(f934(x79431,a922))))),f335(f335(f6(x79431,a927),x79432),x79433))+P1(f335(f335(f337(x79431),x79434),x79433)) % 186.01/186.03 [7948]~P76(x79481)+E(f335(f172(x79481),f335(f335(f161(a927,x79481),x79482),f146(a927,f335(f310(a927,x79483),x79484)))),f335(f335(f6(a927,x79481),x79482),f335(f179(a927),f146(a927,f335(f310(a927,x79483),x79484))))) % 186.01/186.03 [7949]~P76(x79491)+E(f335(f335(f6(a927,x79491),x79492),f335(f179(a927),f146(a927,f335(f310(a927,x79493),x79494)))),f335(f172(x79491),f335(f335(f161(a927,x79491),x79492),f146(a927,f335(f310(a927,x79493),x79494))))) % 186.01/186.03 [8059]~E(x80593,x80594)+P1(f335(f68(x80591,x80592,f335(f335(f317(x80591),x80593),f195(f934(x80591,a922)))),x80594)) % 186.01/186.03 [8155]P1(f335(f335(f337(x81551),x81552),f335(f179(x81551),x81553)))+~P1(f335(f335(f337(x81551),x81552),f335(f179(x81551),f335(f335(f182(x81551),x81554),x81553)))) % 186.01/186.03 [8156]P1(f335(f335(f337(x81561),x81562),f335(f179(x81561),x81563)))+~P1(f335(f335(f337(x81561),x81562),f335(f179(x81561),f335(f335(f145(x81561),x81564),x81563)))) % 186.01/186.03 [8227]P1(f335(f335(f337(x82271),x82272),x82273))+~P1(f335(f335(f337(x82271),x82272),f335(f335(f23(f934(x82271,a922)),x82273),x82274))) % 186.01/186.03 [8229]P1(f335(f335(f337(x82291),x82292),x82293))+~P1(f335(f335(f337(x82291),x82292),f335(f335(f108(f934(x82291,a922)),x82294),x82293))) % 186.01/186.03 [8232]P1(f335(f335(f337(x82321),x82322),x82323))+~P1(f335(f335(f337(x82321),x82322),f335(f335(f108(f934(x82321,a922)),x82323),x82324))) % 186.01/186.03 [8247]E(f335(f335(f141(x82471),f335(f335(f182(x82471),x82472),x82473)),f335(f335(f158(x82471),x82474),f335(f335(f145(x82471),f335(a119,x82472)),x82473))),f335(f335(f166(x82471,x82473),x82472),x82474))+~P1(f335(f335(f244(a927),x82472),f335(f196(f928(x82471)),x82473))) % 186.01/186.03 [8270]P1(f335(f335(f337(x82701),x82702),x82703))+~P1(f335(f335(f243(f934(x82701,a922)),f335(f335(f317(x82701),x82702),x82704)),x82703)) % 186.01/186.03 [8307]~P1(f335(f335(f337(x83071),x83072),x83073))+~P1(f335(f335(f337(x83071),x83072),f335(f335(f23(f934(x83071,a922)),x83074),x83073))) % 186.01/186.03 [8337]~P1(f335(f335(f244(a927),x83374),f335(f196(f928(x83371)),x83373)))+P1(f335(f335(f337(x83371),x83372),f335(f179(x83371),f335(f335(f166(x83371,x83373),x83374),x83372)))) % 186.01/186.03 [8388]E(f335(f335(f171(x83881),f335(f335(f145(x83881),x83882),x83883)),x83884),f335(f335(f171(x83881),x83883),f335(f335(f86(a927),x83882),x83884)))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x83882),x83884)),f335(f196(f928(x83881)),x83883))) % 186.01/186.03 [8397]~P146(x83972)+E(f335(f335(f6(x83971,x83972),f335(f335(f8(a927,x83972,x83971),f107(x83972)),x83973)),x83974),f335(f107(x83972),f335(f335(f6(x83971,a927),x83973),x83974))) % 186.01/186.03 [8398]~P140(x83982)+E(f335(f335(f6(x83981,x83982),f335(f335(f8(a1,x83982,x83981),f109(x83982)),x83983)),x83984),f335(f109(x83982),f335(f335(f6(x83981,a1),x83983),x83984))) % 186.01/186.03 [8448]~P69(x84482)+E(f335(f335(f9(x84481,x84482),f335(f335(f8(x84482,x84482,x84481),f81(x84482)),x84483)),x84484),f335(f81(x84482),f335(f335(f9(x84481,x84482),x84483),x84484))) % 186.01/186.03 [8449]~P5(x84492)+E(f335(f335(f6(x84491,x84492),f335(f335(f8(x84492,x84492,x84491),f85(x84492)),x84493)),x84494),f335(f85(x84492),f335(f335(f6(x84491,x84492),x84493),x84494))) % 186.01/186.03 [8451]E(f335(f335(f6(x84511,a927),x84512),f335(f335(f23(f934(x84511,a922)),x84513),f335(f335(f317(x84511),x84514),f195(f934(x84511,a922))))),f335(f335(f23(a927),f335(f335(f6(x84511,a927),x84512),x84513)),f335(x84512,x84514)))+~P1(f335(f335(f337(x84511),x84514),x84513)) % 186.01/186.03 [8471]P1(f335(f335(f243(f934(x84711,a922)),x84712),x84713))+~P1(f335(f335(f243(f934(x84711,a922)),f335(f335(f317(x84711),x84714),x84712)),x84713)) % 186.01/186.03 [8595]~E(f335(f318(x85952,x85953,x85951),f250(f934(x85952,a922))),f250(f934(x85953,a922)))+E(f335(x85951,f335(f97(x85952,x85953,f250(f934(x85952,a922)),x85951),x85954)),x85954) % 186.01/186.03 [8678]P38(x86781,x86782)+~P38(x86781,f335(f335(f317(f933(x86781,x86781)),f335(f335(f260(x86781,x86781),x86783),x86784)),x86782)) % 186.01/186.03 [8679]P59(x86791,x86792)+~P59(x86791,f335(f335(f317(f933(x86791,x86791)),f335(f335(f260(x86791,x86791),x86793),x86794)),x86792)) % 186.01/186.03 [8684]~P109(x86841)+E(f335(f335(f155(x86841,x86841,f5(x86841)),x86842),f335(f335(f155(x86841,x86841,f5(x86841)),x86843),x86844)),f335(f335(f155(x86841,x86841,f5(x86841)),x86843),f335(f335(f155(x86841,x86841,f5(x86841)),x86842),x86844))) % 186.01/186.03 [8699]E(x86991,x86992)+~P1(f335(f68(x86993,x86994,f335(f335(f317(x86993),x86991),f195(f934(x86993,a922)))),x86992)) % 186.01/186.03 [8708]E(f335(f335(f141(x87081),f335(f335(f182(x87081),x87082),x87083)),f335(f335(f182(x87081),x87084),f335(f335(f145(x87081),x87082),x87083))),f335(f335(f182(x87081),f335(f335(f86(a927),x87082),x87084)),x87083))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x87082),x87084)),f335(f196(f928(x87081)),x87083))) % 186.01/186.03 [8748]P1(f335(f67(x87481),x87482))+~E(x87482,f335(f318(a927,x87481,x87483),f335(f270(a927),f335(f335(f7(a927,a927,a922),f244(a927)),x87484)))) % 186.01/186.03 [8768]~P91(x87681)+E(f335(f149(x87681,x87681,f86(x87681),f335(f335(f86(x87681),x87682),x87683)),x87684),f335(f335(f86(x87681),x87682),f335(f149(x87681,x87681,f86(x87681),x87683),x87684))) % 186.01/186.03 [8804]P1(f335(f335(f243(f934(x88041,a922)),f335(f272(x88041,x88042),x88043)),f335(f272(x88041,x88042),x88044)))+~P1(f335(f335(f243(f934(f933(x88041,x88042),a922)),x88043),x88044)) % 186.01/186.03 [8816]~P1(f335(f335(f243(a927),x88162),x88164))+P1(f335(f335(f243(f934(x88161,a922)),f335(f179(x88161),f335(f335(f182(x88161),x88162),x88163))),f335(f179(x88161),f335(f335(f182(x88161),x88164),x88163)))) % 186.01/186.03 [8817]~P1(f335(f335(f243(a927),x88174),x88172))+P1(f335(f335(f243(f934(x88171,a922)),f335(f179(x88171),f335(f335(f145(x88171),x88172),x88173))),f335(f179(x88171),f335(f335(f145(x88171),x88174),x88173)))) % 186.01/186.03 [8874]~P1(f335(f67(x88741),f335(f335(f23(f934(x88741,a922)),x88742),x88744)))+P1(f335(f67(x88741),f335(f335(f23(f934(x88741,a922)),x88742),f335(f335(f317(x88741),x88743),x88744)))) % 186.01/186.03 [8916]P1(f335(f335(f337(f933(x89161,x89161)),x89162),f315(x89161,x89163)))+~P1(f335(f335(f337(f933(x89161,x89161)),x89162),f335(f335(f190(f933(x89161,x89161),a922),x89164),x89163))) % 186.01/186.03 [9002]~P1(f335(f67(x90021),f335(f335(f23(f934(x90021,a922)),x90022),f335(f335(f317(x90021),x90024),x90023))))+P1(f335(f67(x90021),f335(f335(f23(f934(x90021,a922)),x90022),x90023))) % 186.01/186.03 [9217]~P98(x92171)+P1(f335(f335(f243(x92171),f335(f335(f117(x92171),x92172),f335(f335(f108(x92171),x92173),x92174))),f335(f335(f108(x92171),f335(f335(f117(x92171),x92172),x92173)),f335(f335(f117(x92171),x92172),x92174)))) % 186.01/186.03 [9218]~P109(x92181)+P1(f335(f335(f243(x92181),f335(f335(f242(x92181),x92182),f335(f335(f241(x92181),x92183),x92184))),f335(f335(f241(x92181),f335(f335(f242(x92181),x92182),x92183)),f335(f335(f242(x92181),x92182),x92184)))) % 186.01/186.03 [9366]E(x93661,x93662)+~P1(f335(f335(f337(f933(x93663,x93663)),f335(f335(f260(x93663,x93663),x93661),x93662)),f335(f179(f933(x93663,x93663)),f335(f335(f188(x93663,x93663),x93664),x93664)))) % 186.01/186.03 [9396]~P1(f335(f335(f337(f933(x93961,x93961)),f335(f335(f260(x93961,x93961),x93963),x93962)),f315(x93961,x93964)))+~P38(x93961,f335(f335(f317(f933(x93961,x93961)),f335(f335(f260(x93961,x93961),x93962),x93963)),x93964)) % 186.01/186.03 [9397]~P1(f335(f335(f337(f933(x93971,x93971)),f335(f335(f260(x93971,x93971),x93973),x93972)),f315(x93971,x93974)))+~P59(x93971,f335(f335(f317(f933(x93971,x93971)),f335(f335(f260(x93971,x93971),x93972),x93973)),x93974)) % 186.01/186.03 [9401]E(x94011,x94012)+E(f335(f143(x94013,f335(f335(f8(a922,a922,x94013),a330),f335(a332,x94011))),f335(f335(f158(x94013),x94012),x94014)),f335(f335(f158(x94013),x94012),f335(f143(x94013,f335(f335(f8(a922,a922,x94013),a330),f335(a332,x94011))),x94014))) % 186.01/186.03 [9429]~P27(x94292,x94291,x94293,f250(f934(x94292,a922)),f250(f934(x94291,a922)))+E(f335(f318(x94291,x94292,f97(x94292,x94291,f250(f934(x94292,a922)),x94293)),x94294),f335(f319(x94292,x94291,x94293),x94294)) % 186.01/186.03 [9444]~P98(x94441)+P1(f335(f335(f243(x94441),f335(f335(f117(x94441),f335(f335(f108(x94441),x94442),x94443)),f335(f335(f108(x94441),x94442),x94444))),f335(f335(f108(x94441),x94442),f335(f335(f117(x94441),x94443),x94444)))) % 186.01/186.03 [9445]~P109(x94451)+P1(f335(f335(f243(x94451),f335(f335(f242(x94451),f335(f335(f241(x94451),x94452),x94453)),f335(f335(f241(x94451),x94452),x94454))),f335(f335(f241(x94451),x94452),f335(f335(f242(x94451),x94453),x94454)))) % 186.01/186.03 [9506]~P27(x95062,x95061,x95064,f250(f934(x95062,a922)),f250(f934(x95061,a922)))+E(f335(f270(x95061),f335(f335(f8(x95062,a922,x95061),x95063),f97(x95062,x95061,f250(f934(x95062,a922)),x95064))),f335(f318(x95062,x95061,x95064),f335(f270(x95062),x95063))) % 186.01/186.03 [9520]~E(f335(f318(x95202,x95201,x95203),f250(f934(x95202,a922))),f250(f934(x95201,a922)))+P1(f335(f335(f243(f934(x95201,a922)),f335(f85(f934(x95201,a922)),f335(f318(x95202,x95201,x95203),x95204))),f335(f318(x95202,x95201,x95203),f335(f85(f934(x95202,a922)),x95204)))) % 186.01/186.03 [9843]P1(f335(f335(f337(f933(x98431,x98431)),f335(f335(f260(x98431,x98431),x98432),x98433)),f335(f294(x98431,x98431),f335(f335(f297(x98431,x98431,x98431),x98434),f315(x98431,x98434)))))+~P1(f335(f335(f337(f933(x98431,x98431)),f335(f335(f260(x98431,x98431),x98432),x98433)),f335(f335(f297(x98431,x98431,x98431),f335(f294(x98431,x98431),x98434)),f315(x98431,f335(f294(x98431,x98431),x98434))))) % 186.01/186.03 [9844]~P1(f335(f335(f337(f933(x98441,x98441)),f335(f335(f260(x98441,x98441),x98442),x98443)),f335(f294(x98441,x98441),f335(f335(f297(x98441,x98441,x98441),x98444),f315(x98441,x98444)))))+P1(f335(f335(f337(f933(x98441,x98441)),f335(f335(f260(x98441,x98441),x98442),x98443)),f335(f335(f297(x98441,x98441,x98441),f335(f294(x98441,x98441),x98444)),f315(x98441,f335(f294(x98441,x98441),x98444))))) % 186.01/186.03 [9865]~P1(f335(f335(f337(x98652),x98654),f335(f292(x98651,x98652),x98653)))+P1(f335(f335(f337(f933(x98651,x98652)),f335(f335(f260(x98651,x98652),f900(x98653,x98651,x98654,x98652)),x98654)),x98653)) % 186.01/186.03 [9866]~P1(f335(f335(f337(x98662),x98664),f335(f292(x98661,x98662),x98663)))+P1(f335(f335(f337(f933(x98661,x98662)),f335(f335(f260(x98661,x98662),f901(x98663,x98661,x98664,x98662)),x98664)),x98663)) % 186.01/186.03 [9892]~P1(f335(f335(f337(x98921),x98924),f335(f335(f108(f934(x98921,a922)),x98922),x98923)))+P1(f335(f335(f335(f108(f934(x98921,a922)),f335(f335(f7(x98921,f934(x98921,a922),a922),f337(x98921)),x98922)),f335(f335(f7(x98921,f934(x98921,a922),a922),f337(x98921)),x98923)),x98924)) % 186.01/186.03 [9893]~P1(f335(f335(f337(x98931),x98934),f335(f335(f117(f934(x98931,a922)),x98932),x98933)))+P1(f335(f335(f335(f117(f934(x98931,a922)),f335(f335(f7(x98931,f934(x98931,a922),a922),f337(x98931)),x98932)),f335(f335(f7(x98931,f934(x98931,a922),a922),f337(x98931)),x98933)),x98934)) % 186.01/186.03 [9975]~P1(f335(f335(f337(f933(x99751,x99751)),f335(f335(f260(x99751,x99751),x99754),x99753)),f335(f335(f297(x99751,x99751,x99751),x99752),f315(x99751,x99752))))+P1(f335(f335(f337(f933(x99751,x99751)),f335(f335(f260(x99751,x99751),f642(x99752,x99753,x99754,x99751)),x99753)),x99752)) % 186.01/186.03 [10010]P1(f335(f335(f337(x100101),x100102),f335(f335(f108(f934(x100101,a922)),x100103),x100104)))+~P1(f335(f335(f335(f108(f934(x100101,a922)),f335(f335(f7(x100101,f934(x100101,a922),a922),f337(x100101)),x100103)),f335(f335(f7(x100101,f934(x100101,a922),a922),f337(x100101)),x100104)),x100102)) % 186.01/186.03 [10011]P1(f335(f335(f337(x100111),x100112),f335(f335(f117(f934(x100111,a922)),x100113),x100114)))+~P1(f335(f335(f335(f117(f934(x100111,a922)),f335(f335(f7(x100111,f934(x100111,a922),a922),f337(x100111)),x100113)),f335(f335(f7(x100111,f934(x100111,a922),a922),f337(x100111)),x100114)),x100112)) % 186.01/186.03 [10299]P33(x102991,f335(f335(f7(x102991,f934(f933(x102991,x102991),a922),f934(x102991,a922)),f335(f335(f8(f934(x102991,f934(f934(f933(x102991,x102991),a922),a922)),f934(f934(f933(x102991,x102991),a922),f934(x102991,a922)),x102991),f7(x102991,f934(f933(x102991,x102991),a922),a922)),f335(f335(f8(f934(x102991,f933(x102991,x102991)),f934(x102991,f934(f934(f933(x102991,x102991),a922),a922)),x102991),f335(f8(f933(x102991,x102991),f934(f934(f933(x102991,x102991),a922),a922),x102991),f337(f933(x102991,x102991)))),f260(x102991,x102991)))),x102992),x102993,x102994)+~P1(f335(f335(f337(f933(f928(x102991),f928(x102991))),f335(f335(f260(f928(x102991),f928(x102991)),x102993),x102994)),f165(x102991,x102992))) % 186.01/186.03 [10303]P60(x103031,f335(f335(f7(x103031,f934(f933(x103031,x103031),a922),f934(x103031,a922)),f335(f335(f8(f934(x103031,f934(f934(f933(x103031,x103031),a922),a922)),f934(f934(f933(x103031,x103031),a922),f934(x103031,a922)),x103031),f7(x103031,f934(f933(x103031,x103031),a922),a922)),f335(f335(f8(f934(x103031,f933(x103031,x103031)),f934(x103031,f934(f934(f933(x103031,x103031),a922),a922)),x103031),f335(f8(f933(x103031,x103031),f934(f934(f933(x103031,x103031),a922),a922),x103031),f337(f933(x103031,x103031)))),f260(x103031,x103031)))),x103032),x103033,x103034)+~P1(f335(f335(f337(f933(f934(x103031,a922),f934(x103031,a922))),f335(f335(f260(f934(x103031,a922),f934(x103031,a922)),x103033),x103034)),f327(x103031,x103032))) % 186.01/186.03 [10338]E(x103381,x103382)+~E(f335(f335(f7(x103383,f934(f933(x103383,x103384),a922),f934(x103384,a922)),f335(f335(f8(f934(x103384,f934(f934(f933(x103383,x103384),a922),a922)),f934(f934(f933(x103383,x103384),a922),f934(x103384,a922)),x103383),f7(x103384,f934(f933(x103383,x103384),a922),a922)),f335(f335(f8(f934(x103384,f933(x103383,x103384)),f934(x103384,f934(f934(f933(x103383,x103384),a922),a922)),x103383),f335(f8(f933(x103383,x103384),f934(f934(f933(x103383,x103384),a922),a922),x103384),f337(f933(x103383,x103384)))),f260(x103383,x103384)))),x103381),f335(f335(f7(x103383,f934(f933(x103383,x103384),a922),f934(x103384,a922)),f335(f335(f8(f934(x103384,f934(f934(f933(x103383,x103384),a922),a922)),f934(f934(f933(x103383,x103384),a922),f934(x103384,a922)),x103383),f7(x103384,f934(f933(x103383,x103384),a922),a922)),f335(f335(f8(f934(x103384,f933(x103383,x103384)),f934(x103384,f934(f934(f933(x103383,x103384),a922),a922)),x103383),f335(f8(f933(x103383,x103384),f934(f934(f933(x103383,x103384),a922),a922),x103384),f337(f933(x103383,x103384)))),f260(x103383,x103384)))),x103382)) % 186.01/186.03 [10341]~P33(x103411,f335(f335(f7(x103411,f934(f933(x103411,x103411),a922),f934(x103411,a922)),f335(f335(f8(f934(x103411,f934(f934(f933(x103411,x103411),a922),a922)),f934(f934(f933(x103411,x103411),a922),f934(x103411,a922)),x103411),f7(x103411,f934(f933(x103411,x103411),a922),a922)),f335(f335(f8(f934(x103411,f933(x103411,x103411)),f934(x103411,f934(f934(f933(x103411,x103411),a922),a922)),x103411),f335(f8(f933(x103411,x103411),f934(f934(f933(x103411,x103411),a922),a922),x103411),f337(f933(x103411,x103411)))),f260(x103411,x103411)))),x103414),x103412,x103413)+P1(f335(f335(f337(f933(f928(x103411),f928(x103411))),f335(f335(f260(f928(x103411),f928(x103411)),x103412),x103413)),f165(x103411,x103414))) % 186.01/186.03 [10342]~P60(x103421,f335(f335(f7(x103421,f934(f933(x103421,x103421),a922),f934(x103421,a922)),f335(f335(f8(f934(x103421,f934(f934(f933(x103421,x103421),a922),a922)),f934(f934(f933(x103421,x103421),a922),f934(x103421,a922)),x103421),f7(x103421,f934(f933(x103421,x103421),a922),a922)),f335(f335(f8(f934(x103421,f933(x103421,x103421)),f934(x103421,f934(f934(f933(x103421,x103421),a922),a922)),x103421),f335(f8(f933(x103421,x103421),f934(f934(f933(x103421,x103421),a922),a922),x103421),f337(f933(x103421,x103421)))),f260(x103421,x103421)))),x103424),x103422,x103423)+P1(f335(f335(f337(f933(f934(x103421,a922),f934(x103421,a922))),f335(f335(f260(f934(x103421,a922),f934(x103421,a922)),x103422),x103423)),f327(x103421,x103424))) % 186.01/186.03 [7721]~P94(x77211)+E(f335(f335(f87(x77211),f335(f110(x77211),x77212)),f335(f335(f87(x77211),f335(f110(x77211),x77213)),x77214)),f335(f335(f87(x77211),f335(f110(x77211),f335(f335(f87(a1),x77212),x77213))),x77214)) % 186.01/186.03 [7722]~P94(x77221)+E(f335(f335(f86(x77221),f335(f110(x77221),x77222)),f335(f335(f23(x77221),f335(f110(x77221),x77223)),x77224)),f335(f335(f23(x77221),f335(f110(x77221),f335(f335(f86(a1),x77222),x77223))),x77224)) % 186.01/186.03 [7723]~P94(x77231)+E(f335(f335(f86(x77231),f335(f110(x77231),x77232)),f335(f335(f86(x77231),f335(f110(x77231),x77233)),x77234)),f335(f335(f86(x77231),f335(f110(x77231),f335(f335(f86(a1),x77232),x77233))),x77234)) % 186.01/186.03 [7762]~P146(x77621)+E(f335(f172(x77621),f335(f335(f161(x77622,x77621),f335(f16(x77621,x77622),x77623)),x77624)),f335(f335(f87(x77621),f335(f107(x77621),f335(f196(f928(x77622)),x77624))),x77623)) % 186.01/186.03 [7997]E(f335(f276(x79971,f335(f335(f158(f933(a106,x79971)),x79972),x79973)),x79974),f335(f264(a106,x79971),x79972))+~P1(f335(f335(f244(a106),x79974),f335(f259(a106,x79971),x79972))) % 186.01/186.03 [8037]~P94(x80371)+E(f335(f335(f86(x80371),f335(f110(x80371),x80372)),f335(f335(f23(x80371),x80373),f335(f110(x80371),x80374))),f335(f335(f86(x80371),f335(f110(x80371),f335(f335(f86(a1),x80372),f335(f85(a1),x80374)))),x80373)) % 186.01/186.03 [8168]E(f335(f276(x81681,x81682),f335(f335(f23(a106),x81683),f335(f259(a106,x81681),x81684))),f335(f276(x81681,f335(f335(f158(f933(a106,x81681)),x81684),x81682)),x81683))+P1(f335(f335(f244(a106),x81683),f335(f259(a106,x81681),x81684))) % 186.01/186.03 [8601]~P1(f335(f335(f337(x86011),x86012),f335(f179(x86011),f121(x86011,x86014))))+P1(f335(f335(f337(x86011),x86012),f335(f179(x86011),f121(x86011,f335(f335(f141(x86011),x86013),x86014))))) % 186.01/186.03 [8602]~P1(f335(f335(f337(x86021),x86022),f335(f179(x86021),f121(x86021,x86023))))+P1(f335(f335(f337(x86021),x86022),f335(f179(x86021),f121(x86021,f335(f335(f141(x86021),x86023),x86024))))) % 186.01/186.03 [8621]E(f335(f335(f117(f934(x86211,a922)),f335(f335(f108(f934(x86211,a922)),x86212),x86213)),x86214),f335(f335(f108(f934(x86211,a922)),x86212),f335(f335(f117(f934(x86211,a922)),x86213),x86214)))+~P1(f335(f335(f243(f934(x86211,a922)),x86214),x86212)) % 186.01/186.03 [8930]~E(f335(f335(f117(f934(x89301,a922)),f335(f335(f108(f934(x89301,a922)),x89303),x89304)),x89302),f335(f335(f108(f934(x89301,a922)),x89303),f335(f335(f117(f934(x89301,a922)),x89304),x89302)))+P1(f335(f335(f243(f934(x89301,a922)),x89302),x89303)) % 186.01/186.03 [9222]~P1(f335(f335(f243(f934(x92221,a922)),x92222),f335(f335(f117(f934(x92221,a922)),x92223),x92224)))+P1(f335(f335(f243(f934(x92221,a922)),f335(f335(f23(f934(x92221,a922)),x92222),x92223)),x92224)) % 186.01/186.03 [9338]~E(f335(f318(x93381,x93382,x93383),f250(f934(x93381,a922))),f250(f934(x93382,a922)))+E(f335(f318(x93381,x93382,x93383),f335(f318(x93382,x93381,f97(x93381,x93382,f250(f934(x93381,a922)),x93383)),x93384)),x93384) % 186.01/186.03 [9343]P1(f335(f335(f243(f934(x93431,a922)),x93432),f335(f335(f117(f934(x93431,a922)),x93433),x93434)))+~P1(f335(f335(f243(f934(x93431,a922)),f335(f335(f23(f934(x93431,a922)),x93432),x93433)),x93434)) % 186.01/186.03 [9425]~P87(x94251)+E(f335(f81(x94251),f335(f335(f6(x94252,x94251),f335(f335(f8(x94251,x94251,x94252),f81(x94251)),x94253)),x94254)),f335(f335(f6(x94252,x94251),f335(f335(f8(x94251,x94251,x94252),f81(x94251)),x94253)),x94254)) % 186.01/186.03 [9596]~P87(x95961)+P1(f335(f335(f243(x95961),f2(x95961)),f335(f335(f6(x95962,x95961),f335(f335(f8(x95961,x95961,x95962),f81(x95961)),x95963)),x95964))) % 186.01/186.03 [9600]~P5(x96001)+E(f335(f172(x96001),f335(f335(f161(x96002,x96001),f335(f78(x96001,x96001,x96002,f85(x96001)),x96003)),x96004)),f335(f85(x96001),f335(f172(x96001),f335(f335(f161(x96002,x96001),x96003),x96004)))) % 186.01/186.03 [9739]~P87(x97391)+P1(f335(f335(f243(x97391),f335(f81(x97391),f335(f335(f6(x97392,x97391),x97393),x97394))),f335(f335(f6(x97392,x97391),f335(f335(f8(x97391,x97391,x97392),f81(x97391)),x97393)),x97394))) % 186.01/186.03 [9768]~E(f335(f335(f86(a927),x97681),x97684),f335(f335(f86(a927),x97683),x97682))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x97681),x97682)),f335(f335(f260(a927,a927),x97683),x97684))),a115)) % 186.01/186.03 [9769]~P1(f335(f335(f244(a927),x97691),x97693))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x97691),x97692)),f335(f335(f260(a927,a927),x97693),x97694))),a38)) % 186.01/186.03 [9770]~P1(f335(f335(f244(a927),x97701),x97703))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x97701),x97702)),f335(f335(f260(a927,a927),x97703),x97704))),a76)) % 186.01/186.03 [9917]E(f335(f335(f86(a927),x99171),x99172),f335(f335(f86(a927),x99173),x99174))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x99171),x99174)),f335(f335(f260(a927,a927),x99173),x99172))),a115)) % 186.01/186.03 [9949]E(f335(f335(f171(x99491),f335(f335(f145(x99491),f335(f196(f928(x99491)),f184(x99491,x99492,x99493))),x99493)),x99494),f335(f335(f171(x99491),x99493),f335(f335(f86(a927),x99494),f335(f196(f928(x99491)),f184(x99491,x99492,x99493)))))+~P1(f335(f335(f244(a927),x99494),f335(f196(f928(x99491)),f335(f335(f145(x99491),f335(f196(f928(x99491)),f184(x99491,x99492,x99493))),x99493)))) % 186.01/186.03 [9966]~P1(f335(f335(f337(x99662),x99664),f335(f335(f45(x99661,f934(x99662,a922)),f250(f934(x99661,a922))),x99663)))+P1(f335(f335(f335(f45(x99661,f934(x99662,a922)),f250(f934(x99661,a922))),f335(f335(f8(f934(x99662,a922),f934(x99662,a922),x99661),f335(f7(x99662,f934(x99662,a922),a922),f337(x99662))),x99663)),x99664)) % 186.01/186.03 [9967]~P1(f335(f335(f337(x99672),x99674),f335(f335(f46(x99671,f934(x99672,a922)),f250(f934(x99671,a922))),x99673)))+P1(f335(f335(f335(f46(x99671,f934(x99672,a922)),f250(f934(x99671,a922))),f335(f335(f8(f934(x99672,a922),f934(x99672,a922),x99671),f335(f7(x99672,f934(x99672,a922),a922),f337(x99672))),x99673)),x99674)) % 186.01/186.03 [10036]~P1(f335(f55(x100361,x100362),f335(f335(f260(a1,a1),x100364),x100363)))+P1(f335(f55(f335(f85(a1),x100361),x100362),f335(f335(f260(a1,a1),f335(f335(f335(f103(a1),f335(f335(a332,x100363),f2(a1))),f335(f85(a1),x100364)),f335(f335(f23(a1),f335(f85(a1),x100364)),f84(a1)))),f335(f335(f335(f103(a1),f335(f335(a332,x100363),f2(a1))),f2(a1)),f335(f335(f23(a1),x100362),x100363))))) % 186.01/186.03 [10049]P1(f335(f335(f337(x100491),x100492),f335(f335(f45(x100493,f934(x100491,a922)),f250(f934(x100493,a922))),x100494)))+~P1(f335(f335(f335(f45(x100493,f934(x100491,a922)),f250(f934(x100493,a922))),f335(f335(f8(f934(x100491,a922),f934(x100491,a922),x100493),f335(f7(x100491,f934(x100491,a922),a922),f337(x100491))),x100494)),x100492)) % 186.01/186.03 [10050]P1(f335(f335(f337(x100501),x100502),f335(f335(f46(x100503,f934(x100501,a922)),f250(f934(x100503,a922))),x100504)))+~P1(f335(f335(f335(f46(x100503,f934(x100501,a922)),f250(f934(x100503,a922))),f335(f335(f8(f934(x100501,a922),f934(x100501,a922),x100503),f335(f7(x100501,f934(x100501,a922),a922),f337(x100501))),x100504)),x100502)) % 186.01/186.03 [10062]E(f335(f335(f45(a927,f934(x100621,a922)),f250(f934(a927,a922))),x100622),f335(f335(f45(a927,f934(x100621,a922)),f250(f934(a927,a922))),x100623))+~E(f335(f335(f45(a927,f934(x100621,a922)),f335(f310(a927,f2(a927)),f458(x100622,x100624,x100623,x100621))),x100623),f335(f335(f45(a927,f934(x100621,a922)),f335(f310(a927,f2(a927)),f335(f335(f86(a927),f458(x100622,x100624,x100623,x100621)),x100624))),x100622)) % 186.01/186.03 [10420]~P1(f335(f335(f243(f934(f933(x104201,x104202),a922)),x104203),x104204))+P1(f335(f335(f243(f934(x104201,f934(x104202,a922))),f335(f335(f7(x104201,f934(f933(x104201,x104202),a922),f934(x104202,a922)),f335(f335(f8(f934(x104202,f934(f934(f933(x104201,x104202),a922),a922)),f934(f934(f933(x104201,x104202),a922),f934(x104202,a922)),x104201),f7(x104202,f934(f933(x104201,x104202),a922),a922)),f335(f335(f8(f934(x104202,f933(x104201,x104202)),f934(x104202,f934(f934(f933(x104201,x104202),a922),a922)),x104201),f335(f8(f933(x104201,x104202),f934(f934(f933(x104201,x104202),a922),a922),x104202),f337(f933(x104201,x104202)))),f260(x104201,x104202)))),x104203)),f335(f335(f7(x104201,f934(f933(x104201,x104202),a922),f934(x104202,a922)),f335(f335(f8(f934(x104202,f934(f934(f933(x104201,x104202),a922),a922)),f934(f934(f933(x104201,x104202),a922),f934(x104202,a922)),x104201),f7(x104202,f934(f933(x104201,x104202),a922),a922)),f335(f335(f8(f934(x104202,f933(x104201,x104202)),f934(x104202,f934(f934(f933(x104201,x104202),a922),a922)),x104201),f335(f8(f933(x104201,x104202),f934(f934(f933(x104201,x104202),a922),a922),x104202),f337(f933(x104201,x104202)))),f260(x104201,x104202)))),x104204))) % 186.01/186.03 [10436]P1(f335(f335(f243(f934(f933(x104361,x104362),a922)),x104363),x104364))+~P1(f335(f335(f243(f934(x104361,f934(x104362,a922))),f335(f335(f7(x104361,f934(f933(x104361,x104362),a922),f934(x104362,a922)),f335(f335(f8(f934(x104362,f934(f934(f933(x104361,x104362),a922),a922)),f934(f934(f933(x104361,x104362),a922),f934(x104362,a922)),x104361),f7(x104362,f934(f933(x104361,x104362),a922),a922)),f335(f335(f8(f934(x104362,f933(x104361,x104362)),f934(x104362,f934(f934(f933(x104361,x104362),a922),a922)),x104361),f335(f8(f933(x104361,x104362),f934(f934(f933(x104361,x104362),a922),a922),x104362),f337(f933(x104361,x104362)))),f260(x104361,x104362)))),x104363)),f335(f335(f7(x104361,f934(f933(x104361,x104362),a922),f934(x104362,a922)),f335(f335(f8(f934(x104362,f934(f934(f933(x104361,x104362),a922),a922)),f934(f934(f933(x104361,x104362),a922),f934(x104362,a922)),x104361),f7(x104362,f934(f933(x104361,x104362),a922),a922)),f335(f335(f8(f934(x104362,f933(x104361,x104362)),f934(x104362,f934(f934(f933(x104361,x104362),a922),a922)),x104361),f335(f8(f933(x104361,x104362),f934(f934(f933(x104361,x104362),a922),a922),x104362),f337(f933(x104361,x104362)))),f260(x104361,x104362)))),x104364))) % 186.01/186.03 [9471]~P1(f335(f335(f337(f933(x94711,x94711)),x94712),f315(x94711,x94714)))+P1(f335(f335(f337(f933(x94711,x94711)),x94712),f315(x94711,f335(f335(f117(f934(f933(x94711,x94711),a922)),x94713),x94714)))) % 186.01/186.03 [9472]~P1(f335(f335(f337(f933(x94721,x94721)),x94722),f315(x94721,x94723)))+P1(f335(f335(f337(f933(x94721,x94721)),x94722),f315(x94721,f335(f335(f117(f934(f933(x94721,x94721),a922)),x94723),x94724)))) % 186.01/186.03 [10151]~P1(f335(f335(f243(a927),f335(f335(f86(a927),x101511),x101514)),f335(f335(f86(a927),x101513),x101512)))+P1(f335(f335(f243(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x101511),x101512)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x101513),x101514)),f195(f934(f933(a927,a927),a922))))))) % 186.01/186.03 [10152]~P1(f335(f335(f244(a927),f335(f335(f86(a927),x101521),x101524)),f335(f335(f86(a927),x101523),x101522)))+P1(f335(f335(f244(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x101521),x101522)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x101523),x101524)),f195(f934(f933(a927,a927),a922))))))) % 186.01/186.03 [10240]P1(f335(f335(f243(a927),f335(f335(f86(a927),x102401),x102402)),f335(f335(f86(a927),x102403),x102404)))+~P1(f335(f335(f243(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x102401),x102404)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x102403),x102402)),f195(f934(f933(a927,a927),a922))))))) % 186.01/186.03 [10241]P1(f335(f335(f244(a927),f335(f335(f86(a927),x102411),x102412)),f335(f335(f86(a927),x102413),x102414)))+~P1(f335(f335(f244(a1),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x102411),x102414)),f195(f934(f933(a927,a927),a922)))))),f335(a95,f335(f293(f933(a927,a927),f933(a927,a927),a115),f335(f335(f317(f933(a927,a927)),f335(f335(f260(a927,a927),x102413),x102412)),f195(f934(f933(a927,a927),a922))))))) % 186.01/186.03 [10285]P1(f335(f335(f243(f934(x102851,a922)),f335(f335(f45(a927,f934(x102851,a922)),f250(f934(a927,a922))),x102852)),f335(f335(f45(a927,f934(x102851,a922)),f250(f934(a927,a922))),x102853)))+~P1(f335(f335(f243(f934(x102851,a922)),f335(f335(f45(a927,f934(x102851,a922)),f335(f310(a927,f2(a927)),f446(x102853,x102854,x102852,x102851))),x102852)),f335(f335(f45(a927,f934(x102851,a922)),f335(f310(a927,f2(a927)),f335(f335(f86(a927),f446(x102853,x102854,x102852,x102851)),x102854))),x102853))) % 186.01/186.03 [10345]P1(f335(f335(f243(a106),x103454),f2(a106)))+E(f335(f335(f267(f933(a106,a106),f933(x103451,f934(a930,a331)),f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106))),f335(x103452,x103453)),f335(f335(f8(f934(f934(a106,f934(a922,f931(f929(x103451)))),f934(f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106)))),f934(f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106))),f933(x103451,f934(a930,a331))),f335(f267(f933(a106,a106),f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106))),f285(x103451,x103452,f335(f335(f23(a106),x103454),f84(a106)),x103453))),f335(f335(f8(f934(f934(a106,f934(a922,f931(f929(x103451)))),f934(a106,f934(a922,f931(f929(x103451))))),f934(f934(a106,f934(a922,f931(f929(x103451)))),f934(f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106)))),f933(x103451,f934(a930,a331))),f335(f8(f934(a106,f934(a922,f931(f929(x103451)))),f934(f933(a106,a106),f933(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106))),f934(a106,f934(a922,f931(f929(x103451))))),f260(f934(a106,f934(a922,f931(f929(x103451)))),f933(a106,a106)))),f335(f335(f8(f934(a106,f934(a922,f931(f929(x103451)))),f934(f934(a106,f934(a922,f931(f929(x103451)))),f934(a106,f934(a922,f931(f929(x103451))))),f933(x103451,f934(a930,a331))),f50(x103451)),f335(f335(f8(x103451,f934(a106,f934(a922,f931(f929(x103451)))),f933(x103451,f934(a930,a331))),f48(x103451)),f259(x103451,f934(a930,a331))))))),f285(x103451,x103452,x103454,x103453)) % 186.01/186.03 [10408]~P1(f335(f335(f337(x104082),x104084),f335(f292(x104081,x104082),x104083)))+P1(f335(f258(x104081,x104082,f335(f335(f7(x104081,f934(f933(x104081,x104082),a922),f934(x104082,a922)),f335(f335(f8(f934(x104082,f934(f934(f933(x104081,x104082),a922),a922)),f934(f934(f933(x104081,x104082),a922),f934(x104082,a922)),x104081),f7(x104082,f934(f933(x104081,x104082),a922),a922)),f335(f335(f8(f934(x104082,f933(x104081,x104082)),f934(x104082,f934(f934(f933(x104081,x104082),a922),a922)),x104081),f335(f8(f933(x104081,x104082),f934(f934(f933(x104081,x104082),a922),a922),x104082),f337(f933(x104081,x104082)))),f260(x104081,x104082)))),x104083)),x104084)) % 186.01/186.03 [10409]~P1(f335(f335(f337(x104091),x104094),f335(f272(x104091,x104092),x104093)))+P1(f335(f257(x104091,x104092,f335(f335(f7(x104091,f934(f933(x104091,x104092),a922),f934(x104092,a922)),f335(f335(f8(f934(x104092,f934(f934(f933(x104091,x104092),a922),a922)),f934(f934(f933(x104091,x104092),a922),f934(x104092,a922)),x104091),f7(x104092,f934(f933(x104091,x104092),a922),a922)),f335(f335(f8(f934(x104092,f933(x104091,x104092)),f934(x104092,f934(f934(f933(x104091,x104092),a922),a922)),x104091),f335(f8(f933(x104091,x104092),f934(f934(f933(x104091,x104092),a922),a922),x104092),f337(f933(x104091,x104092)))),f260(x104091,x104092)))),x104093)),x104094)) % 186.01/186.03 [10423]P1(f335(f335(f337(x104231),x104232),f335(f292(x104233,x104231),x104234)))+~P1(f335(f258(x104233,x104231,f335(f335(f7(x104233,f934(f933(x104233,x104231),a922),f934(x104231,a922)),f335(f335(f8(f934(x104231,f934(f934(f933(x104233,x104231),a922),a922)),f934(f934(f933(x104233,x104231),a922),f934(x104231,a922)),x104233),f7(x104231,f934(f933(x104233,x104231),a922),a922)),f335(f335(f8(f934(x104231,f933(x104233,x104231)),f934(x104231,f934(f934(f933(x104233,x104231),a922),a922)),x104233),f335(f8(f933(x104233,x104231),f934(f934(f933(x104233,x104231),a922),a922),x104231),f337(f933(x104233,x104231)))),f260(x104233,x104231)))),x104234)),x104232)) % 186.01/186.03 [10424]P1(f335(f335(f337(x104241),x104242),f335(f272(x104241,x104243),x104244)))+~P1(f335(f257(x104241,x104243,f335(f335(f7(x104241,f934(f933(x104241,x104243),a922),f934(x104243,a922)),f335(f335(f8(f934(x104243,f934(f934(f933(x104241,x104243),a922),a922)),f934(f934(f933(x104241,x104243),a922),f934(x104243,a922)),x104241),f7(x104243,f934(f933(x104241,x104243),a922),a922)),f335(f335(f8(f934(x104243,f933(x104241,x104243)),f934(x104243,f934(f934(f933(x104241,x104243),a922),a922)),x104241),f335(f8(f933(x104241,x104243),f934(f934(f933(x104241,x104243),a922),a922),x104243),f337(f933(x104241,x104243)))),f260(x104241,x104243)))),x104244)),x104242)) % 186.01/186.03 [10073]P1(f335(f167(x100731,x100732),x100733))+~P1(f335(f167(x100731,f335(f335(f18(x100731,a922,a922),f335(f335(f8(a922,f934(a922,a922),x100731),a333),x100734)),x100732)),x100733)) % 186.01/186.03 [10074]P1(f335(f167(x100741,x100742),x100743))+~P1(f335(f167(x100741,f335(f335(f18(x100741,a922,a922),f335(f335(f8(a922,f934(a922,a922),x100741),a333),x100742)),x100744)),x100743)) % 186.01/186.03 [10163]~P118(x101631)+E(f335(f335(f87(x101631),f335(f335(f86(x101631),f84(x101631)),f84(x101631))),f335(f335(f6(a927,x101631),f335(f335(f8(x101631,x101631,a927),f335(f86(x101631),x101632)),f335(f335(f7(a927,x101631,x101631),f335(f335(f8(x101631,f934(x101631,x101631),a927),f87(x101631)),f107(x101631))),x101633))),f335(f290(a927),x101634))),f335(f335(f87(x101631),f335(f107(x101631),x101634)),f335(f335(f86(x101631),x101632),f335(f335(f86(x101631),x101632),f335(f335(f87(x101631),f335(f107(x101631),f335(f335(f23(a927),x101634),f84(a927)))),x101633))))) % 186.01/186.03 [10306]P1(f335(x103061,f389(x103062,x103063,x103064,x103061)))+P38(x103062,f335(f270(f933(x103062,x103062)),f335(f265(x103062,x103062,a922),f335(f335(f8(f934(x103062,a922),f934(x103062,a922),x103062),f335(f18(x103062,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103062),a333),x103061))),f335(f335(f7(x103062,f934(x103062,x103062),f934(x103062,a922)),f335(f335(f8(f934(x103062,a922),f934(f934(x103062,x103062),f934(x103062,a922)),x103062),f8(x103062,a922,x103062)),a332)),x103063))))) % 186.01/186.03 [10320]~P1(f335(f335(f244(a927),f335(x103204,f335(x103203,f389(x103201,x103203,x103204,x103202)))),f335(x103204,f389(x103201,x103203,x103204,x103202))))+P38(x103201,f335(f270(f933(x103201,x103201)),f335(f265(x103201,x103201,a922),f335(f335(f8(f934(x103201,a922),f934(x103201,a922),x103201),f335(f18(x103201,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103201),a333),x103202))),f335(f335(f7(x103201,f934(x103201,x103201),f934(x103201,a922)),f335(f335(f8(f934(x103201,a922),f934(f934(x103201,x103201),f934(x103201,a922)),x103201),f8(x103201,a922,x103201)),a332)),x103203))))) % 186.01/186.03 [10393]~P6(x103931)+E(f44(x103931,f335(f270(x103931),f335(f335(f8(f934(f934(x103932,x103931),a922),a922,x103931),f93(f934(x103932,x103931))),f335(f335(f8(f934(f934(x103932,x103931),a922),f934(f934(x103932,x103931),a922),x103931),f335(f18(f934(x103932,x103931),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x103932,x103931)),a333),f335(f335(f7(f934(x103932,x103931),f934(f934(x103932,x103931),a922),a922),f337(f934(x103932,x103931))),x103933)))),f335(f335(f7(x103931,f934(f934(x103932,x103931),x103931),f934(f934(x103932,x103931),a922)),f335(f335(f8(f934(x103931,a922),f934(f934(f934(x103932,x103931),x103931),f934(f934(x103932,x103931),a922)),x103931),f8(x103931,a922,f934(x103932,x103931))),a332)),f335(f335(f7(f934(x103932,x103931),x103932,x103931),f5(f934(x103932,x103931))),x103934)))))),f335(f44(f934(x103932,x103931),x103933),x103934)) % 186.01/186.03 [10394]~P6(x103941)+E(f44(x103941,f335(f270(x103941),f335(f335(f8(f934(f934(x103942,x103941),a922),a922,x103941),f93(f934(x103942,x103941))),f335(f335(f8(f934(f934(x103942,x103941),a922),f934(f934(x103942,x103941),a922),x103941),f335(f18(f934(x103942,x103941),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x103942,x103941)),a333),f335(f335(f7(f934(x103942,x103941),f934(f934(x103942,x103941),a922),a922),f337(f934(x103942,x103941))),x103943)))),f335(f335(f7(x103941,f934(f934(x103942,x103941),x103941),f934(f934(x103942,x103941),a922)),f335(f335(f8(f934(x103941,a922),f934(f934(f934(x103942,x103941),x103941),f934(f934(x103942,x103941),a922)),x103941),f8(x103941,a922,f934(x103942,x103941))),a332)),f335(f335(f7(f934(x103942,x103941),x103942,x103941),f5(f934(x103942,x103941))),x103944)))))),f335(f44(f934(x103942,x103941),x103943),x103944)) % 186.01/186.03 [10395]~P6(x103951)+E(f43(x103951,f335(f270(x103951),f335(f335(f8(f934(f934(x103952,x103951),a922),a922,x103951),f93(f934(x103952,x103951))),f335(f335(f8(f934(f934(x103952,x103951),a922),f934(f934(x103952,x103951),a922),x103951),f335(f18(f934(x103952,x103951),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x103952,x103951)),a333),f335(f335(f7(f934(x103952,x103951),f934(f934(x103952,x103951),a922),a922),f337(f934(x103952,x103951))),x103953)))),f335(f335(f7(x103951,f934(f934(x103952,x103951),x103951),f934(f934(x103952,x103951),a922)),f335(f335(f8(f934(x103951,a922),f934(f934(f934(x103952,x103951),x103951),f934(f934(x103952,x103951),a922)),x103951),f8(x103951,a922,f934(x103952,x103951))),a332)),f335(f335(f7(f934(x103952,x103951),x103952,x103951),f5(f934(x103952,x103951))),x103954)))))),f335(f43(f934(x103952,x103951),x103953),x103954)) % 186.01/186.03 [10396]~P6(x103961)+E(f43(x103961,f335(f270(x103961),f335(f335(f8(f934(f934(x103962,x103961),a922),a922,x103961),f93(f934(x103962,x103961))),f335(f335(f8(f934(f934(x103962,x103961),a922),f934(f934(x103962,x103961),a922),x103961),f335(f18(f934(x103962,x103961),a922,a922),f335(f335(f8(a922,f934(a922,a922),f934(x103962,x103961)),a333),f335(f335(f7(f934(x103962,x103961),f934(f934(x103962,x103961),a922),a922),f337(f934(x103962,x103961))),x103963)))),f335(f335(f7(x103961,f934(f934(x103962,x103961),x103961),f934(f934(x103962,x103961),a922)),f335(f335(f8(f934(x103961,a922),f934(f934(f934(x103962,x103961),x103961),f934(f934(x103962,x103961),a922)),x103961),f8(x103961,a922,f934(x103962,x103961))),a332)),f335(f335(f7(f934(x103962,x103961),x103962,x103961),f5(f934(x103962,x103961))),x103964)))))),f335(f43(f934(x103962,x103961),x103963),x103964)) % 186.01/186.03 [10449]~P1(f335(f335(f337(f933(x104491,x104491)),f335(f335(f260(x104491,x104491),x104493),x104494)),f335(f335(f117(f934(f933(x104491,x104491),a922)),x104492),f315(x104491,f195(f934(f933(x104491,x104491),a922))))))+P1(f335(f335(f335(f335(f117(f934(x104491,f934(x104491,a922))),f335(f335(f7(x104491,f934(f933(x104491,x104491),a922),f934(x104491,a922)),f335(f335(f8(f934(x104491,f934(f934(f933(x104491,x104491),a922),a922)),f934(f934(f933(x104491,x104491),a922),f934(x104491,a922)),x104491),f7(x104491,f934(f933(x104491,x104491),a922),a922)),f335(f335(f8(f934(x104491,f933(x104491,x104491)),f934(x104491,f934(f934(f933(x104491,x104491),a922),a922)),x104491),f335(f8(f933(x104491,x104491),f934(f934(f933(x104491,x104491),a922),a922),x104491),f337(f933(x104491,x104491)))),f260(x104491,x104491)))),x104492)),a332),x104493),x104494)) % 186.01/186.03 [10459]P1(f335(f335(f337(f933(x104591,x104591)),f335(f335(f260(x104591,x104591),x104592),x104593)),f335(f335(f117(f934(f933(x104591,x104591),a922)),x104594),f315(x104591,f195(f934(f933(x104591,x104591),a922))))))+~P1(f335(f335(f335(f335(f117(f934(x104591,f934(x104591,a922))),f335(f335(f7(x104591,f934(f933(x104591,x104591),a922),f934(x104591,a922)),f335(f335(f8(f934(x104591,f934(f934(f933(x104591,x104591),a922),a922)),f934(f934(f933(x104591,x104591),a922),f934(x104591,a922)),x104591),f7(x104591,f934(f933(x104591,x104591),a922),a922)),f335(f335(f8(f934(x104591,f933(x104591,x104591)),f934(x104591,f934(f934(f933(x104591,x104591),a922),a922)),x104591),f335(f8(f933(x104591,x104591),f934(f934(f933(x104591,x104591),a922),a922),x104591),f337(f933(x104591,x104591)))),f260(x104591,x104591)))),x104594)),a332),x104592),x104593)) % 186.01/186.03 [10404]E(f335(f335(f158(f928(x104041)),f335(f335(f158(x104041),x104042),f335(f149(f928(x104041),f928(x104041),f141(x104041),f120(x104041)),f335(f335(f161(f928(x104041),f928(x104041)),f163(f928(x104041),x104041,f120(x104041),f335(f335(f8(f928(x104041),f934(f928(x104041),f928(x104041)),x104041),f16(f928(x104041),f928(x104041))),f335(f335(f7(x104041,f928(x104041),f928(x104041)),f158(x104041)),f120(x104041))))),x104043)))),f186(x104041,f335(f335(f158(f928(x104041)),x104044),f335(f149(f928(f928(x104041)),f928(f928(x104041)),f141(f928(x104041)),f120(f928(x104041))),f335(f335(f161(f928(x104041),f928(f928(x104041))),f163(f928(f928(x104041)),x104041,f120(f928(x104041)),f335(f16(f934(f928(x104041),f928(f928(x104041))),x104041),f335(f335(f7(f928(x104041),f928(f928(x104041)),f928(f928(x104041))),f158(f928(x104041))),f120(f928(x104041)))))),x104043))))),f186(x104041,f335(f335(f158(f928(x104041)),f335(f335(f158(x104041),x104042),x104044)),x104043)))+~P1(f335(f323(f928(f928(x104041)),f187(x104041)),f335(f335(f158(f928(x104041)),f335(f335(f158(x104041),x104042),x104044)),x104043))) % 186.01/186.03 [10448]~P1(f335(f67(x104482),f335(f270(x104482),x104484)))+P1(f335(f67(x104481),f335(f270(x104481),f335(f335(f8(f934(x104482,a922),a922,x104481),f93(x104482)),f335(f335(f7(x104481,f934(x104482,a922),f934(x104482,a922)),f335(f335(f8(f934(x104482,f934(a922,a922)),f934(f934(x104482,a922),f934(x104482,a922)),x104481),f18(x104482,a922,a922)),f335(f335(f8(f934(x104482,a922),f934(x104482,f934(a922,a922)),x104481),f335(f8(a922,f934(a922,a922),x104482),a333)),f335(f335(f7(x104481,f934(x104482,x104481),f934(x104482,a922)),f335(f335(f8(f934(x104481,a922),f934(f934(x104482,x104481),f934(x104482,a922)),x104481),f8(x104481,a922,x104482)),a332)),x104483)))),x104484))))) % 186.01/186.03 [8968]P26(x89681,x89682,x89683,x89684)+~P27(x89681,x89682,x89683,x89684,x89685) % 186.01/186.03 [5507]E(x55071,x55072)+~E(f176(x55073,x55071,x55074),f176(x55073,x55072,x55075)) % 186.01/186.03 [5508]E(x55081,x55082)+~E(f133(x55083,x55084,x55081),f133(x55083,x55085,x55082)) % 186.01/186.03 [5509]E(x55091,x55092)+~E(f133(x55093,x55091,x55094),f133(x55093,x55092,x55095)) % 186.01/186.03 [8300]~E(f335(x83003,x83004),x83005)+E(f80(x83001,x83002,x83003,x83004,x83005),x83003) % 186.01/186.03 [8826]~E(f80(x88264,x88265,x88261,x88262,x88263),x88261)+E(f335(x88261,x88262),x88263) % 186.01/186.03 [9442]~P27(x94422,x94421,x94424,x94423,x94425)+P27(x94421,x94422,f83(x94422,x94421,x94423,x94424),x94425,x94423) % 186.01/186.03 [9443]~P27(x94432,x94431,x94434,x94433,x94435)+P27(x94431,x94432,f97(x94432,x94431,x94433,x94434),x94435,x94433) % 186.01/186.03 [6304]P1(f335(f258(x63041,x63042,x63043),x63044))+~P1(f335(f335(x63043,x63045),x63044)) % 186.01/186.03 [6306]P1(f335(f257(x63061,x63062,x63063),x63064))+~P1(f335(f335(x63063,x63064),x63065)) % 186.01/186.03 [6775]~E(x67755,f2(a106))+E(f335(f205(x67751,x67752,x67753,x67754),x67755),f131(x67752)) % 186.01/186.03 [6776]~E(x67765,f2(a106))+E(f335(f207(x67761,x67762,x67763,x67764),x67765),f122(x67762)) % 186.01/186.03 [6912]~E(x69123,f2(a106))+E(f335(f281(x69121,x69122,x69123,x69124),x69125),f335(f260(x69121,x69122),x69125)) % 186.01/186.03 [7953]~P21(x79534,x79531,x79532,x79535)+E(f335(f78(x79531,x79531,x79531,f335(x79532,x79533)),f335(x79532,x79533)),f335(x79532,x79533)) % 186.01/186.03 [8338]~P17(x83385,x83381,x83382)+E(f335(f78(x83381,x83381,x83381,f335(x83382,x83383)),f335(x83382,x83384)),f335(f78(x83381,x83381,x83381,f335(x83382,x83384)),f335(x83382,x83383))) % 186.01/186.03 [8661]P1(f335(f335(f337(f933(x86611,x86611)),f335(f335(f260(x86611,x86611),x86612),x86613)),f329(x86611,x86614,x86615)))+~P1(f335(f335(f244(a927),f335(x86614,x86612)),f335(x86614,x86613))) % 186.01/186.03 [8754]~P1(f335(f335(f337(x87544),x87543),f307(x87544,x87541,x87542,x87545)))+P1(f335(f335(x87541,x87542),x87543)) % 186.01/186.03 [8755]~P1(f335(f335(f337(x87554),x87553),f298(x87554,x87551,x87552,x87555)))+P1(f335(f335(x87551,x87552),x87553)) % 186.01/186.03 [8756]~P1(f335(f335(f337(x87564),x87562),f307(x87564,x87561,x87565,x87563)))+P1(f335(f335(x87561,x87562),x87563)) % 186.01/186.03 [8757]~P1(f335(f335(f337(x87574),x87572),f298(x87574,x87571,x87575,x87573)))+P1(f335(f335(x87571,x87572),x87573)) % 186.01/186.03 [8838]~P27(x88381,x88383,x88385,x88382,x88384)+E(f335(f41(x88381),x88382),f335(f41(x88383),x88384)) % 186.01/186.03 [8886]~P27(x88861,x88862,x88863,x88864,x88865)+E(f335(f318(x88861,x88862,x88863),x88864),x88865) % 186.01/186.03 [8906]~P58(x89062,x89061,x89065,x89063,x89064)+E(f335(f318(x89061,x89062,x89063),x89064),f250(f934(x89062,a922))) % 186.01/186.03 [9355]~P35(x93551,x93552,x93553,x93554,x93555)+P35(x93551,x93552,x93553,f335(f175(x93551),x93554),f335(f175(x93552),x93555)) % 186.01/186.03 [9357]~P35(x93571,x93572,x93573,f335(f175(x93571),x93574),x93575)+P35(x93571,x93572,x93573,x93574,f335(f175(x93572),x93575)) % 186.01/186.03 [9358]~P35(x93581,x93582,x93583,x93584,f335(f175(x93582),x93585))+P35(x93581,x93582,x93583,f335(f175(x93581),x93584),x93585) % 186.01/186.03 [9364]P35(x93641,x93642,x93643,x93644,x93645)+~P35(x93641,x93642,x93643,f335(f175(x93641),x93644),f335(f175(x93642),x93645)) % 186.01/186.03 [9758]P1(f335(f335(f337(f933(f928(x97581),f928(x97581))),f335(f335(f260(f928(x97581),f928(x97581)),f335(f335(f158(x97581),x97582),x97583)),f335(f335(f158(x97581),x97582),x97584))),f164(x97581,x97585)))+~P1(f335(f335(f337(f933(f928(x97581),f928(x97581))),f335(f335(f260(f928(x97581),f928(x97581)),x97583),x97584)),f164(x97581,x97585))) % 186.01/186.03 [9759]P1(f335(f335(f337(f933(f928(x97591),f928(x97591))),f335(f335(f260(f928(x97591),f928(x97591)),f335(f335(f141(x97591),x97592),x97593)),f335(f335(f141(x97591),x97592),x97594))),f154(x97591,x97595)))+~P1(f335(f335(f337(f933(f928(x97591),f928(x97591))),f335(f335(f260(f928(x97591),f928(x97591)),x97593),x97594)),f154(x97591,x97595))) % 186.01/186.03 [9956]E(f335(f335(f158(x99561),f677(x99562,x99563,x99564,x99565,x99561)),f680(x99562,x99563,x99564,x99565,x99561)),x99565)+~P1(f335(f335(f337(f933(f928(x99561),f928(x99561))),f335(f335(f260(f928(x99561),f928(x99561)),x99565),f335(f335(f158(x99561),x99564),x99563))),f165(x99561,x99562))) % 186.01/186.03 [9978]E(f335(f335(f158(x99781),f678(x99782,x99783,x99784,x99785,x99781)),f679(x99782,x99783,x99784,x99785,x99781)),x99783)+~P1(f335(f335(f337(f933(f928(x99781),f928(x99781))),f335(f335(f260(f928(x99781),f928(x99781)),f335(f335(f158(x99781),x99785),x99784)),x99783)),f165(x99781,x99782))) % 186.01/186.03 [10124]~P1(f335(f335(f337(f933(f928(x101241),f928(x101241))),f335(f335(f260(f928(x101241),f928(x101241)),f335(f335(f158(x101241),x101245),x101242)),x101244)),f165(x101241,x101243)))+P1(f335(f335(f337(f933(f928(x101241),f928(x101241))),f335(f335(f260(f928(x101241),f928(x101241)),x101242),f679(x101243,x101244,x101242,x101245,x101241))),f165(x101241,x101243))) % 186.01/186.03 [10207]~P1(f335(f335(f337(f933(f928(x102071),f928(x102071))),f335(f335(f260(f928(x102071),f928(x102071)),x102075),f335(f335(f158(x102071),x102074),x102073))),f165(x102071,x102072)))+P1(f335(f335(f337(f933(f928(x102071),f928(x102071))),f335(f335(f260(f928(x102071),f928(x102071)),f680(x102072,x102073,x102074,x102075,x102071)),x102073)),f165(x102071,x102072))) % 186.01/186.03 [10397]P1(f335(f335(f337(f933(x103971,x103971)),f335(f335(f260(x103971,x103971),f335(x103972,f335(f335(f86(a927),x103973),x103974))),f335(x103972,x103973))),f315(x103971,x103975)))+~P1(f335(f335(f337(f933(x103971,x103971)),f335(f335(f260(x103971,x103971),f335(x103972,f335(a119,f617(x103974,x103973,x103975,x103972,x103971)))),f335(x103972,f617(x103974,x103973,x103975,x103972,x103971)))),f315(x103971,x103975))) % 186.01/186.03 [5475]E(x54751,x54752)+~E(f335(f335(f158(x54753),x54754),x54751),f335(f335(f158(x54753),x54755),x54752)) % 186.01/186.03 [5476]E(x54761,x54762)+~E(f335(f335(f158(x54763),x54761),x54764),f335(f335(f158(x54763),x54762),x54765)) % 186.01/186.03 [5524]P1(f335(x55241,x55242))+~E(f335(f143(x55243,x55241),x55244),f335(f335(f158(x55243),x55242),x55245)) % 186.01/186.03 [5525]P1(f335(x55251,x55252))+~E(f335(f335(f158(x55253),x55252),x55254),f335(f143(x55253,x55251),x55255)) % 186.01/186.03 [5681]~E(f335(f335(f145(x56811),x56813),x56812),f335(f335(f158(x56811),x56814),x56815))+E(f335(f335(f171(x56811),x56812),x56813),x56814) % 186.01/186.03 [5820]~P15(x58204,x58205,x58201)+E(f335(f335(x58201,x58202),f335(f335(x58201,x58202),x58203)),f335(f335(x58201,x58202),x58203)) % 186.01/186.03 [6362]~E(x63624,f2(a106))+E(f335(f335(f124(x63621,x63622,x63623),x63624),x63625),f335(f335(f260(f928(x63622),x63621),f120(x63622)),x63625)) % 186.01/186.03 [6432]~P109(x64322)+~E(f335(f335(f155(x64321,x64322,x64323),x64324),x64325),f120(x64321)) % 186.01/186.03 [6814]E(x68141,x68142)+~E(f335(f335(f141(x68143),x68144),f335(f335(f158(x68143),x68141),f120(x68143))),f335(f335(f141(x68143),x68145),f335(f335(f158(x68143),x68142),f120(x68143)))) % 186.01/186.03 [6815]E(x68151,x68152)+~E(f335(f335(f141(x68153),x68151),f335(f335(f158(x68153),x68154),f120(x68153))),f335(f335(f141(x68153),x68152),f335(f335(f158(x68153),x68155),f120(x68153)))) % 186.01/186.03 [7126]E(f335(f335(f317(x71261),f335(x71262,x71263)),f335(f318(x71264,x71261,x71262),x71265)),f335(f318(x71264,x71261,x71262),x71265))+~P1(f335(f335(f337(x71264),x71263),x71265)) % 186.01/186.03 [7132]~P1(f335(x71324,f335(x71323,x71325)))+P1(f335(f335(f319(x71321,x71322,x71323),x71324),x71325)) % 186.01/186.03 [7135]~P1(f335(f335(x71353,x71355),x71354))+P1(f335(f335(f251(x71351,x71352,x71353),x71354),x71355)) % 186.01/186.03 [7230]~E(f335(f318(x72301,x72302,x72303),x72304),x72305)+E(f335(f318(f934(x72301,a922),f934(x72302,a922),f318(x72301,x72302,x72303)),f335(f316(x72301),x72304)),f335(f316(x72302),x72305)) % 186.01/186.03 [7257]E(f335(f279(x72571,x72572,x72573,x72574),x72575),f335(x72574,x72575))+~P1(f335(f335(f337(x72571),x72575),x72573)) % 186.01/186.03 [7572]P26(x75721,x75722,x75723,x75724)+~P26(x75721,x75722,x75723,f335(f335(f317(x75721),x75725),x75724)) % 186.01/186.03 [7635]P1(f335(x76351,x76352))+~P1(f335(f335(f99(x76353,x76354,x76351),x76355),x76352)) % 186.01/186.03 [7676]~P1(f335(f335(f337(x76764),x76763),x76765))+P1(f335(f335(f337(x76761),f335(x76762,x76763)),f335(f318(x76764,x76761,x76762),x76765))) % 186.01/186.03 [7697]~P109(x76972)+E(f157(x76971,x76972,x76973,f335(f143(x76971,x76974),x76975)),f335(f143(x76971,x76974),f157(x76971,x76972,x76973,x76975))) % 186.01/186.03 [7727]P1(f335(x77271,f335(x77272,x77273)))+~P1(f335(f335(f319(x77274,x77275,x77272),x77271),x77273)) % 186.01/186.03 [7730]P1(f335(f335(x77301,x77302),x77303))+~P1(f335(f335(f251(x77304,x77305,x77301),x77303),x77302)) % 186.01/186.03 [7731]P1(f335(f335(x77311,x77312),x77313))+~P1(f335(f335(f99(x77314,x77311,x77315),x77312),x77313)) % 186.01/186.03 [7792]~P1(f335(f335(f337(x77923),f335(x77924,x77922)),x77925))+P1(f335(f335(f337(x77921),x77922),f335(f319(x77921,x77923,x77924),x77925))) % 186.01/186.03 [8182]~P1(f335(f335(f337(x81825),x81823),f335(f319(x81825,x81821,x81822),x81824)))+P1(f335(f335(f337(x81821),f335(x81822,x81823)),x81824)) % 186.01/186.03 [8476]~P17(x84762,x84761,x84763)+E(f335(f149(x84761,x84762,f335(f7(x84762,x84761,x84761),x84763),x84764),f159(x84762,x84765)),f335(f335(f70(x84762,x84761,x84763),x84764),f335(f179(x84762),x84765))) % 186.01/186.03 [8498]E(f335(x84981,f408(x84982,x84981,x84983,x84984)),x84984)+~P1(f335(f335(f337(x84985),x84984),f335(f318(x84983,x84985,x84981),x84982))) % 186.01/186.03 [8499]E(f335(x84991,f409(x84992,x84991,x84993,x84994)),x84994)+~P1(f335(f335(f337(x84995),x84994),f335(f318(x84993,x84995,x84991),x84992))) % 186.01/186.03 [8801]~E(x88012,f335(f335(f158(x88011),x88014),x88015))+P1(f335(f335(f337(f933(f928(x88011),f928(x88011))),f335(f335(f260(f928(x88011),f928(x88011)),f120(x88011)),x88012)),f154(x88011,x88013))) % 186.01/186.03 [8847]E(f335(x88471,f335(f97(x88472,x88473,x88474,x88471),x88475)),x88475)+~P1(f335(f335(f337(x88473),x88475),f335(f318(x88472,x88473,x88471),x88474))) % 186.01/186.03 [8850]P26(x88501,x88502,f97(x88502,x88501,x88503,x88504),x88505)+~P1(f335(f335(f243(f934(x88501,a922)),x88505),f335(f318(x88502,x88501,x88504),x88503))) % 186.01/186.03 [8857]~P35(x88571,x88573,x88575,x88572,x88574)+E(f335(f196(f928(x88571)),x88572),f335(f196(f928(x88573)),x88574)) % 186.01/186.03 [8868]P1(f335(f335(f243(f934(x88681,a922)),f335(f335(f46(x88682,f934(x88681,a922)),x88683),x88684)),f335(x88684,x88685)))+~P1(f335(f335(f337(x88682),x88685),x88683)) % 186.01/186.03 [8922]~P58(x89221,x89222,x89223,x89225,x89224)+E(f335(f318(x89221,x89222,x89223),f250(f934(x89221,a922))),x89224) % 186.01/186.03 [9149]E(f335(f143(x91491,x91492),f764(x91493,x91494,x91495,x91492,x91491)),x91493)+~E(f335(f143(x91491,x91492),x91495),f335(f335(f158(x91491),x91494),x91493)) % 186.01/186.03 [9150]E(f335(f143(x91501,x91502),f765(x91503,x91502,x91504,x91505,x91501)),x91504)+~E(f335(f335(f158(x91501),x91505),x91504),f335(f143(x91501,x91502),x91503)) % 186.01/186.03 [9243]E(f335(f196(f928(x92431)),x92432),x92433)+~P1(f335(f335(f337(f933(f928(x92431),f928(x92431))),f335(f335(f260(f928(x92431),f928(x92431)),x92434),x92432)),f335(f150(x92431,x92435),x92433))) % 186.01/186.03 [9244]E(f335(f196(f928(x92441)),x92442),x92443)+~P1(f335(f335(f337(f933(f928(x92441),f928(x92441))),f335(f335(f260(f928(x92441),f928(x92441)),x92442),x92444)),f335(f150(x92441,x92445),x92443))) % 186.01/186.03 [9313]P1(f335(f335(f337(x93131),f408(x93132,x93133,x93131,x93134)),x93132))+~P1(f335(f335(f337(x93135),x93134),f335(f318(x93131,x93135,x93133),x93132))) % 186.01/186.03 [9314]P1(f335(f335(f337(x93141),f409(x93142,x93143,x93141,x93144)),x93142))+~P1(f335(f335(f337(x93145),x93144),f335(f318(x93141,x93145,x93143),x93142))) % 186.01/186.03 [9469]E(f335(f318(x94691,x94692,x94693),f483(x94694,x94693,x94691,x94695,x94692)),x94695)+~P1(f335(f335(f243(f934(x94692,a922)),x94695),f335(f318(x94691,x94692,x94693),x94694))) % 186.01/186.03 [9776]P1(f335(f335(f337(f933(f928(x97761),f928(x97761))),f335(f335(f260(f928(x97761),f928(x97761)),f335(f335(f158(x97761),x97762),x97763)),f335(f335(f158(x97761),x97762),x97764))),f315(f928(x97761),f164(x97761,x97765))))+~P1(f335(f335(f337(f933(f928(x97761),f928(x97761))),f335(f335(f260(f928(x97761),f928(x97761)),x97763),x97764)),f315(f928(x97761),f164(x97761,x97765)))) % 186.01/186.03 [9807]~E(f335(x98073,f717(x98075,x98074,x98073,x98072,x98071)),f335(x98075,f717(x98075,x98074,x98073,x98072,x98071)))+E(f335(f335(f161(x98071,x98072),x98073),x98074),f335(f335(f161(x98071,x98072),x98075),x98074)) % 186.01/186.03 [9883]~E(f335(f143(x98831,x98835),x98834),f335(f335(f158(x98831),x98833),x98832))+E(f335(f335(f141(x98831),f769(x98832,x98833,x98834,x98835,x98831)),f335(f335(f158(x98831),x98833),f764(x98832,x98833,x98834,x98835,x98831))),x98834) % 186.01/186.03 [9884]~E(f335(f335(f158(x98841),x98845),x98844),f335(f143(x98841,x98843),x98842))+E(f335(f335(f141(x98841),f766(x98842,x98843,x98844,x98845,x98841)),f335(f335(f158(x98841),x98845),f765(x98842,x98843,x98844,x98845,x98841))),x98842) % 186.01/186.03 [9888]E(f335(f335(f161(x98881,x98882),x98883),x98884),f335(f335(f161(x98881,x98882),x98885),x98884))+P1(f335(f335(f337(x98881),f717(x98883,x98884,x98885,x98882,x98881)),f335(f179(x98881),x98884))) % 186.01/186.03 [9918]~P1(f335(f335(f337(x99185),x99184),f335(f293(x99181,x99185,x99183),x99182)))+P1(f335(f335(f337(x99181),f768(x99182,x99183,x99181,x99184,x99185)),x99182)) % 186.01/186.03 [9919]~P1(f335(f335(f337(x99195),x99194),f335(f293(x99191,x99195,x99193),x99192)))+P1(f335(f335(f337(x99191),f852(x99192,x99193,x99191,x99194,x99195)),x99192)) % 186.01/186.03 [9950]~P1(f335(f335(f243(f934(x99505,a922)),x99504),f335(f318(x99501,x99505,x99503),x99502)))+P1(f335(f335(f243(f934(x99501,a922)),f483(x99502,x99503,x99501,x99504,x99505)),x99502)) % 186.01/186.03 [10399]E(x103991,f2(a106))+E(f232(f933(f928(x103992),x103993),f933(x103992,x103993),f335(f335(f260(f928(x103992),x103993),f120(x103992)),x103994),f335(f265(x103992,x103993,f933(f928(x103992),x103993)),f335(f335(f7(x103992,f934(x103993,f933(f928(x103992),x103993)),f934(x103993,f933(f928(x103992),x103993))),f335(f335(f8(f934(f933(f928(x103992),x103993),f933(f928(x103992),x103993)),f934(f934(x103993,f933(f928(x103992),x103993)),f934(x103993,f933(f928(x103992),x103993))),x103992),f8(f933(f928(x103992),x103993),f933(f928(x103992),x103993),x103993)),f335(f335(f8(f934(f928(x103992),f934(x103993,f933(f928(x103992),x103993))),f934(f933(f928(x103992),x103993),f933(f928(x103992),x103993)),x103992),f265(f928(x103992),x103993,f933(f928(x103992),x103993))),f335(f335(f8(f934(f928(x103992),f928(x103992)),f934(f928(x103992),f934(x103993,f933(f928(x103992),x103993))),x103992),f335(f8(f928(x103992),f934(x103993,f933(f928(x103992),x103993)),f928(x103992)),f260(f928(x103992),x103993))),f158(x103992))))),f335(f124(x103993,x103992,x103995),f335(f335(f23(a106),x103991),f84(a106))))),f335(x103995,x103994)),f335(f335(f124(x103993,x103992,x103995),x103991),x103994)) % 186.01/186.03 [6243]E(x62431,x62432)+~E(f335(f264(x62433,x62434),f335(f335(f260(x62433,x62434),x62435),x62431)),x62432) % 186.01/186.03 [6244]E(x62441,x62442)+~E(f335(f259(x62443,x62444),f335(f335(f260(x62443,x62444),x62441),x62445)),x62442) % 186.01/186.03 [6505]~E(x65053,f335(f335(f141(x65051),x65054),f335(f335(f158(x65051),x65052),x65055)))+P1(f335(f335(f337(x65051),x65052),f335(f179(x65051),x65053))) % 186.01/186.03 [6899]E(f335(f318(x68991,x68992,f335(f16(x68992,x68991),x68993)),x68994),f335(f335(f317(x68992),x68993),f195(f934(x68992,a922))))+~P1(f335(f335(f337(x68991),x68995),x68994)) % 186.01/186.03 [6971]E(f335(f335(f117(f934(x69711,a922)),f335(f179(x69711),x69712)),f335(f179(x69711),x69713)),f335(f179(x69711),x69714))+~E(f173(x69711,x69715,x69714),f335(f335(f260(f928(x69711),f928(x69711)),x69712),x69713)) % 186.01/186.03 [7069]~P109(x70692)+E(f335(f196(f928(x70691)),f335(f335(f155(x70691,x70692,x70693),x70694),x70695)),f335(a119,f335(f196(f928(x70691)),x70695))) % 186.01/186.03 [7081]~P109(x70812)+E(f335(f179(x70811),f335(f335(f155(x70811,x70812,x70813),x70814),x70815)),f335(f335(f317(x70811),x70814),f335(f179(x70811),x70815))) % 186.01/186.03 [7351]~P118(x73511)+E(f335(f335(f87(x73511),f335(f335(f87(x73511),x73512),x73513)),f335(f335(f87(x73511),x73514),x73515)),f335(f335(f87(x73511),f335(f335(f87(x73511),x73512),x73514)),f335(f335(f87(x73511),x73513),x73515))) % 186.01/186.03 [7352]~P118(x73521)+E(f335(f335(f86(x73521),f335(f335(f86(x73521),x73522),x73523)),f335(f335(f86(x73521),x73524),x73525)),f335(f335(f86(x73521),f335(f335(f86(x73521),x73522),x73524)),f335(f335(f86(x73521),x73523),x73525))) % 186.01/186.03 [7353]~P66(x73531)+E(f335(f335(f299(x73531),f335(f335(f87(x73531),x73532),x73533)),f335(f335(f87(x73531),x73534),x73535)),f335(f335(f87(x73531),f335(f335(f299(x73531),x73532),x73534)),f335(f335(f299(x73531),x73533),x73535))) % 186.01/186.03 [7367]~P109(x73671)+E(f314(x73671,f335(f335(f242(x73671),x73672),x73673),f335(f335(f241(x73671),x73674),x73675)),f335(f335(f108(f934(x73671,a922)),f314(x73671,x73672,x73674)),f314(x73671,x73673,x73675))) % 186.01/186.03 [7368]~P109(x73681)+E(f313(x73681,f335(f335(f242(x73681),x73682),x73683),f335(f335(f241(x73681),x73684),x73685)),f335(f335(f108(f934(x73681,a922)),f313(x73681,x73682,x73684)),f313(x73681,x73683,x73685))) % 186.01/186.03 [7369]~P109(x73691)+E(f311(x73691,f335(f335(f242(x73691),x73692),x73693),f335(f335(f241(x73691),x73694),x73695)),f335(f335(f108(f934(x73691,a922)),f311(x73691,x73692,x73694)),f311(x73691,x73693,x73695))) % 186.01/186.03 [7370]~P109(x73701)+E(f335(f335(f108(f934(x73701,a922)),f335(f310(x73701,x73702),x73703)),f335(f310(x73701,x73704),x73705)),f335(f310(x73701,f335(f335(f242(x73701),x73702),x73704)),f335(f335(f241(x73701),x73703),x73705))) % 186.01/186.03 [7489]~P1(f335(x74891,f363(x74893,x74892,x74891)))+P1(f335(x74891,f335(f335(f260(x74892,x74893),x74894),x74895))) % 186.01/186.03 [7602]~E(x76022,f335(x76024,x76025))+P1(f335(f335(f337(x76021),x76022),f335(f318(x76023,x76021,x76024),f250(f934(x76023,a922))))) % 186.01/186.03 [7673]~P15(x76733,x76732,x76734)+P15(x76731,x76732,f335(f335(f8(x76733,f934(x76732,x76732),x76731),x76734),x76735)) % 186.01/186.03 [7674]~P17(x76743,x76742,x76744)+P17(x76741,x76742,f335(f335(f8(x76743,f934(x76742,x76742),x76741),x76744),x76745)) % 186.01/186.03 [7809]~P26(x78091,x78092,x78093,x78094)+P26(x78091,x78092,x78093,f335(f335(f23(f934(x78091,a922)),x78094),x78095)) % 186.01/186.03 [7962]~P1(f335(f335(x79623,x79624),x79625))+P1(f335(f335(f265(x79621,x79622,a922),x79623),f335(f335(f260(x79621,x79622),x79624),x79625))) % 186.01/186.03 [8072]~P1(f335(x80722,x80724))+~E(f335(f335(f145(x80721),f335(f196(f928(x80721)),f184(x80721,x80722,x80723))),x80723),f335(f335(f158(x80721),x80724),x80725)) % 186.01/186.03 [8092]P26(x80921,x80922,x80923,x80924)+~P26(x80921,x80922,x80923,f335(f335(f117(f934(x80921,a922)),x80925),x80924)) % 186.01/186.03 [8093]P26(x80931,x80932,x80933,x80934)+~P26(x80931,x80932,x80933,f335(f335(f117(f934(x80931,a922)),x80934),x80935)) % 186.01/186.03 [8139]~P109(x81392)+E(f335(f335(f155(x81391,x81392,x81393),x81394),f157(x81391,x81392,x81393,x81395)),f157(x81391,x81392,x81393,f335(f335(f158(x81391),x81394),x81395))) % 186.01/186.03 [8452]~P15(x84522,x84521,x84523)+E(f335(f149(x84521,x84522,f335(f7(x84522,x84521,x84521),x84523),x84524),x84525),f335(f335(f70(x84522,x84521,x84523),x84524),f335(f179(x84522),x84525))) % 186.01/186.03 [8481]~E(f335(f335(f145(x84811),f335(f196(f928(x84811)),f184(x84811,x84812,x84813))),x84813),f335(f335(f158(x84811),x84814),x84815))+E(f335(f335(f141(x84811),f184(x84811,x84812,x84813)),f335(f335(f158(x84811),x84814),x84815)),x84813) % 186.01/186.03 [8509]P1(f335(f335(x85091,x85092),x85093))+~P1(f335(f335(f265(x85094,x85095,a922),x85091),f335(f335(f260(x85094,x85095),x85092),x85093))) % 186.01/186.03 [8985]P1(f335(f335(f243(f934(x89851,a922)),f335(f318(x89852,x89851,x89853),x89854)),f335(f318(x89852,x89851,x89853),x89855)))+~P1(f335(f335(f243(f934(x89852,a922)),x89854),x89855)) % 186.01/186.03 [8986]P1(f335(f335(f243(f934(x89861,a922)),f335(f319(x89861,x89862,x89863),x89864)),f335(f319(x89861,x89862,x89863),x89865)))+~P1(f335(f335(f243(f934(x89862,a922)),x89864),x89865)) % 186.01/186.03 [9065]E(x90651,f2(a106))+E(f335(f335(f267(x90652,x90653,x90652,f933(x90653,x90652)),f335(x90654,x90655)),f281(x90653,x90652,f335(f335(f23(a106),x90651),f84(a106)),x90654)),f335(f281(x90653,x90652,x90651,x90654),x90655)) % 186.01/186.03 [9176]P1(f335(f335(f263(x91761,x91762,a922,x91763),x91764),x91765))+~P1(f335(x91763,f335(f335(f260(x91761,x91762),x91764),x91765))) % 186.01/186.03 [9448]~P1(f335(f335(f263(x94482,x94483,a922,x94481),x94484),x94485))+P1(f335(x94481,f335(f335(f260(x94482,x94483),x94484),x94485))) % 186.01/186.03 [9628]~P1(f335(f335(f337(x96282),x96285),f335(f318(x96281,x96282,x96284),x96283)))+P1(f335(f335(f337(x96281),f335(f97(x96281,x96282,x96283,x96284),x96285)),x96283)) % 186.01/186.03 [9718]~P1(f335(f67(x97183),f335(f318(x97182,x97183,x97185),f250(f934(x97182,a922)))))+P1(f335(f67(x97181),f335(f318(x97182,x97181,f335(f335(f8(x97183,x97181,x97182),x97184),x97185)),f250(f934(x97182,a922))))) % 186.01/186.03 [9743]P1(f335(f335(f243(f934(f934(x97431,a922),a922)),f335(f318(f934(x97432,a922),f934(x97431,a922),f318(x97432,x97431,x97433)),f335(f316(x97432),x97434))),f335(f316(x97431),x97435)))+~P1(f335(f335(f243(f934(x97431,a922)),f335(f318(x97432,x97431,x97433),x97434)),x97435)) % 186.01/186.03 [9815]E(x98151,x98152)+~P1(f335(f72(x98153,x98154,x98155,x98151,f195(f934(x98153,a922))),x98152)) % 186.01/186.03 [9831]E(f335(f335(f260(x98311,x98312),f542(x98313,x98314,x98315,x98312,x98311)),f543(x98313,x98314,x98315,x98312,x98311)),x98315)+~P1(f335(f335(f337(f933(x98311,x98312)),x98315),f335(f335(f262(x98311,x98312),x98314),x98313))) % 186.01/186.03 [9924]P1(f335(f335(f337(x99241),f542(x99242,x99243,x99244,x99245,x99241)),x99243))+~P1(f335(f335(f337(f933(x99241,x99245)),x99244),f335(f335(f262(x99241,x99245),x99243),x99242))) % 186.01/186.03 [9934]P1(f335(f335(f337(x99341),f550(x99342,x99343,x99344,x99345,x99341)),x99345))+P1(f335(f335(f243(f934(x99344,a922)),f335(f318(x99341,x99344,x99343),x99345)),x99342)) % 186.01/186.03 [10046]P25(x100465,x100464,f335(f335(f317(f926(x100465)),f98(x100465,x100461,x100463,x100462)),f195(f934(f926(x100465),a922))))+P1(f335(f335(x100461,f562(x100462,x100463,x100464,x100465,x100461)),f676(x100462,x100463,x100464,x100465,x100461))) % 186.01/186.03 [10082]P1(f335(f335(f337(x100821),f543(x100822,x100823,x100824,x100821,x100825)),f335(x100822,f542(x100822,x100823,x100824,x100821,x100825))))+~P1(f335(f335(f337(f933(x100825,x100821)),x100824),f335(f335(f262(x100825,x100821),x100823),x100822))) % 186.01/186.03 [10102]P1(f335(f335(f337(f933(x101021,x101021)),f335(f335(f260(x101021,x101021),x101022),f639(x101023,x101024,x101025,x101022,x101021))),x101023))+~P1(f335(f335(f337(f933(x101021,x101021)),f335(f335(f260(x101021,x101021),x101022),x101025)),f335(f335(f190(f933(x101021,x101021),a922),f335(a119,x101024)),x101023))) % 186.01/186.03 [10103]P1(f335(f335(f337(f933(x101031,x101031)),f335(f335(f260(x101031,x101031),x101032),f641(x101033,x101034,x101035,x101032,x101031))),x101033))+~P1(f335(f335(f337(f933(x101031,x101031)),f335(f335(f260(x101031,x101031),x101032),x101035)),f335(f335(f190(f933(x101031,x101031),a922),f335(a119,x101034)),x101033))) % 186.01/186.03 [10109]~P25(x101091,x101092,f335(f335(f317(f926(x101091)),f98(x101091,f99(x101091,x101093,x101094),x101095,x101093)),f195(f934(f926(x101091),a922))))+P25(x101091,x101092,f335(f335(f317(f926(x101091)),f98(x101091,x101093,f31(x101094,x101095),f99(x101091,x101093,f335(f78(a922,a922,a923,a330),x101094)))),f195(f934(f926(x101091),a922)))) % 186.01/186.03 [10121]~P1(f335(f335(f337(f933(f928(x101211),f928(x101211))),f335(f335(f260(f928(x101211),f928(x101211)),f335(f335(f158(x101211),x101212),x101215)),x101214)),f165(x101211,x101213)))+P1(f335(f335(f337(f933(x101211,x101211)),f335(f335(f260(x101211,x101211),x101212),f678(x101213,x101214,x101215,x101212,x101211))),x101213)) % 186.01/186.03 [10143]~P1(f335(f335(f337(x101431),f335(x101433,f550(x101435,x101433,x101431,x101434,x101432))),x101435))+P1(f335(f335(f243(f934(x101431,a922)),f335(f318(x101432,x101431,x101433),x101434)),x101435)) % 186.01/186.03 [10388]P25(x103881,x103882,f335(f335(f317(f926(x103881)),f98(x103881,x103883,x103884,x103885)),f195(f934(f926(x103881),a922))))+~P25(x103881,x103882,f335(f335(f317(f926(x103881)),f98(x103881,f335(f16(f934(a923,a922),x103881),f335(f335(f7(a923,a923,a922),a332),f676(x103885,x103884,x103882,x103881,x103883))),x103884,f335(f16(f934(a923,a922),x103881),f335(x103885,f562(x103885,x103884,x103882,x103881,x103883))))),f195(f934(f926(x103881),a922)))) % 186.01/186.03 [6581]P1(f335(x65812,x65814))+E(f184(x65811,x65812,f335(f335(f141(x65811),x65813),f335(f335(f158(x65811),x65814),x65815))),f184(x65811,x65812,x65813)) % 186.01/186.03 [6630]~P3(x66302)+E(f335(f335(f335(f23(f934(x66301,x66302)),x66303),x66304),x66305),f335(f335(f23(x66302),f335(x66303,x66305)),f335(x66304,x66305))) % 186.01/186.03 [6632]~P98(x66322)+E(f335(f335(f335(f108(f934(x66321,x66322)),x66323),x66324),x66325),f335(f335(f108(x66322),f335(x66323,x66325)),f335(x66324,x66325))) % 186.01/186.03 [6634]~P98(x66342)+E(f335(f335(f335(f117(f934(x66341,x66342)),x66343),x66344),x66345),f335(f335(f117(x66342),f335(x66343,x66345)),f335(x66344,x66345))) % 186.01/186.03 [6651]E(x66511,x66512)+E(f335(f335(f171(x66513),f335(f335(f166(x66513,x66514),x66511),x66515)),x66512),f335(f335(f171(x66513),x66514),x66512)) % 186.01/186.03 [6918]~E(x69184,f195(f934(x69183,a922)))+E(f335(f335(f23(f934(x69181,a922)),x69182),f335(f335(f45(x69183,f934(x69181,a922)),x69184),x69185)),x69182) % 186.01/186.03 [6919]~E(x69194,f195(f934(x69193,a922)))+E(f335(f335(f108(f934(x69191,a922)),x69192),f335(f335(f46(x69193,f934(x69191,a922)),x69194),x69195)),x69192) % 186.01/186.03 [6920]~E(x69204,f195(f934(x69203,a922)))+E(f335(f335(f117(f934(x69201,a922)),x69202),f335(f335(f45(x69203,f934(x69201,a922)),x69204),x69205)),x69202) % 186.01/186.03 [6935]~E(x69354,f195(f934(x69353,a922)))+E(f335(f335(f317(x69351),x69352),f335(f335(f45(x69353,f934(x69351,a922)),x69354),x69355)),f335(f335(f317(x69351),x69352),f195(f934(x69351,a922)))) % 186.01/186.03 [7719]E(f335(f335(f171(x77191),f335(f335(f161(x77192,x77191),x77193),x77194)),x77195),f335(x77193,f335(f335(f171(x77192),x77194),x77195)))+~P1(f335(f335(f244(a927),x77195),f335(f196(f928(x77192)),x77194))) % 186.01/186.03 [7780]E(f335(f335(f108(f934(x77801,a922)),f335(x77802,x77803)),f335(f335(f46(x77804,f934(x77801,a922)),x77805),x77802)),f335(f335(f46(x77804,f934(x77801,a922)),x77805),x77802))+~P1(f335(f335(f337(x77804),x77803),x77805)) % 186.01/186.03 [7781]E(f335(f335(f117(f934(x77811,a922)),f335(x77812,x77813)),f335(f335(f45(x77814,f934(x77811,a922)),x77815),x77812)),f335(f335(f45(x77814,f934(x77811,a922)),x77815),x77812))+~P1(f335(f335(f337(x77814),x77813),x77815)) % 186.01/186.03 [8375]~E(x83753,f195(f934(x83751,a922)))+E(f335(f335(f45(x83751,f934(x83752,a922)),x83753),f335(f335(f8(f934(x83752,a922),f934(x83752,a922),x83751),f335(f317(x83752),x83754)),x83755)),f195(f934(x83752,a922))) % 186.01/186.03 [8380]~P1(f335(f335(f337(x83804),x83803),x83805))+P1(f335(f335(f243(f934(x83801,a922)),f335(x83802,x83803)),f335(f335(f45(x83804,f934(x83801,a922)),x83805),x83802))) % 186.01/186.03 [8508]~E(f335(x85084,x85082),x85085)+P1(f335(f335(f337(x85081),x85082),f335(f319(x85081,x85083,x85084),f335(f335(f317(x85083),x85085),f195(f934(x85083,a922)))))) % 186.01/186.03 [8555]~P56(x85551,x85552,f335(f294(x85552,x85551),x85553))+E(f335(f335(f108(f934(x85551,a922)),f335(f293(x85552,x85551,x85553),x85554)),f335(f293(x85552,x85551,x85553),x85555)),f335(f293(x85552,x85551,x85553),f335(f335(f108(f934(x85552,a922)),x85554),x85555))) % 186.01/186.03 [8630]E(x86301,f2(a106))+E(f335(f125(x86302,x86303,f335(x86304,f335(f335(f23(a106),x86301),f84(a106)))),f335(f335(f7(x86302,a106,f929(x86303)),x86305),x86301)),f335(f207(x86302,x86303,x86304,x86305),x86301)) % 186.01/186.03 [8668]E(x86681,f195(f934(x86682,a922)))+E(f335(f335(f45(x86682,f934(x86683,a922)),x86681),f335(f335(f8(f934(x86683,a922),f934(x86683,a922),x86682),f335(f317(x86683),x86684)),x86685)),f335(f335(f317(x86683),x86684),f335(f335(f45(x86682,f934(x86683,a922)),x86681),x86685))) % 186.01/186.03 [8719]~P26(x87192,x87191,x87193,f250(f934(x87192,a922)))+E(f335(f335(f23(f934(x87191,a922)),f335(f318(x87192,x87191,x87193),x87194)),f335(f318(x87192,x87191,x87193),x87195)),f335(f318(x87192,x87191,x87193),f335(f335(f23(f934(x87192,a922)),x87194),x87195))) % 186.01/186.03 [8720]~P26(x87202,x87201,x87203,f250(f934(x87202,a922)))+E(f335(f335(f108(f934(x87201,a922)),f335(f318(x87202,x87201,x87203),x87204)),f335(f318(x87202,x87201,x87203),x87205)),f335(f318(x87202,x87201,x87203),f335(f335(f108(f934(x87202,a922)),x87204),x87205))) % 186.01/186.03 [8788]~P1(f335(f335(f73(x87881,x87882,x87885),x87883),x87884))+P1(f335(f335(f337(f933(x87881,x87882)),f335(f335(f260(x87881,x87882),x87883),x87884)),x87885)) % 186.01/186.03 [8820]P1(f335(f335(f337(x88201),x88202),f335(f292(x88203,x88201),x88204)))+~P1(f335(f335(f337(f933(x88203,x88201)),f335(f335(f260(x88203,x88201),x88205),x88202)),x88204)) % 186.01/186.03 [8822]P1(f335(f335(f337(x88221),x88222),f335(f272(x88221,x88223),x88224)))+~P1(f335(f335(f337(f933(x88221,x88223)),f335(f335(f260(x88221,x88223),x88222),x88225)),x88224)) % 186.01/186.03 [8969]P1(f335(f335(f73(x89691,x89692,x89693),x89694),x89695))+~P1(f335(f335(f337(f933(x89691,x89692)),f335(f335(f260(x89691,x89692),x89694),x89695)),x89693)) % 186.01/186.03 [9008]E(f335(x90081,x90082),x90083)+~P1(f335(f335(f337(x90084),x90082),f335(f319(x90084,x90085,x90081),f335(f335(f317(x90085),x90083),f195(f934(x90085,a922)))))) % 186.01/186.03 [9240]P1(f335(f335(f337(f933(x92401,x92402)),f335(f335(f260(x92401,x92402),x92403),x92404)),f335(f294(x92402,x92401),x92405)))+~P1(f335(f335(f337(f933(x92402,x92401)),f335(f335(f260(x92402,x92401),x92404),x92403)),x92405)) % 186.01/186.03 [9258]~P1(f335(f335(x92581,x92585),x92584))+P1(f335(f335(x92581,f335(f264(x92582,x92583),f335(f335(f260(x92582,x92583),x92584),x92585))),f335(f259(x92582,x92583),f335(f335(f260(x92582,x92583),x92584),x92585)))) % 186.01/186.03 [9288]~P1(f335(f335(f337(f933(x92882,x92881)),f335(f335(f260(x92882,x92881),x92884),x92883)),f335(f294(x92881,x92882),x92885)))+P1(f335(f335(f337(f933(x92881,x92882)),f335(f335(f260(x92881,x92882),x92883),x92884)),x92885)) % 186.01/186.03 [9321]~P1(f335(f335(f337(f933(x93213,x93211)),f335(f335(f260(x93213,x93211),x93215),x93212)),x93214))+P1(f335(f335(f337(x93211),x93212),f335(f293(x93213,x93211,x93214),f335(f335(f317(x93213),x93215),f195(f934(x93213,a922)))))) % 186.01/186.03 [9368]P1(f335(f335(f337(f933(x93681,x93682)),f335(f335(f260(x93681,x93682),x93683),x93684)),x93685))+~P1(f335(f335(f337(x93682),x93684),f335(f293(x93681,x93682,x93685),f335(f335(f317(x93681),x93683),f195(f934(x93681,a922)))))) % 186.01/186.03 [9455]~P76(x94551)+E(f335(f335(f6(a927,x94551),x94552),f311(a927,f335(f335(f86(a927),x94553),x94554),f335(f335(f86(a927),x94555),x94554))),f335(f335(f6(a927,x94551),f335(f335(f8(a927,x94551,a927),x94552),f335(f335(f7(a927,a927,a927),f86(a927)),x94554))),f311(a927,x94553,x94555))) % 186.01/186.03 [9474]~P76(x94741)+E(f335(f335(f6(a927,x94741),x94742),f335(f310(a927,f335(f335(f86(a927),x94743),x94744)),f335(f335(f86(a927),x94745),x94744))),f335(f335(f6(a927,x94741),f335(f335(f8(a927,x94741,a927),x94742),f335(f335(f7(a927,a927,a927),f86(a927)),x94744))),f335(f310(a927,x94743),x94745))) % 186.01/186.03 [9530]~P26(x95301,x95302,x95303,f250(f934(x95301,a922)))+E(f335(f335(f161(x95301,x95302),x95303),f335(f143(x95301,f335(f335(f8(a922,a922,x95301),a330),f335(a332,x95304))),x95305)),f335(f143(x95302,f335(f335(f8(a922,a922,x95302),a330),f335(a332,f335(x95303,x95304)))),f335(f335(f161(x95301,x95302),x95303),x95305))) % 186.01/186.03 [9548]~P26(x95481,x95482,x95483,f335(f335(f317(x95481),x95484),f335(f179(x95481),x95485)))+E(f335(f335(f161(x95481,x95482),x95483),f335(f143(x95481,f335(f335(f8(a922,a922,x95481),a330),f335(a332,x95484))),x95485)),f335(f143(x95482,f335(f335(f8(a922,a922,x95482),a330),f335(a332,f335(x95483,x95484)))),f335(f335(f161(x95481,x95482),x95483),x95485))) % 186.01/186.03 [9706]P1(f335(f335(f337(f933(f928(x97061),f928(x97061))),f335(f335(f260(f928(x97061),f928(x97061)),f335(f335(f158(x97061),x97062),x97063)),f335(f335(f158(x97061),x97064),x97063))),f164(x97061,x97065)))+~P1(f335(f335(f337(f933(x97061,x97061)),f335(f335(f260(x97061,x97061),x97062),x97064)),x97065)) % 186.01/186.03 [9826]E(f335(f335(f317(x98261),f851(x98262,x98263,x98264,x98265,x98261)),f876(x98262,x98263,x98264,x98265,x98261)),f335(f335(f317(x98261),x98264),x98263))+~P1(f335(f68(x98261,x98265,f335(f335(f317(x98261),x98264),x98263)),x98262)) % 186.01/186.03 [9827]E(f335(f335(f317(x98271),f879(x98272,x98273,x98274,x98275,x98271)),f880(x98272,x98273,x98274,x98275,x98271)),f335(f335(f317(x98271),x98274),x98273))+~P1(f335(f68(x98271,x98275,f335(f335(f317(x98271),x98274),x98273)),x98272)) % 186.01/186.03 [9909]P1(f335(f335(f337(x99091),f656(x99092,x99093,x99094,x99095,x99091)),x99094))+P1(f335(f335(f335(f46(x99091,f934(x99095,a922)),x99094),x99093),x99092)) % 186.01/186.03 [9914]P1(f335(f335(f337(x99141),f653(x99142,x99143,x99141,x99144,x99145)),x99143))+P1(f335(f335(f337(x99145),x99144),f335(f335(f46(x99141,f934(x99145,a922)),x99143),x99142))) % 186.01/186.03 [9922]P1(f335(f335(f337(x99221),f654(x99222,x99223,x99221,x99224,x99225)),x99223))+P1(f335(f335(f243(f934(x99225,a922)),x99224),f335(f335(f46(x99221,f934(x99225,a922)),x99223),x99222))) % 186.01/186.03 [9923]P1(f335(f335(f337(x99231),f854(x99232,x99233,x99234,x99235,x99231)),x99235))+P1(f335(f335(f243(f934(x99234,a922)),x99233),f335(f335(f46(x99231,f934(x99234,a922)),x99235),x99232))) % 186.01/186.03 [9925]P1(f335(f335(x99251,f619(x99252,x99251,x99253,x99254,x99255)),x99252))+~P1(f335(f335(f335(f45(x99255,f934(x99254,a922)),x99253),x99251),x99252)) % 186.01/186.03 [9929]P1(f335(f335(f337(x99291),f619(x99292,x99293,x99294,x99295,x99291)),x99294))+~P1(f335(f335(f335(f45(x99291,f934(x99295,a922)),x99294),x99293),x99292)) % 186.01/186.03 [9930]P54(x99304,f335(f335(f46(x99301,f934(x99304,a922)),x99305),x99303),f335(f335(f46(x99301,f934(f933(x99304,x99304),a922)),x99305),x99302))+P1(f335(f335(f337(x99301),f801(x99302,x99303,x99304,x99305,x99301)),x99305)) % 186.01/186.03 [9931]P54(x99314,f335(f335(f45(x99311,f934(x99314,a922)),x99315),x99313),f335(f335(f45(x99311,f934(f933(x99314,x99314),a922)),x99315),x99312))+P1(f335(f335(f337(x99311),f847(x99312,x99313,x99314,x99315,x99311)),x99315)) % 186.01/186.03 [9942]P1(f335(f335(f337(x99421),f686(x99422,x99423,x99421,x99424,x99425)),x99423))+~P1(f335(f335(f337(x99425),x99424),f335(f335(f45(x99421,f934(x99425,a922)),x99423),x99422))) % 186.01/186.03 [9948]P1(f335(f335(f337(x99481),x99482),f335(x99483,f686(x99483,x99484,x99485,x99482,x99481))))+~P1(f335(f335(f337(x99481),x99482),f335(f335(f45(x99485,f934(x99481,a922)),x99484),x99483))) % 186.01/186.03 [10030]~P1(f335(f335(x100304,f656(x100305,x100304,x100303,x100302,x100301)),x100305))+P1(f335(f335(f335(f46(x100301,f934(x100302,a922)),x100303),x100304),x100305)) % 186.01/186.03 [10033]~P1(f335(f335(f337(x100331),x100332),f335(x100335,f653(x100335,x100334,x100333,x100332,x100331))))+P1(f335(f335(f337(x100331),x100332),f335(f335(f46(x100333,f934(x100331,a922)),x100334),x100335))) % 186.01/186.03 [10037]~P54(x100371,f335(x100374,f847(x100375,x100374,x100371,x100373,x100372)),f335(x100375,f847(x100375,x100374,x100371,x100373,x100372)))+P54(x100371,f335(f335(f45(x100372,f934(x100371,a922)),x100373),x100374),f335(f335(f45(x100372,f934(f933(x100371,x100371),a922)),x100373),x100375)) % 186.01/186.03 [10038]~P54(x100381,f335(x100384,f801(x100385,x100384,x100381,x100383,x100382)),f335(x100385,f801(x100385,x100384,x100381,x100383,x100382)))+P54(x100381,f335(f335(f46(x100382,f934(x100381,a922)),x100383),x100384),f335(f335(f46(x100382,f934(f933(x100381,x100381),a922)),x100383),x100385)) % 186.01/186.03 [10039]~P1(f335(f335(f243(f934(x100391,a922)),x100392),f335(x100395,f654(x100395,x100394,x100393,x100392,x100391))))+P1(f335(f335(f243(f934(x100391,a922)),x100392),f335(f335(f46(x100393,f934(x100391,a922)),x100394),x100395))) % 186.01/186.03 [10040]~P1(f335(f335(f243(f934(x100401,a922)),x100402),f335(x100405,f854(x100405,x100402,x100401,x100404,x100403))))+P1(f335(f335(f243(f934(x100401,a922)),x100402),f335(f335(f46(x100403,f934(x100401,a922)),x100404),x100405))) % 186.01/186.03 [10106]~P1(f335(f335(f337(x101061),f851(x101065,x101064,x101063,x101062,x101061)),f876(x101065,x101064,x101063,x101062,x101061)))+~P1(f335(f68(x101061,x101062,f335(f335(f317(x101061),x101063),x101064)),x101065)) % 186.01/186.03 [10107]~P1(f335(f335(f337(x101071),f879(x101075,x101074,x101073,x101072,x101071)),f880(x101075,x101074,x101073,x101072,x101071)))+~P1(f335(f68(x101071,x101072,f335(f335(f317(x101071),x101073),x101074)),x101075)) % 186.01/186.03 [10108]~P1(f335(f335(f337(f933(x101081,x101081)),f335(f335(f260(x101081,x101081),x101082),x101085)),f335(f335(f190(f933(x101081,x101081),a922),f335(a119,x101084)),x101083)))+P1(f335(f335(f337(f933(x101081,x101081)),f335(f335(f260(x101081,x101081),x101082),f640(x101083,x101084,x101085,x101082,x101081))),f335(f335(f190(f933(x101081,x101081),a922),x101084),x101083))) % 186.01/186.03 [10115]P1(f335(f72(x101151,x101151,x101152,f851(x101153,x101154,x101155,x101152,x101151),f876(x101153,x101154,x101155,x101152,x101151)),x101153))+~P1(f335(f68(x101151,x101152,f335(f335(f317(x101151),x101155),x101154)),x101153)) % 186.01/186.03 [10116]P1(f335(f72(x101161,x101161,x101162,f879(x101163,x101164,x101165,x101162,x101161),f880(x101163,x101164,x101165,x101162,x101161)),x101163))+~P1(f335(f68(x101161,x101162,f335(f335(f317(x101161),x101165),x101164)),x101163)) % 186.01/186.03 [10126]~P109(x101261)+P14(x101261,f335(f335(f161(x101262,x101261),x101263),f335(f143(x101262,f335(f335(f7(x101262,x101261,a922),f335(f335(f8(x101261,f934(x101261,a922),x101262),a332),x101263)),f335(x101264,x101265))),x101265))) % 186.01/186.03 [10179]~P1(f335(f335(f337(x101792),x101795),f335(f293(x101791,x101792,x101794),x101793)))+P1(f335(f335(f337(f933(x101791,x101792)),f335(f335(f260(x101791,x101792),f768(x101793,x101794,x101791,x101795,x101792)),x101795)),x101794)) % 186.01/186.03 [10180]~P1(f335(f335(f337(x101802),x101805),f335(f293(x101801,x101802,x101804),x101803)))+P1(f335(f335(f337(f933(x101801,x101802)),f335(f335(f260(x101801,x101802),f852(x101803,x101804,x101801,x101805,x101802)),x101805)),x101804)) % 186.01/186.03 [10200]~P1(f335(f335(f337(f933(x102001,x102001)),f335(f335(f260(x102001,x102001),x102005),x102004)),f335(f335(f190(f933(x102001,x102001),a922),f335(a119,x102003)),x102002)))+P1(f335(f335(f337(f933(x102001,x102001)),f335(f335(f260(x102001,x102001),f640(x102002,x102003,x102004,x102005,x102001)),x102004)),x102002)) % 186.01/186.03 [10203]~P1(f335(f335(f337(f933(x102031,x102031)),f335(f335(f260(x102031,x102031),x102035),x102034)),f335(f335(f190(f933(x102031,x102031),a922),f335(a119,x102033)),x102032)))+P1(f335(f335(f337(f933(x102031,x102031)),f335(f335(f260(x102031,x102031),f639(x102032,x102033,x102034,x102035,x102031)),x102034)),f335(f335(f190(f933(x102031,x102031),a922),x102033),x102032))) % 186.01/186.03 [10204]~P1(f335(f335(f337(f933(x102041,x102041)),f335(f335(f260(x102041,x102041),x102045),x102044)),f335(f335(f190(f933(x102041,x102041),a922),f335(a119,x102043)),x102042)))+P1(f335(f335(f337(f933(x102041,x102041)),f335(f335(f260(x102041,x102041),f641(x102042,x102043,x102044,x102045,x102041)),x102044)),f335(f335(f190(f933(x102041,x102041),a922),x102043),x102042))) % 186.01/186.03 [10205]~P1(f335(f335(f337(f933(f928(x102051),f928(x102051))),f335(f335(f260(f928(x102051),f928(x102051)),x102055),f335(f335(f158(x102051),x102054),x102053))),f165(x102051,x102052)))+P1(f335(f335(f337(f933(x102051,x102051)),f335(f335(f260(x102051,x102051),f677(x102052,x102053,x102054,x102055,x102051)),x102054)),x102052)) % 186.01/186.03 [7801]~E(x78013,f195(f934(x78012,a922)))+E(f335(f335(f108(f934(x78011,a922)),f335(f335(f46(x78012,f934(x78011,a922)),x78013),x78014)),x78015),x78015) % 186.01/186.03 [7802]~E(x78023,f195(f934(x78022,a922)))+E(f335(f335(f117(f934(x78021,a922)),f335(f335(f45(x78022,f934(x78021,a922)),x78023),x78024)),x78025),x78025) % 186.01/186.03 [8221]~E(x82213,f195(f934(x82212,a922)))+E(f335(f335(f23(f934(x82211,a922)),f335(f335(f46(x82212,f934(x82211,a922)),x82213),x82214)),x82215),f335(f335(f23(f934(x82211,a922)),f250(f934(x82211,a922))),x82215)) % 186.01/186.03 [8349]E(f335(f335(f166(x83491,f335(f335(f141(x83491),x83492),x83493)),x83494),x83495),f335(f335(f141(x83491),f335(f335(f166(x83491,x83492),x83494),x83495)),x83493))+~P1(f335(f335(f244(a927),x83494),f335(f196(f928(x83491)),x83492))) % 186.01/186.03 [8620]E(f335(f335(f171(x86201),f335(f335(f161(a927,x86201),x86202),f146(a927,f335(f310(a927,x86203),x86204)))),x86205),f335(x86202,f335(f335(f86(a927),x86203),x86205)))+~P1(f335(f335(f244(a927),x86205),f335(f335(f23(a927),x86204),x86203))) % 186.01/186.03 [8634]E(x86341,f2(a106))+E(f129(x86342,x86343,f335(x86344,f335(f335(f23(a106),x86341),f84(a106))),f335(f335(f7(x86342,a106,f929(f931(x86343))),x86345),x86341)),f335(f205(x86342,x86343,x86344,x86345),x86341)) % 186.01/186.03 [8658]~E(x86583,f195(f934(x86581,a922)))+E(f335(f335(f45(x86581,f934(x86582,a922)),x86583),f335(f335(f8(f934(x86582,a922),f934(x86582,a922),x86581),f335(f117(f934(x86582,a922)),x86584)),x86585)),f195(f934(x86582,a922))) % 186.01/186.03 [8659]~E(x86593,f195(f934(x86591,a922)))+E(f335(f335(f46(x86591,f934(x86592,a922)),x86593),f335(f335(f8(f934(x86592,a922),f934(x86592,a922),x86591),f335(f23(f934(x86592,a922)),x86594)),x86595)),f250(f934(x86592,a922))) % 186.01/186.03 [8660]~E(x86603,f195(f934(x86601,a922)))+E(f335(f335(f46(x86601,f934(x86602,a922)),x86603),f335(f335(f8(f934(x86602,a922),f934(x86602,a922),x86601),f335(f108(f934(x86602,a922)),x86604)),x86605)),f250(f934(x86602,a922))) % 186.01/186.03 [8662]~P145(x86622)+E(f335(f335(f6(x86621,x86622),f335(f335(f8(x86622,x86622,x86621),f335(f87(x86622),x86623)),x86624)),x86625),f335(f335(f87(x86622),x86623),f335(f335(f6(x86621,x86622),x86624),x86625))) % 186.01/186.03 [8953]E(x89531,f195(f934(x89532,a922)))+E(f335(f335(f45(x89532,f934(x89533,a922)),x89531),f335(f335(f8(f934(x89533,a922),f934(x89533,a922),x89532),f335(f117(f934(x89533,a922)),x89534)),x89535)),f335(f335(f117(f934(x89533,a922)),x89534),f335(f335(f45(x89532,f934(x89533,a922)),x89531),x89535))) % 186.01/186.03 [8954]E(x89541,f195(f934(x89542,a922)))+E(f335(f335(f46(x89542,f934(x89543,a922)),x89541),f335(f335(f8(f934(x89543,a922),f934(x89543,a922),x89542),f335(f23(f934(x89543,a922)),x89544)),x89545)),f335(f335(f23(f934(x89543,a922)),x89544),f335(f335(f45(x89542,f934(x89543,a922)),x89541),x89545))) % 186.01/186.03 [8955]E(x89551,f195(f934(x89552,a922)))+E(f335(f335(f46(x89552,f934(x89553,a922)),x89551),f335(f335(f8(f934(x89553,a922),f934(x89553,a922),x89552),f335(f108(f934(x89553,a922)),x89554)),x89555)),f335(f335(f108(f934(x89553,a922)),x89554),f335(f335(f46(x89552,f934(x89553,a922)),x89551),x89555))) % 186.01/186.03 [9158]~P1(f335(f335(f244(a927),f335(x91584,x91582)),f335(x91584,x91583)))+P1(f335(f335(f337(f933(x91581,x91581)),f335(f335(f260(x91581,x91581),x91582),x91583)),f160(x91581,f335(f335(f158(f934(x91581,a927)),x91584),x91585)))) % 186.01/186.03 [9421]~P26(x94212,x94211,x94213,f335(f335(f117(f934(x94212,a922)),x94214),x94215))+E(f335(f335(f108(f934(x94211,a922)),f335(f318(x94212,x94211,x94213),f335(f335(f23(f934(x94212,a922)),x94214),x94215))),f335(f318(x94212,x94211,x94213),f335(f335(f23(f934(x94212,a922)),x94215),x94214))),f195(f934(x94211,a922))) % 186.01/186.03 [9672]~P26(x96723,x96721,x96725,f250(f934(x96723,a922)))+E(f335(f78(x96721,x96722,x96723,f335(f78(x96723,x96722,x96721,x96724),f97(x96723,x96721,f250(f934(x96723,a922)),x96725))),x96725),x96724) % 186.01/186.03 [9702]~P1(f335(f335(f243(f934(x97023,a922)),f335(f293(x97021,x97023,x97024),x97022)),x97025))+P1(f335(f335(f243(f934(x97021,a922)),x97022),f335(f85(f934(x97021,a922)),f335(f293(x97023,x97021,f335(f294(x97021,x97023),x97024)),f335(f85(f934(x97023,a922)),x97025))))) % 186.01/186.03 [9727]~P26(x97271,x97272,x97273,f335(f335(f317(x97271),x97274),x97275))+~P1(f335(f335(f337(x97272),f335(x97273,x97274)),f335(f318(x97271,x97272,x97273),f335(f335(f23(f934(x97271,a922)),x97275),f335(f335(f317(x97271),x97274),f195(f934(x97271,a922))))))) % 186.01/186.03 [9780]P1(f335(f335(f243(f934(x97801,a922)),f335(f293(x97802,x97801,x97803),x97804)),x97805))+~P1(f335(f335(f243(f934(x97802,a922)),x97804),f335(f85(f934(x97802,a922)),f335(f293(x97801,x97802,f335(f294(x97802,x97801),x97803)),f335(f85(f934(x97801,a922)),x97805))))) % 186.01/186.03 [9853]~P87(x98531)+P1(f335(f335(f243(x98531),f335(f81(x98531),f335(f335(f23(x98531),f335(f335(f86(x98531),x98532),x98533)),f335(f335(f86(x98531),x98534),x98535)))),f335(f335(f86(x98531),f335(f81(x98531),f335(f335(f23(x98531),x98532),x98534))),f335(f81(x98531),f335(f335(f23(x98531),x98533),x98535))))) % 186.01/186.03 [9963]P1(f335(f335(f337(x99631),f718(x99632,x99633,x99634,x99631,x99635)),x99634))+P1(f335(f335(f243(f934(x99635,a922)),f335(f335(f45(x99631,f934(x99635,a922)),x99634),x99633)),x99632)) % 186.01/186.03 [9964]P1(f335(f335(f337(x99641),f906(x99642,x99643,x99644,x99645,x99641)),x99645))+P1(f335(f335(f243(f934(x99644,a922)),f335(f335(f45(x99641,f934(x99644,a922)),x99645),x99643)),x99642)) % 186.01/186.03 [10145]~P1(f335(f335(f243(f934(x101451,a922)),f335(x101454,f718(x101455,x101454,x101453,x101452,x101451))),x101455))+P1(f335(f335(f243(f934(x101451,a922)),f335(f335(f45(x101452,f934(x101451,a922)),x101453),x101454)),x101455)) % 186.01/186.03 [10146]~P1(f335(f335(f243(f934(x101461,a922)),f335(x101464,f906(x101465,x101464,x101461,x101463,x101462))),x101465))+P1(f335(f335(f243(f934(x101461,a922)),f335(f335(f45(x101462,f934(x101461,a922)),x101463),x101464)),x101465)) % 186.01/186.03 [8767]E(f335(f335(f141(x87671),x87672),f335(f335(f166(x87671,x87673),f335(f335(f23(a927),x87674),f335(f196(f928(x87671)),x87672))),x87675)),f335(f335(f166(x87671,f335(f335(f141(x87671),x87672),x87673)),x87674),x87675))+P1(f335(f335(f244(a927),x87674),f335(f196(f928(x87671)),x87672))) % 186.01/186.03 [8795]~P141(x87951)+E(f335(f335(f86(x87951),f335(f335(f87(x87951),x87952),x87953)),f335(f335(f86(x87951),f335(f335(f87(x87951),x87954),x87953)),x87955)),f335(f335(f86(x87951),f335(f335(f87(x87951),f335(f335(f86(x87951),x87952),x87954)),x87953)),x87955)) % 186.01/186.03 [9377]~P145(x93771)+E(f335(f172(x93771),f335(f335(f161(x93772,x93771),f335(f335(f8(x93771,x93771,x93772),f335(f87(x93771),x93773)),x93774)),x93775)),f335(f335(f87(x93771),x93773),f335(f172(x93771),f335(f335(f161(x93772,x93771),x93774),x93775)))) % 186.01/186.03 [9547]E(f335(f196(f928(x95471)),f335(f335(f182(x95471),f335(f335(f241(a927),f335(f196(f928(x95471)),x95472)),f335(f196(f928(x95473)),x95474))),x95472)),f335(f196(f928(x95473)),f335(f335(f182(x95473),f335(f335(f241(a927),f335(f196(f928(x95471)),x95472)),f335(f196(f928(x95473)),x95474))),x95474)))+P1(f335(x95475,f335(f335(f188(x95471,x95473),x95472),x95474))) % 186.01/186.03 [9790]~P145(x97902)+E(f335(f335(f6(x97901,x97902),f335(f335(f7(x97901,x97902,x97902),f335(f335(f8(x97902,f934(x97902,x97902),x97901),f87(x97902)),x97903)),x97904)),x97905),f335(f335(f87(x97902),f335(f335(f6(x97901,x97902),x97903),x97905)),x97904)) % 186.01/186.03 [9791]~P67(x97912)+E(f335(f335(f6(x97911,x97912),f335(f335(f7(x97911,x97912,x97912),f335(f335(f8(x97912,f934(x97912,x97912),x97911),f299(x97912)),x97913)),x97914)),x97915),f335(f335(f299(x97912),f335(f335(f6(x97911,x97912),x97913),x97915)),x97914)) % 186.01/186.03 [9798]~P5(x97982)+E(f335(f335(f6(x97981,x97982),f335(f335(f18(x97981,x97982,x97982),f335(f335(f8(x97982,f934(x97982,x97982),x97981),f23(x97982)),x97983)),x97984)),x97985),f335(f335(f23(x97982),f335(f335(f6(x97981,x97982),x97983),x97985)),f335(f335(f6(x97981,x97982),x97984),x97985))) % 186.01/186.03 [9799]~P76(x97992)+E(f335(f335(f6(x97991,x97992),f335(f335(f18(x97991,x97992,x97992),f335(f335(f8(x97992,f934(x97992,x97992),x97991),f86(x97992)),x97993)),x97994)),x97995),f335(f335(f86(x97992),f335(f335(f6(x97991,x97992),x97993),x97995)),f335(f335(f6(x97991,x97992),x97994),x97995))) % 186.01/186.03 [9800]~P72(x98002)+E(f335(f335(f9(x98001,x98002),f335(f335(f18(x98001,x98002,x98002),f335(f335(f8(x98002,f934(x98002,x98002),x98001),f87(x98002)),x98003)),x98004)),x98005),f335(f335(f87(x98002),f335(f335(f9(x98001,x98002),x98003),x98005)),f335(f335(f9(x98001,x98002),x98004),x98005))) % 186.01/186.03 [9838]~E(x98383,f195(f934(x98381,a922)))+E(f335(f335(f45(x98381,f934(x98382,a922)),x98383),f335(f335(f7(x98381,f934(x98382,a922),f934(x98382,a922)),f335(f335(f8(f934(x98382,a922),f934(f934(x98382,a922),f934(x98382,a922)),x98381),f117(f934(x98382,a922))),x98384)),x98385)),f195(f934(x98382,a922))) % 186.01/186.03 [9839]~E(x98393,f195(f934(x98391,a922)))+E(f335(f335(f46(x98391,f934(x98392,a922)),x98393),f335(f335(f7(x98391,f934(x98392,a922),f934(x98392,a922)),f335(f335(f8(f934(x98392,a922),f934(f934(x98392,a922),f934(x98392,a922)),x98391),f23(f934(x98392,a922))),x98394)),x98395)),f250(f934(x98392,a922))) % 186.01/186.03 [9840]~E(x98403,f195(f934(x98401,a922)))+E(f335(f335(f46(x98401,f934(x98402,a922)),x98403),f335(f335(f7(x98401,f934(x98402,a922),f934(x98402,a922)),f335(f335(f8(f934(x98402,a922),f934(f934(x98402,a922),f934(x98402,a922)),x98401),f108(f934(x98402,a922))),x98404)),x98405)),f250(f934(x98402,a922))) % 186.01/186.03 [9861]E(x98611,f195(f934(x98612,a922)))+E(f335(f335(f45(x98612,f934(x98613,a922)),x98611),f335(f335(f7(x98612,f934(x98613,a922),f934(x98613,a922)),f335(f335(f8(f934(x98613,a922),f934(f934(x98613,a922),f934(x98613,a922)),x98612),f117(f934(x98613,a922))),x98614)),x98615)),f335(f335(f117(f934(x98613,a922)),f335(f335(f45(x98612,f934(x98613,a922)),x98611),x98614)),x98615)) % 186.01/186.03 [9862]E(x98621,f195(f934(x98622,a922)))+E(f335(f335(f46(x98622,f934(x98623,a922)),x98621),f335(f335(f7(x98622,f934(x98623,a922),f934(x98623,a922)),f335(f335(f8(f934(x98623,a922),f934(f934(x98623,a922),f934(x98623,a922)),x98622),f23(f934(x98623,a922))),x98624)),x98625)),f335(f335(f23(f934(x98623,a922)),f335(f335(f46(x98622,f934(x98623,a922)),x98621),x98624)),x98625)) % 186.01/186.03 [9863]E(x98631,f195(f934(x98632,a922)))+E(f335(f335(f46(x98632,f934(x98633,a922)),x98631),f335(f335(f7(x98632,f934(x98633,a922),f934(x98633,a922)),f335(f335(f8(f934(x98633,a922),f934(f934(x98633,a922),f934(x98633,a922)),x98632),f108(f934(x98633,a922))),x98634)),x98635)),f335(f335(f108(f934(x98633,a922)),f335(f335(f46(x98632,f934(x98633,a922)),x98631),x98634)),x98635)) % 186.01/186.03 [9426]~P1(f335(f335(f243(a927),x94261),x94264))+E(f335(f335(f23(a927),f335(f335(f86(a927),f335(f335(f87(a927),x94261),x94262)),x94263)),f335(f335(f86(a927),f335(f335(f87(a927),x94264),x94262)),x94265)),f335(f335(f23(a927),x94263),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x94264),x94261)),x94262)),x94265))) % 186.01/186.03 [10013]~P145(x100131)+E(f335(f172(x100131),f335(f335(f161(x100132,x100131),f335(f335(f7(x100132,x100131,x100131),f335(f335(f8(x100131,f934(x100131,x100131),x100132),f87(x100131)),x100133)),x100134)),x100135)),f335(f335(f87(x100131),f335(f172(x100131),f335(f335(f161(x100132,x100131),x100133),x100135))),x100134)) % 186.01/186.03 [10019]~P5(x100191)+E(f335(f172(x100191),f335(f335(f161(x100192,x100191),f335(f335(f18(x100192,x100191,x100191),f335(f335(f8(x100191,f934(x100191,x100191),x100192),f23(x100191)),x100193)),x100194)),x100195)),f335(f335(f23(x100191),f335(f172(x100191),f335(f335(f161(x100192,x100191),x100193),x100195))),f335(f172(x100191),f335(f335(f161(x100192,x100191),x100194),x100195)))) % 186.01/186.03 [10020]~P76(x100201)+E(f335(f172(x100201),f335(f335(f161(x100202,x100201),f335(f335(f18(x100202,x100201,x100201),f335(f335(f8(x100201,f934(x100201,x100201),x100202),f86(x100201)),x100203)),x100204)),x100205)),f335(f335(f86(x100201),f335(f172(x100201),f335(f335(f161(x100202,x100201),x100203),x100205))),f335(f172(x100201),f335(f335(f161(x100202,x100201),x100204),x100205)))) % 186.01/186.03 [10171]P1(f335(x101711,f335(f335(f188(x101712,x101713),x101714),x101715)))+~P1(f335(x101711,f335(f335(f188(x101712,x101713),f335(f335(f182(x101712),f335(f335(f241(a927),f335(f196(f928(x101712)),x101714)),f335(f196(f928(x101713)),x101715))),x101714)),f335(f335(f182(x101713),f335(f335(f241(a927),f335(f196(f928(x101712)),x101714)),f335(f196(f928(x101713)),x101715))),x101715)))) % 186.01/186.03 [10435]~P1(f335(f335(f337(f933(x104352,x104351)),f335(f335(f260(x104352,x104351),x104354),x104355)),f335(f294(x104351,x104352),x104353)))+P1(f335(f335(f251(x104351,x104352,f335(f335(f7(x104351,f934(f933(x104351,x104352),a922),f934(x104352,a922)),f335(f335(f8(f934(x104352,f934(f934(f933(x104351,x104352),a922),a922)),f934(f934(f933(x104351,x104352),a922),f934(x104352,a922)),x104351),f7(x104352,f934(f933(x104351,x104352),a922),a922)),f335(f335(f8(f934(x104352,f933(x104351,x104352)),f934(x104352,f934(f934(f933(x104351,x104352),a922),a922)),x104351),f335(f8(f933(x104351,x104352),f934(f934(f933(x104351,x104352),a922),a922),x104352),f337(f933(x104351,x104352)))),f260(x104351,x104352)))),x104353)),x104354),x104355)) % 186.01/186.03 [10445]P1(f335(f335(f337(f933(x104451,x104452)),f335(f335(f260(x104451,x104452),x104453),x104454)),f335(f294(x104452,x104451),x104455)))+~P1(f335(f335(f251(x104452,x104451,f335(f335(f7(x104452,f934(f933(x104452,x104451),a922),f934(x104451,a922)),f335(f335(f8(f934(x104451,f934(f934(f933(x104452,x104451),a922),a922)),f934(f934(f933(x104452,x104451),a922),f934(x104451,a922)),x104452),f7(x104451,f934(f933(x104452,x104451),a922),a922)),f335(f335(f8(f934(x104451,f933(x104452,x104451)),f934(x104451,f934(f934(f933(x104452,x104451),a922),a922)),x104452),f335(f8(f933(x104452,x104451),f934(f934(f933(x104452,x104451),a922),a922),x104451),f337(f933(x104452,x104451)))),f260(x104452,x104451)))),x104455)),x104453),x104454)) % 186.01/186.03 [9671]~P1(f335(f335(f243(a927),x96714),x96711))+E(f335(f335(f23(a927),f335(f335(f86(a927),f335(f335(f87(a927),x96711),x96712)),x96713)),f335(f335(f86(a927),f335(f335(f87(a927),x96714),x96712)),x96715)),f335(f335(f23(a927),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x96711),x96714)),x96712)),x96713)),x96715)) % 186.01/186.03 [5501]E(x55011,x55012)+~E(f29(x55013,x55014,x55011),f29(x55015,x55016,x55012)) % 186.01/186.03 [5502]E(x55021,x55022)+~E(f29(x55023,x55021,x55024),f29(x55025,x55022,x55026)) % 186.01/186.03 [5503]E(x55031,x55032)+~E(f29(x55031,x55033,x55034),f29(x55032,x55035,x55036)) % 186.01/186.03 [5504]E(x55041,x55042)+~E(f28(x55043,x55044,x55041),f28(x55045,x55046,x55042)) % 186.01/186.03 [5505]E(x55051,x55052)+~E(f28(x55053,x55051,x55054),f28(x55055,x55052,x55056)) % 186.01/186.03 [5506]E(x55061,x55062)+~E(f28(x55061,x55063,x55064),f28(x55062,x55065,x55066)) % 186.01/186.03 [7500]E(x75001,x75002)+~E(f229(x75003,x75004,x75005,x75001),f229(x75003,x75004,x75006,x75002)) % 186.01/186.03 [7501]E(x75011,x75012)+~E(f229(x75013,x75014,x75011,x75015),f229(x75013,x75014,x75012,x75016)) % 186.01/186.03 [8604]~P20(x86045,x86041,x86042,x86046)+E(f335(f78(x86041,x86041,x86041,f335(x86042,x86043)),f335(x86042,x86044)),f335(f78(x86041,x86041,x86041,f335(x86042,x86044)),f335(x86042,x86043))) % 186.01/186.03 [8839]~P58(x88394,x88395,x88392,x88391,x88396)+E(f335(x88391,f335(x88392,x88393)),x88393) % 186.01/186.03 [9006]P26(x90061,x90062,x90063,x90064)+~P26(x90061,x90065,f335(f78(x90062,x90065,x90061,x90066),x90063),x90064) % 186.01/186.03 [9079]~E(x90796,x90794)+E(f335(f80(x90791,x90792,x90793,x90794,x90795),x90796),x90795) % 186.01/186.03 [9085]E(x90851,x90852)+E(f335(f80(x90853,x90854,x90855,x90852,x90856),x90851),f335(x90855,x90851)) % 186.01/186.03 [9097]~P26(x90974,x90972,f335(f78(x90971,x90972,x90974,x90973),x90975),x90976)+P26(x90971,x90972,x90973,f335(f318(x90974,x90971,x90975),x90976)) % 186.01/186.03 [9801]P1(f335(f67(x98011),x98012))+~P1(f335(f72(x98011,x98013,x98014,x98015,x98012),x98016)) % 186.01/186.03 [9810]~P1(f335(f335(f337(x98104),x98103),f308(x98104,x98105,x98101,x98102,x98106)))+P1(f335(f335(x98101,x98102),x98103)) % 186.01/186.03 [9811]~P1(f335(f335(f337(x98114),x98113),f305(x98114,x98111,x98115,x98112,x98116)))+P1(f335(f335(x98111,x98112),x98113)) % 186.01/186.03 [9812]~P1(f335(f335(f337(x98124),x98122),f308(x98124,x98121,x98125,x98126,x98123)))+P1(f335(f335(x98121,x98122),x98123)) % 186.01/186.03 [9813]~P1(f335(f335(f337(x98134),x98132),f305(x98134,x98135,x98131,x98136,x98133)))+P1(f335(f335(x98131,x98132),x98133)) % 186.01/186.03 [10321]P13(x103211,x103212,x103213,x103214,x103215,x103216)+~E(f335(f335(x103216,f907(x103213,x103216,x103215,x103212,x103214,x103211)),f909(x103213,x103216,x103215,x103212,x103214,x103211)),f335(f335(x103216,f908(x103213,x103216,x103215,x103212,x103214,x103211)),f910(x103213,x103216,x103215,x103212,x103214,x103211))) % 186.01/186.03 [6010]E(x60101,x60102)+~E(f335(f335(f260(x60103,x60104),x60105),x60101),f335(f335(f260(x60103,x60104),x60106),x60102)) % 186.01/186.03 [6012]E(x60121,x60122)+~E(f335(f335(f260(x60123,x60124),x60121),x60125),f335(f335(f260(x60123,x60124),x60122),x60126)) % 186.01/186.03 [6144]~P17(x61445,x61446,x61441)+E(f335(f335(x61441,x61442),f335(f335(x61441,x61443),x61444)),f335(f335(x61441,x61443),f335(f335(x61441,x61442),x61444))) % 186.01/186.03 [7566]~P33(x75664,x75661,f335(f335(f158(x75664),x75662),x75665),f335(f335(f158(x75664),x75663),x75666))+P1(f335(f335(x75661,x75662),x75663)) % 186.01/186.03 [7915]P33(x79151,x79152,x79153,x79154)+~P33(x79151,x79152,f335(f335(f158(x79151),x79155),x79153),f335(f335(f158(x79151),x79156),x79154)) % 186.01/186.03 [8943]~P58(x89435,x89431,x89432,x89436,x89434)+P1(f335(f335(f337(x89431),f335(x89432,x89433)),x89434)) % 186.01/186.03 [9125]E(f335(f82(x91251,x91252,x91253,x91254,x91255),x91256),f335(x91253,x91256))+P1(f335(f335(f337(x91251),x91256),x91255)) % 186.01/186.03 [9147]~E(x91473,f335(f335(f158(x91471),x91475),x91476))+P1(f335(f335(f337(f933(f928(x91471),f928(x91471))),f335(f335(f260(f928(x91471),f928(x91471)),x91472),f335(f335(f141(x91471),x91472),x91473))),f154(x91471,x91474))) % 186.01/186.03 [9152]E(f335(f82(x91521,x91522,x91523,x91524,x91525),x91526),f335(x91524,x91526))+~P1(f335(f335(f337(x91521),x91526),x91525)) % 186.01/186.03 [9383]~P35(x93831,x93832,x93833,x93835,x93836)+P35(x93831,x93832,x93833,f335(f335(f182(x93831),x93834),x93835),f335(f335(f182(x93832),x93834),x93836)) % 186.01/186.03 [9384]~P35(x93841,x93842,x93843,x93845,x93846)+P35(x93841,x93842,x93843,f335(f335(f145(x93841),x93844),x93845),f335(f335(f145(x93842),x93844),x93846)) % 186.01/186.03 [9638]E(f335(f318(x96381,x96382,f80(x96381,x96382,x96383,x96384,x96385)),x96386),f335(f318(x96381,x96382,x96383),x96386))+P1(f335(f335(f337(x96381),x96384),x96386)) % 186.01/186.03 [9641]E(f335(f335(f161(x96411,x96412),f80(x96411,x96412,x96413,x96414,x96415)),x96416),f335(f335(f161(x96411,x96412),x96413),x96416))+P1(f335(f335(f337(x96411),x96414),f335(f179(x96411),x96416))) % 186.01/186.03 [9873]~P24(x98734,x98732,x98735,x98733,x98736,x98731)+E(f335(x98731,f195(f934(x98732,a922))),x98733) % 186.01/186.03 [10110]~E(f335(x101104,f335(f259(x101101,x101103),x101105)),f335(x101106,f335(f259(x101101,x101103),x101105)))+E(f335(f266(x101101,x101102,x101103,x101103,x101104,f25(x101103)),x101105),f335(f266(x101101,x101102,x101103,x101103,x101106,f25(x101103)),x101105)) % 186.01/186.03 [10111]~E(f335(x101114,f335(f264(x101111,x101112),x101115)),f335(x101116,f335(f264(x101111,x101112),x101115)))+E(f335(f266(x101111,x101111,x101112,x101113,f25(x101111),x101114),x101115),f335(f266(x101111,x101111,x101112,x101113,f25(x101111),x101116),x101115)) % 186.01/186.03 [10166]~E(f335(f266(x101662,x101666,x101663,x101663,x101661,f25(x101663)),x101664),f335(f266(x101662,x101666,x101663,x101663,x101665,f25(x101663)),x101664))+E(f335(x101661,f335(f259(x101662,x101663),x101664)),f335(x101665,f335(f259(x101662,x101663),x101664))) % 186.01/186.03 [10167]~E(f335(f266(x101672,x101672,x101673,x101676,f25(x101672),x101671),x101674),f335(f266(x101672,x101672,x101673,x101676,f25(x101672),x101675),x101674))+E(f335(x101671,f335(f264(x101672,x101673),x101674)),f335(x101675,f335(f264(x101672,x101673),x101674))) % 186.01/186.03 [9046]P1(f335(f335(f337(x90461),x90462),x90463))+~P1(f335(f335(f337(f933(x90461,x90464)),f335(f335(f260(x90461,x90464),x90462),x90465)),f335(f335(f262(x90461,x90464),x90463),x90466))) % 186.01/186.03 [9062]P1(f335(f335(f337(x90621),x90622),f335(x90623,x90624)))+~P1(f335(f335(f337(f933(x90625,x90621)),f335(f335(f260(x90625,x90621),x90624),x90622)),f335(f335(f262(x90625,x90621),x90626),x90623))) % 186.01/186.03 [9497]P1(f335(f335(f337(f933(x94971,x94971)),f335(f335(f260(x94971,x94971),f335(x94972,x94973)),f335(x94972,x94974))),x94975))+~P1(f335(f335(f337(f933(x94976,x94976)),f335(f335(f260(x94976,x94976),x94973),x94974)),f335(f335(f296(x94971,x94976),x94975),x94972))) % 186.01/186.03 [9517]~P1(f335(f335(f337(f933(x95174,x95174)),f335(f335(f260(x95174,x95174),f335(x95176,x95172)),f335(x95176,x95173))),x95175))+P1(f335(f335(f337(f933(x95171,x95171)),f335(f335(f260(x95171,x95171),x95172),x95173)),f335(f335(f296(x95174,x95171),x95175),x95176))) % 186.01/186.03 [10169]E(f335(f335(f260(x101691,x101692),f667(x101693,x101694,x101695,x101696,x101692,x101691)),f668(x101693,x101694,x101695,x101696,x101692,x101691)),x101696)+~P1(f335(f335(f337(f933(x101691,x101692)),x101696),f335(f335(f297(x101691,x101695,x101692),x101694),x101693))) % 186.01/186.03 [10389]~P1(f335(f335(f337(f933(x103891,x103896)),x103895),f335(f335(f297(x103891,x103892,x103896),x103894),x103893)))+P1(f335(f335(f337(f933(x103891,x103892)),f335(f335(f260(x103891,x103892),f667(x103893,x103894,x103892,x103895,x103896,x103891)),f669(x103893,x103894,x103892,x103895,x103896,x103891))),x103894)) % 186.01/186.03 [10390]~P1(f335(f335(f337(f933(x103906,x103902)),x103905),f335(f335(f297(x103906,x103901,x103902),x103904),x103903)))+P1(f335(f335(f337(f933(x103901,x103902)),f335(f335(f260(x103901,x103902),f669(x103903,x103904,x103901,x103905,x103902,x103906)),f668(x103903,x103904,x103901,x103905,x103902,x103906))),x103903)) % 186.01/186.03 [10391]P13(x103911,x103912,x103913,x103914,x103915,x103916)+P1(f335(f335(f337(f933(x103912,x103912)),f335(f335(f260(x103912,x103912),f910(x103913,x103916,x103915,x103912,x103914,x103911)),f909(x103913,x103916,x103915,x103912,x103914,x103911))),x103915)) % 186.01/186.03 [10392]P13(x103921,x103922,x103923,x103924,x103925,x103926)+P1(f335(f335(f337(f933(x103921,x103921)),f335(f335(f260(x103921,x103921),f908(x103923,x103926,x103925,x103922,x103924,x103921)),f907(x103923,x103926,x103925,x103922,x103924,x103921))),x103924)) % 186.01/186.03 [7985]~P6(x79852)+E(f335(f335(f45(x79851,x79852),x79853),f335(f335(f7(x79851,x79854,x79852),x79855),x79856)),f335(f335(f335(f45(x79851,f934(x79854,x79852)),x79853),x79855),x79856)) % 186.01/186.03 [7986]~P6(x79862)+E(f335(f335(f46(x79861,x79862),x79863),f335(f335(f7(x79861,x79864,x79862),x79865),x79866)),f335(f335(f335(f46(x79861,f934(x79864,x79862)),x79863),x79865),x79866)) % 186.01/186.03 [8749]E(f335(f335(f45(x87491,f934(x87492,a922)),x87493),f335(f335(f8(f934(x87492,a922),f934(x87492,a922),x87491),f335(f317(x87492),x87494)),x87495)),f335(f335(f317(x87492),x87494),f335(f335(f45(x87491,f934(x87492,a922)),x87493),x87495)))+~P1(f335(f335(f337(x87491),x87496),x87493)) % 186.01/186.03 [9202]~P6(x92022)+E(f335(f335(f45(x92021,x92022),x92023),f335(f335(f8(f934(x92024,x92022),x92022,x92021),f335(f45(x92024,x92022),x92025)),f335(f7(x92024,x92021,x92022),x92026))),f335(f335(f45(x92024,x92022),x92025),f335(f335(f8(f934(x92021,x92022),x92022,x92024),f335(f45(x92021,x92022),x92023)),x92026))) % 186.01/186.03 [9203]~P6(x92032)+E(f335(f335(f46(x92031,x92032),x92033),f335(f335(f8(f934(x92034,x92032),x92032,x92031),f335(f46(x92034,x92032),x92035)),f335(f7(x92034,x92031,x92032),x92036))),f335(f335(f46(x92034,x92032),x92035),f335(f335(f8(f934(x92031,x92032),x92032,x92034),f335(f46(x92031,x92032),x92033)),x92036))) % 186.01/186.03 [9408]P1(f335(f335(f337(x94081),x94082),f335(f179(x94081),x94083)))+~P1(f335(f335(f337(f933(x94084,x94081)),f335(f335(f260(x94084,x94081),x94085),x94082)),f335(f179(f933(x94084,x94081)),f335(f335(f188(x94084,x94081),x94086),x94083)))) % 186.01/186.03 [9409]P1(f335(f335(f337(x94091),x94092),f335(f179(x94091),x94093)))+~P1(f335(f335(f337(f933(x94091,x94094)),f335(f335(f260(x94091,x94094),x94092),x94095)),f335(f179(f933(x94091,x94094)),f335(f335(f188(x94091,x94094),x94093),x94096)))) % 186.01/186.03 [9513]P1(f335(f335(f243(f934(x95131,a922)),f335(f293(x95132,x95131,x95133),x95134)),x95135))+~P1(f335(f335(f243(f934(f933(x95132,x95131),a922)),x95133),f335(f335(f262(x95132,x95131),x95136),f335(f16(f934(x95131,a922),x95132),x95135)))) % 186.01/186.03 [9518]~P27(x95184,x95182,x95185,f250(f934(x95184,a922)),f250(f934(x95182,a922)))+E(f335(f335(f46(x95181,f934(x95182,a922)),x95183),f335(f335(f8(f934(x95184,a922),f934(x95182,a922),x95181),f318(x95184,x95182,x95185)),x95186)),f335(f318(x95184,x95182,x95185),f335(f335(f46(x95181,f934(x95184,a922)),x95183),x95186))) % 186.01/186.03 [9705]P1(f335(f335(f337(f933(f928(x97051),f928(x97051))),f335(f335(f260(f928(x97051),f928(x97051)),f335(f335(f158(x97051),x97052),x97053)),f335(f335(f158(x97051),x97054),x97055))),f154(x97051,x97056)))+~P1(f335(f335(f337(f933(x97051,x97051)),f335(f335(f260(x97051,x97051),x97052),x97054)),x97056)) % 186.01/186.03 [10165]E(f335(f335(f260(x101651,x101652),f596(x101653,x101654,x101655,x101652,x101651,x101656)),f597(x101653,x101654,x101655,x101652,x101651,x101656)),x101656)+P1(f335(f335(f337(x101655),x101654),f335(f335(f265(x101651,x101652,f934(x101655,a922)),x101653),x101656))) % 186.01/186.03 [10172]E(f335(f335(f260(x101721,x101722),f598(x101723,x101724,x101722,x101721,x101725,x101726)),f599(x101723,x101724,x101722,x101721,x101725,x101726)),x101723)+~P1(f335(f335(f337(x101726),x101725),f335(f335(f265(x101721,x101722,f934(x101726,a922)),x101724),x101723))) % 186.01/186.03 [10336]P1(f335(f335(f337(x103361),x103362),f335(f335(x103363,f598(x103364,x103363,x103365,x103366,x103362,x103361)),f599(x103364,x103363,x103365,x103366,x103362,x103361))))+~P1(f335(f335(f337(x103361),x103362),f335(f335(f265(x103366,x103365,f934(x103361,a922)),x103363),x103364))) % 186.01/186.03 [10361]~P1(f335(f335(f337(x103611),x103612),f335(f335(x103615,f596(x103615,x103612,x103611,x103614,x103613,x103616)),f597(x103615,x103612,x103611,x103614,x103613,x103616))))+P1(f335(f335(f337(x103611),x103612),f335(f335(f265(x103613,x103614,f934(x103611,a922)),x103615),x103616))) % 186.01/186.03 [8650]E(x86501,x86502)+E(f335(f335(f166(x86503,f335(f335(f166(x86503,x86504),x86501),x86505)),x86502),x86506),f335(f335(f166(x86503,f335(f335(f166(x86503,x86504),x86502),x86506)),x86501),x86505)) % 186.01/186.03 [9765]~P1(f335(f335(f337(x97653),x97656),x97655))+E(f335(f335(f317(x97651),x97652),f335(f318(x97653,x97651,x97654),f335(f335(f23(f934(x97653,a922)),x97655),f335(f335(f317(x97653),x97656),f195(f934(x97653,a922)))))),f335(f318(x97653,x97651,f80(x97653,x97651,x97654,x97656,x97652)),x97655)) % 186.01/186.03 [9281]~P1(f335(f335(x92814,x92815),x92816))+P1(f335(f335(f335(f335(f117(f934(x92811,f934(x92812,a922))),x92813),x92814),x92815),x92816)) % 186.01/186.03 [9283]~P1(f335(f335(x92833,x92835),x92836))+P1(f335(f335(f335(f335(f117(f934(x92831,f934(x92832,a922))),x92833),x92834),x92835),x92836)) % 186.01/186.03 [9568]P1(f335(f335(x95681,x95682),x95683))+~P1(f335(f335(f335(f335(f108(f934(x95684,f934(x95685,a922))),x95686),x95681),x95682),x95683)) % 186.01/186.03 [9569]P1(f335(f335(x95691,x95692),x95693))+~P1(f335(f335(f335(f335(f108(f934(x95694,f934(x95695,a922))),x95691),x95696),x95692),x95693)) % 186.01/186.03 [10001]~P76(x100012)+E(f335(f335(f6(x100011,x100012),f335(f335(f7(x100011,f934(x100013,a922),x100012),f335(f335(f8(f934(x100013,x100012),f934(f934(x100013,a922),x100012),x100011),f6(x100013,x100012)),x100014)),x100015)),x100016),f335(f335(f6(f933(x100011,x100013),x100012),f335(f265(x100011,x100013,x100012),x100014)),f335(f335(f262(x100011,x100013),x100016),f335(f16(f934(x100013,a922),x100011),x100015)))) % 186.01/186.03 [10002]~P72(x100022)+E(f335(f335(f9(x100021,x100022),f335(f335(f7(x100021,f934(x100023,a922),x100022),f335(f335(f8(f934(x100023,x100022),f934(f934(x100023,a922),x100022),x100021),f9(x100023,x100022)),x100024)),x100025)),x100026),f335(f335(f9(f933(x100021,x100023),x100022),f335(f265(x100021,x100023,x100022),x100024)),f335(f335(f262(x100021,x100023),x100026),f335(f16(f934(x100023,a922),x100021),x100025)))) % 186.01/186.03 [10135]~P76(x101352)+E(f335(f335(f6(x101351,x101352),f335(f335(f7(x101351,f934(x101353,a922),x101352),f335(f335(f8(f934(x101353,x101352),f934(f934(x101353,a922),x101352),x101351),f6(x101353,x101352)),f335(f7(x101353,x101351,x101352),x101354))),x101355)),x101356),f335(f335(f6(x101353,x101352),f335(f335(f7(x101353,f934(x101351,a922),x101352),f335(f335(f8(f934(x101351,x101352),f934(f934(x101351,a922),x101352),x101353),f6(x101351,x101352)),x101354)),x101356)),x101355)) % 186.01/186.03 [10457]~P1(f335(f335(f337(f933(x104571,x104572)),f335(f335(f260(x104571,x104572),x104575),x104576)),f335(f335(f108(f934(f933(x104571,x104572),a922)),x104573),x104574)))+P1(f335(f335(f335(f335(f108(f934(x104571,f934(x104572,a922))),f335(f335(f7(x104571,f934(f933(x104571,x104572),a922),f934(x104572,a922)),f335(f335(f8(f934(x104572,f934(f934(f933(x104571,x104572),a922),a922)),f934(f934(f933(x104571,x104572),a922),f934(x104572,a922)),x104571),f7(x104572,f934(f933(x104571,x104572),a922),a922)),f335(f335(f8(f934(x104572,f933(x104571,x104572)),f934(x104572,f934(f934(f933(x104571,x104572),a922),a922)),x104571),f335(f8(f933(x104571,x104572),f934(f934(f933(x104571,x104572),a922),a922),x104572),f337(f933(x104571,x104572)))),f260(x104571,x104572)))),x104573)),f335(f335(f7(x104571,f934(f933(x104571,x104572),a922),f934(x104572,a922)),f335(f335(f8(f934(x104572,f934(f934(f933(x104571,x104572),a922),a922)),f934(f934(f933(x104571,x104572),a922),f934(x104572,a922)),x104571),f7(x104572,f934(f933(x104571,x104572),a922),a922)),f335(f335(f8(f934(x104572,f933(x104571,x104572)),f934(x104572,f934(f934(f933(x104571,x104572),a922),a922)),x104571),f335(f8(f933(x104571,x104572),f934(f934(f933(x104571,x104572),a922),a922),x104572),f337(f933(x104571,x104572)))),f260(x104571,x104572)))),x104574)),x104575),x104576)) % 186.01/186.03 [10458]~P1(f335(f335(f337(f933(x104581,x104582)),f335(f335(f260(x104581,x104582),x104585),x104586)),f335(f335(f117(f934(f933(x104581,x104582),a922)),x104583),x104584)))+P1(f335(f335(f335(f335(f117(f934(x104581,f934(x104582,a922))),f335(f335(f7(x104581,f934(f933(x104581,x104582),a922),f934(x104582,a922)),f335(f335(f8(f934(x104582,f934(f934(f933(x104581,x104582),a922),a922)),f934(f934(f933(x104581,x104582),a922),f934(x104582,a922)),x104581),f7(x104582,f934(f933(x104581,x104582),a922),a922)),f335(f335(f8(f934(x104582,f933(x104581,x104582)),f934(x104582,f934(f934(f933(x104581,x104582),a922),a922)),x104581),f335(f8(f933(x104581,x104582),f934(f934(f933(x104581,x104582),a922),a922),x104582),f337(f933(x104581,x104582)))),f260(x104581,x104582)))),x104583)),f335(f335(f7(x104581,f934(f933(x104581,x104582),a922),f934(x104582,a922)),f335(f335(f8(f934(x104582,f934(f934(f933(x104581,x104582),a922),a922)),f934(f934(f933(x104581,x104582),a922),f934(x104582,a922)),x104581),f7(x104582,f934(f933(x104581,x104582),a922),a922)),f335(f335(f8(f934(x104582,f933(x104581,x104582)),f934(x104582,f934(f934(f933(x104581,x104582),a922),a922)),x104581),f335(f8(f933(x104581,x104582),f934(f934(f933(x104581,x104582),a922),a922),x104582),f337(f933(x104581,x104582)))),f260(x104581,x104582)))),x104584)),x104585),x104586)) % 186.01/186.03 [10467]P1(f335(f335(f337(f933(x104671,x104672)),f335(f335(f260(x104671,x104672),x104673),x104674)),f335(f335(f108(f934(f933(x104671,x104672),a922)),x104675),x104676)))+~P1(f335(f335(f335(f335(f108(f934(x104671,f934(x104672,a922))),f335(f335(f7(x104671,f934(f933(x104671,x104672),a922),f934(x104672,a922)),f335(f335(f8(f934(x104672,f934(f934(f933(x104671,x104672),a922),a922)),f934(f934(f933(x104671,x104672),a922),f934(x104672,a922)),x104671),f7(x104672,f934(f933(x104671,x104672),a922),a922)),f335(f335(f8(f934(x104672,f933(x104671,x104672)),f934(x104672,f934(f934(f933(x104671,x104672),a922),a922)),x104671),f335(f8(f933(x104671,x104672),f934(f934(f933(x104671,x104672),a922),a922),x104672),f337(f933(x104671,x104672)))),f260(x104671,x104672)))),x104675)),f335(f335(f7(x104671,f934(f933(x104671,x104672),a922),f934(x104672,a922)),f335(f335(f8(f934(x104672,f934(f934(f933(x104671,x104672),a922),a922)),f934(f934(f933(x104671,x104672),a922),f934(x104672,a922)),x104671),f7(x104672,f934(f933(x104671,x104672),a922),a922)),f335(f335(f8(f934(x104672,f933(x104671,x104672)),f934(x104672,f934(f934(f933(x104671,x104672),a922),a922)),x104671),f335(f8(f933(x104671,x104672),f934(f934(f933(x104671,x104672),a922),a922),x104672),f337(f933(x104671,x104672)))),f260(x104671,x104672)))),x104676)),x104673),x104674)) % 186.01/186.03 [10468]P1(f335(f335(f337(f933(x104681,x104682)),f335(f335(f260(x104681,x104682),x104683),x104684)),f335(f335(f117(f934(f933(x104681,x104682),a922)),x104685),x104686)))+~P1(f335(f335(f335(f335(f117(f934(x104681,f934(x104682,a922))),f335(f335(f7(x104681,f934(f933(x104681,x104682),a922),f934(x104682,a922)),f335(f335(f8(f934(x104682,f934(f934(f933(x104681,x104682),a922),a922)),f934(f934(f933(x104681,x104682),a922),f934(x104682,a922)),x104681),f7(x104682,f934(f933(x104681,x104682),a922),a922)),f335(f335(f8(f934(x104682,f933(x104681,x104682)),f934(x104682,f934(f934(f933(x104681,x104682),a922),a922)),x104681),f335(f8(f933(x104681,x104682),f934(f934(f933(x104681,x104682),a922),a922),x104682),f337(f933(x104681,x104682)))),f260(x104681,x104682)))),x104685)),f335(f335(f7(x104681,f934(f933(x104681,x104682),a922),f934(x104682,a922)),f335(f335(f8(f934(x104682,f934(f934(f933(x104681,x104682),a922),a922)),f934(f934(f933(x104681,x104682),a922),f934(x104682,a922)),x104681),f7(x104682,f934(f933(x104681,x104682),a922),a922)),f335(f335(f8(f934(x104682,f933(x104681,x104682)),f934(x104682,f934(f934(f933(x104681,x104682),a922),a922)),x104681),f335(f8(f933(x104681,x104682),f934(f934(f933(x104681,x104682),a922),a922),x104682),f337(f933(x104681,x104682)))),f260(x104681,x104682)))),x104686)),x104683),x104684)) % 186.01/186.03 [10451]~P1(f335(f335(f337(f933(x104512,x104513)),f335(f335(f260(x104512,x104513),x104515),x104516)),f335(f335(f45(x104511,f934(f933(x104512,x104513),a922)),f250(f934(x104511,a922))),x104514)))+P1(f335(f335(f335(f335(f45(x104511,f934(x104512,f934(x104513,a922))),f250(f934(x104511,a922))),f335(f335(f8(f934(f933(x104512,x104513),a922),f934(x104512,f934(x104513,a922)),x104511),f335(f7(x104512,f934(f933(x104512,x104513),a922),f934(x104513,a922)),f335(f335(f8(f934(x104513,f934(f934(f933(x104512,x104513),a922),a922)),f934(f934(f933(x104512,x104513),a922),f934(x104513,a922)),x104512),f7(x104513,f934(f933(x104512,x104513),a922),a922)),f335(f335(f8(f934(x104513,f933(x104512,x104513)),f934(x104513,f934(f934(f933(x104512,x104513),a922),a922)),x104512),f335(f8(f933(x104512,x104513),f934(f934(f933(x104512,x104513),a922),a922),x104513),f337(f933(x104512,x104513)))),f260(x104512,x104513))))),x104514)),x104515),x104516)) % 186.01/186.03 [10452]~P1(f335(f335(f337(f933(x104522,x104523)),f335(f335(f260(x104522,x104523),x104525),x104526)),f335(f335(f46(x104521,f934(f933(x104522,x104523),a922)),f250(f934(x104521,a922))),x104524)))+P1(f335(f335(f335(f335(f46(x104521,f934(x104522,f934(x104523,a922))),f250(f934(x104521,a922))),f335(f335(f8(f934(f933(x104522,x104523),a922),f934(x104522,f934(x104523,a922)),x104521),f335(f7(x104522,f934(f933(x104522,x104523),a922),f934(x104523,a922)),f335(f335(f8(f934(x104523,f934(f934(f933(x104522,x104523),a922),a922)),f934(f934(f933(x104522,x104523),a922),f934(x104523,a922)),x104522),f7(x104523,f934(f933(x104522,x104523),a922),a922)),f335(f335(f8(f934(x104523,f933(x104522,x104523)),f934(x104523,f934(f934(f933(x104522,x104523),a922),a922)),x104522),f335(f8(f933(x104522,x104523),f934(f934(f933(x104522,x104523),a922),a922),x104523),f337(f933(x104522,x104523)))),f260(x104522,x104523))))),x104524)),x104525),x104526)) % 186.01/186.03 [10461]P1(f335(f335(f337(f933(x104611,x104612)),f335(f335(f260(x104611,x104612),x104613),x104614)),f335(f335(f45(x104615,f934(f933(x104611,x104612),a922)),f250(f934(x104615,a922))),x104616)))+~P1(f335(f335(f335(f335(f45(x104615,f934(x104611,f934(x104612,a922))),f250(f934(x104615,a922))),f335(f335(f8(f934(f933(x104611,x104612),a922),f934(x104611,f934(x104612,a922)),x104615),f335(f7(x104611,f934(f933(x104611,x104612),a922),f934(x104612,a922)),f335(f335(f8(f934(x104612,f934(f934(f933(x104611,x104612),a922),a922)),f934(f934(f933(x104611,x104612),a922),f934(x104612,a922)),x104611),f7(x104612,f934(f933(x104611,x104612),a922),a922)),f335(f335(f8(f934(x104612,f933(x104611,x104612)),f934(x104612,f934(f934(f933(x104611,x104612),a922),a922)),x104611),f335(f8(f933(x104611,x104612),f934(f934(f933(x104611,x104612),a922),a922),x104612),f337(f933(x104611,x104612)))),f260(x104611,x104612))))),x104616)),x104613),x104614)) % 186.01/186.03 [10462]P1(f335(f335(f337(f933(x104621,x104622)),f335(f335(f260(x104621,x104622),x104623),x104624)),f335(f335(f46(x104625,f934(f933(x104621,x104622),a922)),f250(f934(x104625,a922))),x104626)))+~P1(f335(f335(f335(f335(f46(x104625,f934(x104621,f934(x104622,a922))),f250(f934(x104625,a922))),f335(f335(f8(f934(f933(x104621,x104622),a922),f934(x104621,f934(x104622,a922)),x104625),f335(f7(x104621,f934(f933(x104621,x104622),a922),f934(x104622,a922)),f335(f335(f8(f934(x104622,f934(f934(f933(x104621,x104622),a922),a922)),f934(f934(f933(x104621,x104622),a922),f934(x104622,a922)),x104621),f7(x104622,f934(f933(x104621,x104622),a922),a922)),f335(f335(f8(f934(x104622,f933(x104621,x104622)),f934(x104622,f934(f934(f933(x104621,x104622),a922),a922)),x104621),f335(f8(f933(x104621,x104622),f934(f934(f933(x104621,x104622),a922),a922),x104622),f337(f933(x104621,x104622)))),f260(x104621,x104622))))),x104626)),x104623),x104624)) % 186.01/186.03 [7497]E(x74971,x74972)+~E(f98(x74973,x74974,x74975,x74971),f98(x74973,x74976,x74977,x74972)) % 186.01/186.03 [7498]E(x74981,x74982)+~E(f98(x74983,x74984,x74981,x74985),f98(x74983,x74986,x74982,x74987)) % 186.01/186.03 [7499]E(x74991,x74992)+~E(f98(x74993,x74991,x74994,x74995),f98(x74993,x74992,x74996,x74997)) % 186.01/186.03 [7669]E(f335(x76691,f335(x76692,x76693)),f335(x76694,x76693))+~E(f335(f78(x76695,x76696,x76697,x76691),x76692),x76694) % 186.01/186.03 [9781]E(x97811,x97812)+E(f80(x97813,x97814,f80(x97813,x97814,x97815,x97811,x97816),x97812,x97817),f80(x97813,x97814,f80(x97813,x97814,x97815,x97812,x97817),x97811,x97816)) % 186.01/186.03 [9872]~P23(x98723,x98724,x98721,x98725,x98726,x98727)+E(f335(f335(x98721,x98722),x98722),x98722) % 186.01/186.03 [6245]~E(f335(f335(f161(x62451,x62455),x62456),x62452),f335(f335(f161(x62453,x62455),x62457),x62454))+E(f335(f196(f928(x62451)),x62452),f335(f196(f928(x62453)),x62454)) % 186.01/186.03 [8681]E(f335(x86811,f335(x86812,x86813)),f335(x86814,x86813))+~E(f335(f78(x86815,x86816,x86817,x86811),x86812),f335(f78(x86816,x86816,x86817,f25(x86816)),x86814)) % 186.01/186.03 [9035]~P35(x90354,x90355,x90351,f335(f335(f158(x90354),x90352),x90356),f335(f335(f158(x90355),x90353),x90357))+P1(f335(f335(x90351,x90352),x90353)) % 186.01/186.03 [9415]P35(x94151,x94152,x94153,x94154,x94155)+~P35(x94151,x94152,x94153,f335(f335(f158(x94151),x94156),x94154),f335(f335(f158(x94152),x94157),x94155)) % 186.01/186.03 [10034]P1(f335(f335(x100341,x100342),f362(x100343,x100342,x100344,x100341)))+~P1(f335(f335(f261(x100345,x100346,x100347,x100341,x100344),x100342),x100343)) % 186.01/186.03 [10059]P1(f335(f335(x100591,f362(x100592,x100593,x100591,x100594)),x100592))+~P1(f335(f335(f261(x100595,x100596,x100597,x100594,x100591),x100593),x100592)) % 186.01/186.03 [9156]~P21(x91566,x91561,x91563,x91567)+E(f335(f78(x91561,x91561,x91562,f335(x91563,x91564)),f335(f78(x91561,x91561,x91562,f335(x91563,x91564)),x91565)),f335(f78(x91561,x91561,x91562,f335(x91563,x91564)),x91565)) % 186.01/186.03 [9521]~P35(x95213,x95212,x95214,f335(f335(f161(x95211,x95213),x95215),x95216),x95217)+P35(x95211,x95212,f335(f335(f8(x95213,f934(x95212,a922),x95211),x95214),x95215),x95216,x95217) % 186.01/186.03 [9544]P35(x95441,x95442,x95443,f335(f335(f161(x95444,x95441),x95445),x95446),x95447)+~P35(x95444,x95442,f335(f335(f8(x95441,f934(x95442,a922),x95444),x95443),x95445),x95446,x95447) % 186.01/186.03 [9155]~P1(f335(f335(f337(x91551),x91552),f335(f335(x91555,x91556),x91557)))+P1(f335(f335(f337(x91551),x91552),f335(f335(f265(x91553,x91554,f934(x91551,a922)),x91555),f335(f335(f260(x91553,x91554),x91556),x91557)))) % 186.01/186.03 [9438]P1(f335(f335(f335(x94381,x94382),x94383),x94384))+~P1(f335(f335(f335(f265(x94385,x94386,f934(x94387,a922)),x94381),f335(f335(f260(x94385,x94386),x94382),x94383)),x94384)) % 186.01/186.03 [9583]P1(f335(f335(f337(x95831),f335(f335(x95832,x95833),x95834)),f335(f318(f933(x95835,x95836),x95831,f335(f265(x95835,x95836,x95831),x95832)),x95837)))+~P1(f335(f335(f337(f933(x95835,x95836)),f335(f335(f260(x95835,x95836),x95833),x95834)),x95837)) % 186.01/186.03 [9920]P1(f335(f335(f337(f933(f928(x99201),f928(x99201))),f335(f335(f260(f928(x99201),f928(x99201)),f335(f335(f141(x99201),x99202),f335(f335(f158(x99201),x99203),x99204))),f335(f335(f141(x99201),x99202),f335(f335(f158(x99201),x99205),x99206)))),f154(x99201,x99207)))+~P1(f335(f335(f337(f933(x99201,x99201)),f335(f335(f260(x99201,x99201),x99203),x99205)),x99207)) % 186.01/186.03 [9986]~P35(x99861,x99863,x99864,x99866,f335(f335(f161(x99862,x99863),x99865),x99867))+P35(x99861,x99862,f335(f335(f7(x99861,f934(x99862,x99863),f934(x99862,a922)),f335(f335(f8(f934(x99863,a922),f934(f934(x99862,x99863),f934(x99862,a922)),x99861),f8(x99863,a922,x99862)),x99864)),x99865),x99866,x99867) % 186.01/186.03 [10063]P35(x100631,x100632,x100633,x100634,f335(f335(f161(x100635,x100632),x100636),x100637))+~P35(x100631,x100635,f335(f335(f7(x100631,f934(x100635,x100632),f934(x100635,a922)),f335(f335(f8(f934(x100632,a922),f934(f934(x100635,x100632),f934(x100635,a922)),x100631),f8(x100632,a922,x100635)),x100633)),x100636),x100634,x100637) % 186.01/186.03 [10375]P1(f335(f335(f337(x103751),f660(x103752,x103753,x103754,x103755,x103756,x103757,x103751)),x103755))+P1(f335(f335(f335(f335(f46(x103751,f934(x103757,f934(x103756,a922))),x103755),x103754),x103753),x103752)) % 186.01/186.03 [10376]P1(f335(f335(f337(x103761),f812(x103762,x103763,x103764,x103765,x103766,x103767,x103761)),x103767))+P1(f335(f335(f335(f335(f46(x103761,f934(x103763,f934(x103762,a922))),x103767),x103766),x103765),x103764)) % 186.01/186.03 [10377]P1(f335(f335(f337(x103771),f818(x103772,x103773,x103774,x103775,x103776,x103777,x103771)),x103775))+~P1(f335(f335(f335(f335(f45(x103771,f934(x103777,f934(x103776,a922))),x103775),x103774),x103773),x103772)) % 186.01/186.03 [10378]P1(f335(f335(f337(x103781),f896(x103782,x103783,x103784,x103785,x103786,x103787,x103781)),x103785))+~P1(f335(f335(f335(f335(f45(x103781,f934(x103787,f934(x103786,a922))),x103785),x103784),x103783),x103782)) % 186.01/186.03 [10415]P1(f335(f335(f335(x104151,f818(x104152,x104153,x104151,x104154,x104155,x104156,x104157)),x104153),x104152))+~P1(f335(f335(f335(f335(f45(x104157,f934(x104156,f934(x104155,a922))),x104154),x104151),x104153),x104152)) % 186.01/186.03 [10416]P1(f335(f335(f335(x104161,f896(x104162,x104163,x104161,x104164,x104165,x104166,x104167)),x104163),x104162))+~P1(f335(f335(f335(f335(f45(x104167,f934(x104166,f934(x104165,a922))),x104164),x104161),x104163),x104162)) % 186.01/186.03 [10432]~P1(f335(f335(f335(x104325,f660(x104327,x104326,x104325,x104324,x104323,x104322,x104321)),x104326),x104327))+P1(f335(f335(f335(f335(f46(x104321,f934(x104322,f934(x104323,a922))),x104324),x104325),x104326),x104327)) % 186.01/186.03 [10433]~P1(f335(f335(f335(x104335,f812(x104333,x104332,x104337,x104336,x104335,x104334,x104331)),x104336),x104337))+P1(f335(f335(f335(f335(f46(x104331,f934(x104332,f934(x104333,a922))),x104334),x104335),x104336),x104337)) % 186.01/186.03 [10450]~P1(f335(f335(f337(f933(x104501,x104503)),f335(f335(f260(x104501,x104503),x104506),x104507)),f335(f335(f297(x104501,x104502,x104503),x104504),x104505)))+P1(f335(f335(f261(x104501,x104502,x104503,f335(f335(f7(x104501,f934(f933(x104501,x104502),a922),f934(x104502,a922)),f335(f335(f8(f934(x104502,f934(f934(f933(x104501,x104502),a922),a922)),f934(f934(f933(x104501,x104502),a922),f934(x104502,a922)),x104501),f7(x104502,f934(f933(x104501,x104502),a922),a922)),f335(f335(f8(f934(x104502,f933(x104501,x104502)),f934(x104502,f934(f934(f933(x104501,x104502),a922),a922)),x104501),f335(f8(f933(x104501,x104502),f934(f934(f933(x104501,x104502),a922),a922),x104502),f337(f933(x104501,x104502)))),f260(x104501,x104502)))),x104504),f335(f335(f7(x104502,f934(f933(x104502,x104503),a922),f934(x104503,a922)),f335(f335(f8(f934(x104503,f934(f934(f933(x104502,x104503),a922),a922)),f934(f934(f933(x104502,x104503),a922),f934(x104503,a922)),x104502),f7(x104503,f934(f933(x104502,x104503),a922),a922)),f335(f335(f8(f934(x104503,f933(x104502,x104503)),f934(x104503,f934(f934(f933(x104502,x104503),a922),a922)),x104502),f335(f8(f933(x104502,x104503),f934(f934(f933(x104502,x104503),a922),a922),x104503),f337(f933(x104502,x104503)))),f260(x104502,x104503)))),x104505)),x104506),x104507)) % 186.01/186.03 [10460]P1(f335(f335(f337(f933(x104601,x104602)),f335(f335(f260(x104601,x104602),x104603),x104604)),f335(f335(f297(x104601,x104605,x104602),x104606),x104607)))+~P1(f335(f335(f261(x104601,x104605,x104602,f335(f335(f7(x104601,f934(f933(x104601,x104605),a922),f934(x104605,a922)),f335(f335(f8(f934(x104605,f934(f934(f933(x104601,x104605),a922),a922)),f934(f934(f933(x104601,x104605),a922),f934(x104605,a922)),x104601),f7(x104605,f934(f933(x104601,x104605),a922),a922)),f335(f335(f8(f934(x104605,f933(x104601,x104605)),f934(x104605,f934(f934(f933(x104601,x104605),a922),a922)),x104601),f335(f8(f933(x104601,x104605),f934(f934(f933(x104601,x104605),a922),a922),x104605),f337(f933(x104601,x104605)))),f260(x104601,x104605)))),x104606),f335(f335(f7(x104605,f934(f933(x104605,x104602),a922),f934(x104602,a922)),f335(f335(f8(f934(x104602,f934(f934(f933(x104605,x104602),a922),a922)),f934(f934(f933(x104605,x104602),a922),f934(x104602,a922)),x104605),f7(x104602,f934(f933(x104605,x104602),a922),a922)),f335(f335(f8(f934(x104602,f933(x104605,x104602)),f934(x104602,f934(f934(f933(x104605,x104602),a922),a922)),x104605),f335(f8(f933(x104605,x104602),f934(f934(f933(x104605,x104602),a922),a922),x104602),f337(f933(x104605,x104602)))),f260(x104605,x104602)))),x104607)),x104603),x104604)) % 186.01/186.03 [10387]~P145(x103872)+E(f335(f335(f6(x103871,x103872),f335(f335(f7(x103871,f934(x103873,a922),x103872),f335(f335(f8(f934(x103873,x103872),f934(f934(x103873,a922),x103872),x103871),f6(x103873,x103872)),f335(f335(f7(x103871,f934(x103873,x103872),f934(x103873,x103872)),f335(f335(f8(f934(x103872,x103872),f934(f934(x103873,x103872),f934(x103873,x103872)),x103871),f8(x103872,x103872,x103873)),f335(f335(f8(x103872,f934(x103872,x103872),x103871),f87(x103872)),x103874))),x103875))),x103876)),x103877),f335(f335(f87(x103872),f335(f335(f6(x103871,x103872),x103874),x103877)),f335(f335(f6(x103873,x103872),x103875),x103876))) % 186.01/186.03 [9470]~P20(x94707,x94701,x94703,x94708)+E(f335(f78(x94701,x94701,x94702,f335(x94703,x94704)),f335(f78(x94701,x94701,x94702,f335(x94703,x94705)),x94706)),f335(f78(x94701,x94701,x94702,f335(x94703,x94705)),f335(f78(x94701,x94701,x94702,f335(x94703,x94704)),x94706))) % 186.01/186.03 [10414]P25(x104141,x104142,f335(f335(f317(f926(x104141)),f98(x104141,f335(f335(f8(f934(a923,a922),f934(a923,a922),x104141),f335(f18(a923,a922,a922),f335(f335(f8(a922,f934(a922,a922),a923),a333),f335(a332,x104143)))),f335(f335(f7(x104141,f934(a923,a923),f934(a923,a922)),f335(f335(f8(f934(a923,a922),f934(f934(a923,a923),f934(a923,a922)),x104141),f8(a923,a922,a923)),x104144)),f335(f335(f18(a923,a927,a923),f335(f335(f7(a923,a925,f934(a927,a923)),a203),f33(x104145))),x104146))),f28(x104145,x104146,x104147),x104148)),f195(f934(f926(x104141),a922))))+~P25(x104141,x104142,f335(f335(f317(f926(x104141)),f98(x104141,x104144,x104147,f335(f335(f7(x104141,f934(a923,a923),f934(a923,a922)),f335(f335(f8(f934(a923,a922),f934(f934(a923,a923),f934(a923,a922)),x104141),f8(a923,a922,a923)),x104148)),f335(f335(f7(a923,a927,a923),f335(f335(f7(a923,a925,f934(a927,a923)),a203),f33(x104145))),f204(x104143,x104145))))),f195(f934(f926(x104141),a922)))) % 186.01/186.03 [10455]E(f335(f335(f260(x104551,x104552),f335(x104553,f548(x104554,x104555,x104553,x104556,x104557,x104558,x104552,x104551))),f335(x104555,f549(x104554,x104555,x104553,x104556,x104557,x104558,x104552,x104551))),x104558)+~P1(f335(f335(f337(f933(x104551,x104552)),x104558),f335(f318(f933(x104557,x104556),f933(x104551,x104552),f266(x104557,x104551,x104556,x104552,x104553,x104555)),x104554))) % 186.01/186.03 [10473]~P1(f335(f335(f337(f933(x104738,x104737)),x104736),f335(f318(f933(x104731,x104732),f933(x104738,x104737),f266(x104731,x104738,x104732,x104737,x104735,x104734)),x104733)))+P1(f335(f335(f337(f933(x104731,x104732)),f335(f335(f260(x104731,x104732),f548(x104733,x104734,x104735,x104732,x104731,x104736,x104737,x104738)),f549(x104733,x104734,x104735,x104732,x104731,x104736,x104737,x104738))),x104733)) % 186.01/186.03 [9910]P1(f335(f335(f337(f933(f933(x99101,x99102),f933(x99101,x99102))),f335(f335(f260(f933(x99101,x99102),f933(x99101,x99102)),f335(f335(f260(x99101,x99102),x99103),x99104)),f335(f335(f260(x99101,x99102),x99105),x99106))),f328(x99101,x99102,x99107,x99108)))+~P1(f335(f335(f337(f933(x99101,x99101)),f335(f335(f260(x99101,x99101),x99103),x99105)),x99107)) % 186.01/186.03 [10444]E(f335(f149(x104441,x104442,f335(f7(x104442,x104441,x104441),x104443),f335(x104444,x104445)),x104446),f335(x104444,f335(f149(x104447,x104442,f335(f7(x104442,x104447,x104447),x104448),x104445),x104446)))+P1(f335(f335(f337(x104442),f756(x104445,x104448,x104444,x104443,x104447,x104441,x104446,x104442)),f335(f179(x104442),x104446))) % 186.01/186.03 [10463]~E(f335(f78(x104631,x104631,x104637,f335(x104633,f756(x104635,x104638,x104634,x104633,x104637,x104631,x104636,x104632))),x104634),f335(f78(x104637,x104631,x104637,x104634),f335(x104638,f756(x104635,x104638,x104634,x104633,x104637,x104631,x104636,x104632))))+E(f335(f149(x104631,x104632,f335(f7(x104632,x104631,x104631),x104633),f335(x104634,x104635)),x104636),f335(x104634,f335(f149(x104637,x104632,f335(f7(x104632,x104637,x104637),x104638),x104635),x104636))) % 186.01/186.03 [8686]E(f335(x86861,f335(x86862,x86863)),f335(x86864,f335(x86865,x86863)))+~E(f335(f78(x86866,x86867,x86868,x86861),x86862),f335(f78(x86869,x86867,x86868,x86864),x86865)) % 186.01/186.03 [10300]P1(f335(f335(f337(f933(x103001,x103002)),f335(f335(f260(x103001,x103002),f335(x103003,x103004)),f335(x103005,x103006))),f335(f318(f933(x103007,x103008),f933(x103001,x103002),f266(x103007,x103001,x103008,x103002,x103003,x103005)),x103009)))+~P1(f335(f335(f337(f933(x103007,x103008)),f335(f335(f260(x103007,x103008),x103004),x103006)),x103009)) % 186.01/186.03 [8981]~E(f335(x89814,f335(x89815,x89816)),f335(x89819,f335(x898110,x898111)))+E(f335(f335(f78(x89811,x89812,x89813,x89814),x89815),x89816),f335(f335(f78(x89817,x89812,x89818,x89819),x898110),x898111)) % 186.01/186.03 [4819]~P109(x48191)+~P97(x48191)+E(f108(x48191),f241(x48191)) % 186.01/186.03 [4820]~P109(x48201)+~P103(x48201)+E(f117(x48201),f242(x48201)) % 186.01/186.03 [5071]~P113(x50711)+~P94(x50711)+E(f335(f81(x50711),f335(f110(x50711),a104)),f84(x50711)) % 186.01/186.03 [5359]E(x53591,f2(a1))+E(f88(a1,x53591),f335(f85(a1),f84(a1)))+P1(f335(f335(f244(a1),f2(a1)),x53591)) % 186.01/186.03 [5567]E(x55671,f2(a1))+E(f88(a1,x55671),f84(a1))+~P1(f335(f335(f244(a1),f2(a1)),x55671)) % 186.01/186.03 [7570]~P41(x75701)+P1(f335(f67(a1),x75701))+~P1(f335(f67(a927),f335(f318(a1,a927,a111),x75701))) % 186.01/186.03 [9871]E(x98711,f195(f934(f933(a927,a927),a922)))+~P1(f335(f67(f933(a927,a927)),x98711))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f195(f934(f933(a927,a927),a922))),x98711)),a40)) % 186.01/186.03 [10035]E(x100351,f2(a927))+E(x100351,f335(a119,f2(a927)))+~P1(f335(f335(f244(a927),x100351),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.03 [10331]E(x103311,f2(a106))+E(f335(f335(f86(a1),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(a22,f335(f335(f42(a106),x103311),f335(f110(a106),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))),f84(a1)),f335(a22,x103311))+E(f51(a106,x103311,f335(f110(a106),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f2(a106)) % 186.01/186.03 [10176]E(x101761,f2(a106))+~E(f51(a106,x101761,f335(f110(a106),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f2(a106))+E(f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(a22,f335(f335(f42(a106),x101761),f335(f110(a106),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f335(a22,x101761)) % 186.01/186.03 [4900]~P59(x49001,x49002)+P44(x49001,x49002)+~P45(a922) % 186.01/186.03 [4829]~P146(x48291)+P29(x48291,x48292)+~E(x48292,f2(x48291)) % 186.01/186.03 [4830]~P109(x48301)+P14(x48301,x48302)+~E(x48302,f120(x48301)) % 186.01/186.03 [4839]~P113(x48391)+~E(x48392,f2(x48391))+E(f88(x48391,x48392),f2(x48391)) % 186.01/186.03 [4840]~P90(x48401)+~E(x48402,f2(x48401))+E(f88(x48401,x48402),f2(x48401)) % 186.01/186.03 [4848]~P146(x48482)+~P29(x48482,x48481)+E(x48481,f2(x48482)) % 186.01/186.03 [4893]~P113(x48932)+~E(f88(x48932,x48931),f2(x48932))+E(x48931,f2(x48932)) % 186.01/186.03 [4907]~P62(x49072)+~P62(x49071)+P62(f934(x49071,x49072)) % 186.01/186.03 [4908]~P62(x49082)+~P62(x49081)+P62(f933(x49081,x49082)) % 186.01/186.03 [4909]~P62(x49092)+~P62(x49091)+P62(f935(x49091,x49092)) % 186.01/186.03 [4910]~P7(x49102)+~P7(x49101)+P7(f201(x49101,x49102)) % 186.01/186.03 [4911]~P65(x49112)+~P65(x49111)+P65(f934(x49111,x49112)) % 186.01/186.03 [4912]~P65(x49122)+~P65(x49121)+P65(f933(x49121,x49122)) % 186.01/186.03 [4913]~P65(x49132)+~P65(x49131)+P65(f935(x49131,x49132)) % 186.01/186.03 [4914]~P105(x49142)+~P105(x49141)+P105(f933(x49141,x49142)) % 186.01/186.03 [5043]~P109(x50431)+~P14(x50431,x50432)+P14(x50431,f159(x50431,x50432)) % 186.01/186.03 [5286]~P7(x52862)+~P7(x52861)+P7(f51(a1,x52861,x52862)) % 186.01/186.03 [4850]~P78(x48501)+~E(x48502,f2(x48501))+E(f335(f85(x48501),x48502),x48502) % 186.01/186.03 [4865]~P140(x48651)+~E(x48652,f2(a1))+E(f335(f109(x48651),x48652),f2(x48651)) % 186.01/186.03 [4866]~P93(x48661)+~E(x48662,f2(a1))+E(f335(f109(x48661),x48662),f2(x48661)) % 186.01/186.03 [4890]~P4(x48901)+~E(f2(x48901),x48902)+E(f335(f85(x48901),x48902),f2(x48901)) % 186.01/186.03 [4891]~P4(x48911)+~E(x48912,f2(x48911))+E(f335(f85(x48911),x48912),f2(x48911)) % 186.01/186.03 [4892]~P87(x48921)+~E(x48922,f2(x48921))+E(f335(f81(x48921),x48922),f2(x48921)) % 186.01/186.03 [4916]~P78(x49162)+E(x49161,f2(x49162))+~E(f335(f85(x49162),x49161),x49161) % 186.01/186.03 [4924]E(x49241,f335(a111,x49242))+~E(x49241,f2(a927))+~E(x49242,f335(f107(a1),x49241)) % 186.01/186.03 [4925]E(f335(a111,x49251),x49252)+~E(x49252,f2(a927))+~E(x49251,f335(f107(a1),x49252)) % 186.01/186.03 [4929]~P93(x49292)+E(x49291,f2(a1))+~E(f335(f109(x49292),x49291),f2(x49292)) % 186.01/186.03 [4933]~P4(x49332)+E(x49331,f2(x49332))+~E(f335(f85(x49332),x49331),f2(x49332)) % 186.01/186.03 [4934]~P87(x49342)+E(x49341,f2(x49342))+~E(f335(f81(x49342),x49341),f2(x49342)) % 186.01/186.03 [4935]~P4(x49351)+E(f2(x49351),x49352)+~E(f335(f85(x49351),x49352),f2(x49351)) % 186.01/186.03 [5118]~P109(x51181)+~P14(x51181,x51182)+P14(x51181,f335(f178(x51181),x51182)) % 186.01/186.03 [5145]~P1(x51452)+~P1(x51451)+P1(f335(f335(a333,x51451),x51452)) % 186.01/186.03 [5179]~E(f84(a927),f2(a927))+E(f335(f41(x51791),x51792),f2(a927))+~P1(f335(f67(x51791),x51792)) % 186.01/186.03 [5215]~P145(x52151)+~P117(x52151)+E(f335(f335(f252(x52151),f2(x52151)),f335(a119,x52152)),f2(x52151)) % 186.01/186.03 [5254]~P109(x52541)+P14(x52541,f146(x52541,x52542))+~P1(f335(f67(x52541),x52542)) % 186.01/186.03 [5255]~P109(x52551)+P14(x52551,f748(x52552,x52551))+~P1(f335(f67(x52551),x52552)) % 186.01/186.03 [5278]~P109(x52781)+E(f335(f179(x52781),f146(x52781,x52782)),x52782)+~P1(f335(f67(x52781),x52782)) % 186.01/186.03 [5279]~P109(x52791)+E(f335(f179(x52791),f748(x52792,x52791)),x52792)+~P1(f335(f67(x52791),x52792)) % 186.01/186.03 [5308]P1(x53081)+P1(x53082)+~P1(f335(f335(a334,x53082),x53081)) % 186.01/186.03 [5321]E(x53211,f195(f934(x53212,a922)))+~E(f335(f41(x53212),x53211),f2(a927))+~P1(f335(f67(x53212),x53211)) % 186.01/186.03 [5326]P1(x53261)+~P1(x53262)+~P1(f335(f335(a338,x53262),x53261)) % 186.01/186.03 [5377]~P75(x53771)+E(f335(f81(x53771),x53772),x53772)+P1(f335(f335(f244(x53771),x53772),f2(x53771))) % 186.01/186.03 [5437]~P65(x54372)+~P1(f335(f62(x54372),x54371))+P1(f335(x54371,f749(x54371,x54372))) % 186.01/186.03 [5438]~P65(x54382)+~P1(f335(f62(x54382),x54381))+P1(f335(x54381,f757(x54381,x54382))) % 186.01/186.03 [5479]E(x54791,f120(x54792))+P1(f335(f144(x54792),f121(x54792,x54791)))+~P1(f335(f144(x54792),x54791)) % 186.01/186.03 [5484]~P109(x54841)+~P1(f335(f67(x54841),x54842))+P1(f335(f144(x54841),f146(x54841,x54842))) % 186.01/186.03 [5485]~P109(x54851)+~P1(f335(f67(x54851),x54852))+P1(f335(f144(x54851),f748(x54852,x54851))) % 186.01/186.03 [5490]~P140(x54901)+E(f335(f107(x54901),f335(a111,x54902)),f335(f109(x54901),x54902))+P1(f335(f335(f244(a1),x54902),f2(a1))) % 186.01/186.03 [5517]P8(x55172,x55171)+E(f335(x55171,f842(x55171)),f335(x55171,f888(x55171)))+P1(f335(f335(x55171,f842(x55171)),f888(x55171))) % 186.01/186.03 [5529]E(f335(f107(a1),f443(x55291,x55292)),x55291)+P1(f335(x55292,f335(a111,x55291)))+~P1(f335(x55292,f2(a927))) % 186.01/186.03 [5541]~P65(x55411)+~P1(f335(x55412,f762(x55412,x55411)))+P1(f335(f63(x55411),x55412)) % 186.01/186.03 [5542]~P65(x55421)+~P1(f335(x55422,f772(x55422,x55421)))+P1(f335(f63(x55421),x55422)) % 186.01/186.03 [5577]~P113(x55771)+~E(f88(x55771,x55772),f335(f85(x55771),f84(x55771)))+P1(f335(f335(f244(x55771),x55772),f2(x55771))) % 186.01/186.03 [5650]~E(x56502,f2(a1))+E(f224(x56501,x56502),f335(f335(f260(a1,a1),f2(a1)),f84(a1)))+P1(f335(f335(f244(a1),x56502),f2(a1))) % 186.01/186.03 [5651]~E(x56511,f2(a1))+E(f224(x56511,x56512),f335(f335(f260(a1,a1),f2(a1)),f84(a1)))+P1(f335(f335(f244(a1),x56512),f2(a1))) % 186.01/186.03 [5704]E(f335(f107(a1),f443(x57041,x57042)),x57041)+P1(f335(x57042,f335(a111,x57041)))+P1(f335(f335(f244(a1),x57041),f2(a1))) % 186.01/186.03 [5771]~P113(x57711)+E(f88(x57711,x57712),f335(f85(x57711),f84(x57711)))+~P1(f335(f335(f244(x57711),x57712),f2(x57711))) % 186.01/186.03 [5772]~P87(x57721)+E(f335(f81(x57721),x57722),f335(f85(x57721),x57722))+~P1(f335(f335(f243(x57721),x57722),f2(x57721))) % 186.01/186.03 [5773]~P87(x57731)+E(f335(f81(x57731),x57732),f335(f85(x57731),x57732))+~P1(f335(f335(f244(x57731),x57732),f2(x57731))) % 186.01/186.03 [5774]~P75(x57741)+E(f335(f81(x57741),x57742),f335(f85(x57741),x57742))+~P1(f335(f335(f244(x57741),x57742),f2(x57741))) % 186.01/186.03 [5873]~P1(f335(x58731,f443(x58732,x58731)))+P1(f335(x58731,f335(a111,x58732)))+~P1(f335(x58731,f2(a927))) % 186.01/186.03 [5880]E(x58801,f2(a927))+E(f335(a119,f385(x58802,x58801)),x58801)+~P1(f335(f335(f244(a927),x58801),f335(a119,x58802))) % 186.01/186.03 [5884]P8(x58841,x58842)+~E(f335(x58842,f842(x58842)),f335(x58842,f888(x58842)))+~P1(f335(f335(x58842,f842(x58842)),f888(x58842))) % 186.01/186.03 [5902]~P109(x59021)+P14(x59021,x59022)+P1(f335(f335(f243(a927),f732(x59022,x59021)),f733(x59022,x59021))) % 186.01/186.03 [5903]~P109(x59031)+P14(x59031,x59032)+P1(f335(f335(f243(a927),f739(x59032,x59031)),f744(x59032,x59031))) % 186.01/186.03 [5989]~P87(x59891)+~E(x59892,f2(x59891))+P1(f335(f335(f243(x59891),f335(f81(x59891),x59892)),f2(x59891))) % 186.01/186.03 [6077]~P1(f335(x60771,f443(x60772,x60771)))+P1(f335(x60771,f335(a111,x60772)))+P1(f335(f335(f244(a1),x60772),f2(a1))) % 186.01/186.03 [6102]~P1(f335(x61021,f335(a111,x61022)))+P1(f335(x61021,f2(a927)))+~P1(f335(f335(f244(a1),x61022),f2(a1))) % 186.01/186.03 [6442]~P113(x64421)+~P1(f335(f335(f244(x64421),x64422),f2(x64421)))+P1(f335(f335(f244(x64421),f88(x64421,x64422)),f2(x64421))) % 186.01/186.03 [6555]~P113(x65551)+P1(f335(f335(f243(x65551),f335(f109(x65551),x65552)),f2(x65551)))+~P1(f335(f335(f243(a1),x65552),f2(a1))) % 186.01/186.03 [6556]~P113(x65561)+P1(f335(f335(f244(x65561),f335(f109(x65561),x65562)),f2(x65561)))+~P1(f335(f335(f244(a1),x65562),f2(a1))) % 186.01/186.03 [6565]~P87(x65652)+E(x65651,f2(x65652))+~P1(f335(f335(f243(x65652),f335(f81(x65652),x65651)),f2(x65652))) % 186.01/186.03 [6640]~P140(x66401)+~P1(f335(f335(f337(x66401),x66402),f116(x66401)))+P1(f335(f335(f337(x66401),f335(f85(x66401),x66402)),f116(x66401))) % 186.01/186.03 [6673]~P113(x66731)+~P1(f335(f335(f244(x66731),f88(x66731,x66732)),f2(x66731)))+P1(f335(f335(f244(x66731),x66732),f2(x66731))) % 186.01/186.03 [6844]~P113(x68442)+~P1(f335(f335(f243(x68442),f335(f109(x68442),x68441)),f2(x68442)))+P1(f335(f335(f243(a1),x68441),f2(a1))) % 186.01/186.03 [6845]~P113(x68452)+~P1(f335(f335(f244(x68452),f335(f109(x68452),x68451)),f2(x68452)))+P1(f335(f335(f244(a1),x68451),f2(a1))) % 186.01/186.03 [7344]~P78(x73441)+~P1(f335(f335(f243(x73441),x73442),f2(x73441)))+P1(f335(f335(f243(x73441),f335(f335(f86(x73441),x73442),x73442)),f2(x73441))) % 186.01/186.03 [7345]~P113(x73451)+~P1(f335(f335(f244(x73451),x73452),f2(x73451)))+P1(f335(f335(f244(x73451),f335(f335(f86(x73451),x73452),x73452)),f2(x73451))) % 186.01/186.03 [7346]~P78(x73461)+~P1(f335(f335(f244(x73461),x73462),f2(x73461)))+P1(f335(f335(f244(x73461),f335(f335(f86(x73461),x73462),x73462)),f2(x73461))) % 186.01/186.03 [7909]~P78(x79091)+~P1(f335(f335(f243(x79091),f335(f335(f86(x79091),x79092),x79092)),f2(x79091)))+P1(f335(f335(f243(x79091),x79092),f2(x79091))) % 186.01/186.03 [7910]~P113(x79101)+~P1(f335(f335(f244(x79101),f335(f335(f86(x79101),x79102),x79102)),f2(x79101)))+P1(f335(f335(f244(x79101),x79102),f2(x79101))) % 186.01/186.03 [7911]~P78(x79111)+~P1(f335(f335(f244(x79111),f335(f335(f86(x79111),x79112),x79112)),f2(x79111)))+P1(f335(f335(f244(x79111),x79112),f2(x79111))) % 186.01/186.03 [4970]~E(x49702,f84(a927))+~E(x49701,f84(a927))+E(f335(f335(f87(a927),x49701),x49702),f84(a927)) % 186.01/186.03 [4971]~E(x49712,f84(a1))+~E(x49711,f84(a1))+E(f335(f335(f87(a1),x49711),x49712),f84(a1)) % 186.01/186.03 [4972]~E(x49722,f2(a927))+~E(x49721,f2(a927))+E(f335(f335(f86(a927),x49721),x49722),f2(a927)) % 186.01/186.03 [5027]~P63(x50272)+E(x50271,f2(x50272))+E(f335(f335(f42(x50272),x50271),x50271),f84(x50272)) % 186.01/186.03 [5028]~P121(x50282)+E(x50281,f2(x50282))+E(f335(f335(f299(x50282),x50281),x50281),f84(x50282)) % 186.01/186.03 [5029]~P122(x50292)+E(x50291,f2(x50292))+E(f335(f335(f299(x50292),x50291),x50291),f84(x50292)) % 186.01/186.03 [5049]~P139(x50491)+~E(x50492,f84(x50491))+E(f335(f335(f87(x50491),x50492),x50492),f84(x50491)) % 186.01/186.03 [5050]~P78(x50501)+~E(x50502,f2(x50501))+E(f335(f335(f86(x50501),x50502),x50502),f2(x50501)) % 186.01/186.03 [5051]~P122(x50511)+~E(x50512,f2(x50511))+E(f335(f335(f299(x50511),x50512),x50512),f2(x50511)) % 186.01/186.03 [5096]~E(x50962,f2(a927))+~E(x50961,f2(a927))+E(f335(f85(a1),f335(f107(a1),x50961)),f335(f107(a1),x50962)) % 186.01/186.03 [5115]E(x51151,f84(a927))+E(x51152,f2(a927))+~E(f335(f335(f87(a927),x51152),x51151),x51152) % 186.01/186.03 [5127]E(x51271,f2(a927))+E(x51272,f2(a927))+~E(f335(f335(f87(a927),x51272),x51271),f2(a927)) % 186.01/186.03 [5154]~E(x51542,f2(a927))+~E(x51541,f335(a119,f2(a927)))+E(f335(f335(f86(a927),x51541),x51542),f335(a119,f2(a927))) % 186.01/186.03 [5155]~E(x51551,f2(a927))+~E(x51552,f335(a119,f2(a927)))+E(f335(f335(f86(a927),x51551),x51552),f335(a119,f2(a927))) % 186.01/186.03 [5162]E(x51621,f84(a1))+E(x51622,f335(f110(a1),a104))+~E(f335(f335(f87(a1),x51621),x51622),f84(a1)) % 186.01/186.03 [5163]E(x51631,f84(a1))+E(x51632,f335(f110(a1),a104))+~E(f335(f335(f87(a1),x51632),x51631),f84(a1)) % 186.01/186.03 [5164]E(x51641,f84(a1))+E(x51641,f335(f110(a1),a104))+~E(f335(f335(f87(a1),x51642),x51641),f84(a1)) % 186.01/186.03 [5166]E(x51661,f84(a1))+E(x51661,f335(f110(a1),a104))+~E(f335(f335(f87(a1),x51661),x51662),f84(a1)) % 186.01/186.03 [5187]~P78(x51872)+E(x51871,f2(x51872))+~E(f335(f335(f86(x51872),x51871),x51871),f2(x51872)) % 186.01/186.03 [5193]~E(x51931,f335(f110(a1),a104))+~E(x51932,f335(f110(a1),a104))+E(f335(f335(f87(a1),x51931),x51932),f84(a1)) % 186.01/186.03 [5204]E(x52041,f2(a927))+E(x52042,f2(a927))+~E(f335(f335(f86(a927),x52042),x52041),f335(a119,f2(a927))) % 186.01/186.03 [5214]~P94(x52141)+~P66(x52141)+E(f335(f335(f299(x52141),x52142),f335(f110(x52141),a89)),f2(x52141)) % 186.01/186.03 [5221]~P139(x52211)+~E(x52212,f335(f85(x52211),f84(x52211)))+E(f335(f335(f87(x52211),x52212),x52212),f84(x52211)) % 186.01/186.03 [5226]~P7(x52262)+~P7(x52261)+P7(f335(f335(f87(a1),x52261),x52262)) % 186.01/186.03 [5227]~P7(x52272)+~P7(x52271)+P7(f335(f335(f86(a1),x52271),x52272)) % 186.01/186.03 [5228]~P7(x52282)+~P7(x52281)+P7(f335(f335(f42(a1),x52281),x52282)) % 186.01/186.03 [5230]~E(x52302,f2(a1))+E(x52301,f2(a1))+E(f52(x52301,x52302),f335(f335(f260(a1,a1),f2(a1)),x52301)) % 186.01/186.03 [5252]~E(x52522,f335(a119,f2(a927)))+~E(x52521,f335(a119,f2(a927)))+E(f335(f335(f87(a927),x52521),x52522),f335(a119,f2(a927))) % 186.01/186.03 [5269]E(x52691,f2(a927))+E(x52692,f335(a119,f2(a927)))+~E(f335(f335(f252(a927),x52692),x52691),f335(a119,f2(a927))) % 186.01/186.03 [5270]E(x52701,f2(a927))+E(x52701,f335(a119,f2(a927)))+~E(f335(f335(f86(a927),x52702),x52701),f335(a119,f2(a927))) % 186.01/186.03 [5271]E(x52711,f2(a927))+E(x52711,f335(a119,f2(a927)))+~E(f335(f335(f86(a927),x52711),x52712),f335(a119,f2(a927))) % 186.01/186.03 [5280]~P94(x52801)+~P66(x52801)+E(f335(f335(f299(x52801),x52802),f335(f110(x52801),a104)),f335(f85(x52801),x52802)) % 186.01/186.03 [5300]E(x53001,f335(a111,x53002))+~E(x53001,f2(a927))+P1(f335(f335(f243(a1),f2(a1)),x53002)) % 186.01/186.03 [5301]E(f335(a111,x53011),x53012)+~E(x53012,f2(a927))+P1(f335(f335(f243(a1),f2(a1)),x53011)) % 186.01/186.03 [5317]E(x53171,f335(a119,f2(a927)))+E(x53172,f335(a119,f2(a927)))+~E(f335(f335(f86(a927),x53171),x53172),f335(a119,f2(a927))) % 186.01/186.03 [5328]~E(x53281,f335(a111,x53282))+E(x53281,f2(a927))+P1(f335(f335(f243(a1),f2(a1)),x53282)) % 186.01/186.03 [5329]~E(f335(a111,x53292),x53291)+E(x53291,f2(a927))+P1(f335(f335(f243(a1),f2(a1)),x53292)) % 186.01/186.03 [5352]~P98(x53521)+E(f335(f69(x53521,f117(x53521)),x53522),f13(x53521,x53522))+~P1(f335(f67(x53521),x53522)) % 186.01/186.03 [5353]~P98(x53531)+E(f335(f69(x53531,f108(x53531)),x53532),f10(x53531,x53532))+~P1(f335(f67(x53531),x53532)) % 186.01/186.03 [5354]~P109(x53541)+E(f335(f69(x53541,f242(x53541)),x53542),f14(x53541,x53542))+~P1(f335(f67(x53541),x53542)) % 186.01/186.03 [5355]~P109(x53551)+E(f335(f69(x53551,f241(x53551)),x53552),f15(x53551,x53552))+~P1(f335(f67(x53551),x53552)) % 186.01/186.03 [5432]E(x54321,x54322)+~E(f335(f335(f23(a927),x54322),x54321),f2(a927))+~E(f335(f335(f23(a927),x54321),x54322),f2(a927)) % 186.01/186.03 [5449]P7(x54491)+~P41(x54492)+~P1(f335(f335(f337(a1),x54491),x54492)) % 186.01/186.03 [5480]~P113(x54801)+~E(f88(x54801,x54802),f84(x54801))+P1(f335(f335(f244(x54801),f2(x54801)),x54802)) % 186.01/186.03 [5491]~P94(x54911)+E(f335(f107(x54911),f335(f110(a927),x54912)),f335(f110(x54911),x54912))+P1(f335(a200,f335(f110(a1),x54912))) % 186.01/186.03 [5496]~P44(x54961,x54962)+P45(a922)+P1(f335(f67(f933(x54961,x54961)),x54962)) % 186.01/186.03 [5569]~P109(x55691)+E(f335(f69(x55691,f242(x55691)),x55692),f11(x55691,f242(x55691),x55692))+~P1(f335(f67(x55691),x55692)) % 186.01/186.03 [5570]~P109(x55701)+E(f335(f69(x55701,f241(x55701)),x55702),f12(x55701,f241(x55701),x55702))+~P1(f335(f67(x55701),x55702)) % 186.01/186.03 [5584]E(x55841,x55842)+P1(f335(f335(f244(a927),x55842),x55841))+P1(f335(f335(f244(a927),x55841),x55842)) % 186.01/186.03 [5585]E(x55851,x55852)+P1(f335(f335(f244(a1),x55852),x55851))+P1(f335(f335(f244(a1),x55851),x55852)) % 186.01/186.03 [5637]~P94(x56371)+E(f335(f107(x56371),f335(f110(a927),x56372)),f2(x56371))+~P1(f335(a200,f335(f110(a1),x56372))) % 186.01/186.03 [5640]~E(x56402,f335(a111,x56401))+E(x56401,f335(f107(a1),x56402))+~P1(f335(f335(f243(a1),f2(a1)),x56401)) % 186.01/186.03 [5641]~E(f335(a111,x56411),x56412)+E(x56411,f335(f107(a1),x56412))+~P1(f335(f335(f243(a1),f2(a1)),x56411)) % 186.01/186.03 [5642]~E(x56421,f335(a111,x56422))+E(f335(f107(a1),x56421),x56422)+~P1(f335(f335(f243(a1),f2(a1)),x56422)) % 186.01/186.03 [5652]E(x56521,f335(a111,x56522))+~E(x56522,f335(f107(a1),x56521))+~P1(f335(f335(f243(a1),f2(a1)),x56522)) % 186.01/186.03 [5653]E(f335(a111,x56531),x56532)+~E(x56531,f335(f107(a1),x56532))+~P1(f335(f335(f243(a1),f2(a1)),x56531)) % 186.01/186.03 [5684]~P118(x56842)+E(x56841,f2(x56842))+~P1(f335(f335(f295(x56842),f2(x56842)),x56841)) % 186.01/186.03 [5695]~P87(x56952)+E(x56951,f2(x56952))+P1(f335(f335(f244(x56952),f2(x56952)),f335(f81(x56952),x56951))) % 186.01/186.03 [5760]~P113(x57601)+E(f88(x57601,x57602),f84(x57601))+~P1(f335(f335(f244(x57601),f2(x57601)),x57602)) % 186.01/186.03 [5764]~P94(x57641)+E(f335(f107(x57641),f335(f110(a927),x57642)),f2(x57641))+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x57642))) % 186.01/186.03 [5775]~P87(x57751)+E(f335(f81(x57751),x57752),x57752)+~P1(f335(f335(f243(x57751),f2(x57751)),x57752)) % 186.01/186.03 [5776]~P87(x57761)+E(f335(f81(x57761),x57762),x57762)+~P1(f335(f335(f244(x57761),f2(x57761)),x57762)) % 186.01/186.03 [5785]E(x57851,f2(a927))+~E(f146(a927,f335(f310(a927,x57852),x57851)),f120(a927))+P1(f335(f335(f243(a927),x57851),x57852)) % 186.01/186.03 [5795]~P76(x57951)+E(f335(f335(f6(x57951,x57951),f5(x57951)),f335(f179(x57951),x57952)),f335(f172(x57951),x57952))+~P1(f335(f144(x57951),x57952)) % 186.01/186.03 [5798]~P140(x57981)+E(f335(f107(x57981),f335(a111,x57982)),f335(f109(x57981),x57982))+~P1(f335(f335(f243(a1),f2(a1)),x57982)) % 186.01/186.03 [5825]E(x58251,x58252)+P1(f335(f335(f244(a927),x58251),x58252))+~P1(f335(f335(f243(a927),x58251),x58252)) % 186.01/186.03 [5826]E(x58261,x58262)+P1(f335(f335(f244(a1),x58261),x58262))+~P1(f335(f335(f243(a1),x58261),x58262)) % 186.01/186.03 [5829]E(x58291,f84(a1))+~E(f335(f335(f87(a1),x58292),x58291),f84(a1))+~P1(f335(f335(f244(a1),f2(a1)),x58292)) % 186.01/186.03 [5830]E(x58301,f84(a1))+~E(f335(f335(f87(a1),x58301),x58302),f84(a1))+~P1(f335(f335(f244(a1),f2(a1)),x58301)) % 186.01/186.03 [5870]~P41(x58702)+P1(f335(f335(f243(a1),f2(a1)),x58701))+~P1(f335(f335(f337(a1),x58701),x58702)) % 186.01/186.03 [5889]~P59(x58891,x58892)+P38(x58891,x58892)+~P1(f335(f67(f933(x58891,x58891)),x58892)) % 186.01/186.03 [5891]~P59(x58911,x58912)+P44(x58911,x58912)+~P1(f335(f67(f933(x58911,x58911)),x58912)) % 186.01/186.03 [5933]E(x59331,f195(f934(x59332,a922)))+~P1(f335(f67(x59332),x59331))+P1(f335(f335(f244(a927),f2(a927)),f335(f41(x59332),x59331))) % 186.01/186.03 [5960]~P1(f335(x59601,x59602))+P1(f335(x59601,f2(a927)))+P1(f335(f335(f244(a927),f536(x59602,x59601)),x59602)) % 186.01/186.03 [5983]E(x59831,f2(a927))+~E(f335(f172(a927),x59832),f2(a927))+~P1(f335(f335(f337(a927),x59831),f335(f179(a927),x59832))) % 186.01/186.03 [6051]E(x60511,x60512)+~P1(f335(f335(f243(a927),x60512),x60511))+~P1(f335(f335(f243(a927),x60511),x60512)) % 186.01/186.03 [6052]E(x60521,x60522)+~P1(f335(f335(f243(a1),x60522),x60521))+~P1(f335(f335(f243(a1),x60521),x60522)) % 186.01/186.03 [6054]E(f335(f41(x60541),x60542),f2(a927))+~P1(f335(f67(x60541),x60542))+P1(f335(f335(f337(x60541),f602(x60542,x60541)),x60542)) % 186.01/186.03 [6063]E(f56(x60631,x60632),f52(x60631,x60632))+P1(f335(f335(f243(a1),f2(a1)),x60631))+~P1(f335(f335(f244(a1),f2(a1)),x60632)) % 186.01/186.03 [6089]~P1(f335(x60891,f441(x60891)))+P1(f335(x60891,f335(a111,x60892)))+~P1(f335(f335(f243(a1),f2(a1)),x60892)) % 186.01/186.03 [6092]P1(f335(f335(f243(a927),x60921),f350(x60922)))+~P1(f335(f67(a927),x60922))+~P1(f335(f335(f337(a927),x60921),x60922)) % 186.01/186.03 [6093]P1(f335(f335(f244(a927),x60931),f343(x60932)))+~P1(f335(f67(a927),x60932))+~P1(f335(f335(f337(a927),x60931),x60932)) % 186.01/186.03 [6124]E(x61241,x61242)+~P1(f335(f335(f244(a927),x61241),f335(a119,x61242)))+P1(f335(f335(f244(a927),x61241),x61242)) % 186.01/186.03 [6156]E(x61561,f335(a119,x61562))+~P1(f335(f335(f243(a927),x61561),f335(a119,x61562)))+P1(f335(f335(f243(a927),x61561),x61562)) % 186.01/186.03 [6172]P1(f335(x61721,f442(x61721)))+~P1(f335(x61721,f335(a111,x61722)))+~P1(f335(f335(f243(a1),f2(a1)),x61722)) % 186.01/186.03 [6187]~P1(f335(x61871,x61872))+~P1(f335(f335(f243(a1),f2(a1)),x61872))+P1(f335(x61871,f335(f107(a1),f433(x61871)))) % 186.01/186.03 [6198]~P87(x61982)+~E(x61981,f2(x61982))+~P1(f335(f335(f244(x61982),f2(x61982)),f335(f81(x61982),x61981))) % 186.01/186.03 [6223]~P59(x62231,x62232)+P38(x62231,f335(f294(x62231,x62231),x62232))+~P1(f335(f67(f933(x62231,x62231)),x62232)) % 186.01/186.03 [6232]~P94(x62321)+E(f335(f107(x62321),f335(f110(a927),x62322)),f335(f110(x62321),x62322))+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x62322))) % 186.01/186.03 [6235]E(f335(a119,x62351),x62352)+~P1(f335(f335(f244(a927),x62351),x62352))+P1(f335(f335(f244(a927),f335(a119,x62351)),x62352)) % 186.01/186.03 [6251]E(f335(f335(f42(a1),x62511),x62512),f2(a1))+~P1(f335(f335(f243(a1),x62511),f2(a1)))+~P1(f335(f335(f244(a1),x62512),x62511)) % 186.01/186.03 [6261]E(f51(a1,x62611,x62612),x62611)+~P1(f335(f335(f243(a1),x62611),f2(a1)))+~P1(f335(f335(f244(a1),x62612),x62611)) % 186.01/186.03 [6275]E(f53(x62751,x62752),f52(x62751,x62752))+~P1(f335(f335(f243(a1),f2(a1)),x62751))+~P1(f335(f335(f243(a1),f2(a1)),x62752)) % 186.01/186.03 [6285]E(f335(f335(f42(a1),x62851),x62852),f2(a1))+~P1(f335(f335(f243(a1),f2(a1)),x62851))+~P1(f335(f335(f244(a1),x62851),x62852)) % 186.01/186.03 [6296]E(f51(a927,f335(f110(a927),x62961),f335(f110(a927),x62962)),f335(f110(a927),x62961))+P1(f335(a200,f335(f110(a1),x62961)))+~P1(f335(a200,f335(f110(a1),x62962))) % 186.01/186.03 [6298]E(f51(a1,x62981,x62982),x62981)+~P1(f335(f335(f243(a1),f2(a1)),x62981))+~P1(f335(f335(f244(a1),x62981),x62982)) % 186.01/186.03 [6299]E(x62991,x62992)+~P1(f335(f335(f244(a927),x62991),f335(a119,x62992)))+~P1(f335(f335(f243(a927),x62992),x62991)) % 186.01/186.03 [6313]~P78(x63131)+~P1(f335(f335(f243(x63131),x63132),f2(x63131)))+P1(f335(f335(f243(x63131),x63132),f335(f85(x63131),x63132))) % 186.01/186.03 [6314]~P113(x63141)+~P1(f335(f335(f244(x63141),x63142),f2(x63141)))+P1(f335(f335(f244(x63141),x63142),f335(f85(x63141),x63142))) % 186.01/186.03 [6323]~P6(x63231)+E(f335(f335(f70(x63231,x63231,f108(x63231)),f250(x63231)),x63232),f44(x63231,x63232))+~P1(f335(f67(x63231),x63232)) % 186.01/186.03 [6324]~P6(x63241)+E(f335(f335(f70(x63241,x63241,f117(x63241)),f195(x63241)),x63242),f43(x63241,x63242))+~P1(f335(f67(x63241),x63242)) % 186.01/186.03 [6341]~P113(x63411)+~P1(f335(f335(f243(a1),f2(a1)),x63412))+P1(f335(f335(f243(x63411),f2(x63411)),f335(f109(x63411),x63412))) % 186.01/186.03 [6342]~P125(x63421)+~P1(f335(f335(f244(a927),f2(a927)),x63422))+P1(f335(f335(f244(x63421),f2(x63421)),f335(f107(x63421),x63422))) % 186.01/186.03 [6343]~P113(x63431)+~P1(f335(f335(f244(a1),f2(a1)),x63432))+P1(f335(f335(f244(x63431),f2(x63431)),f335(f109(x63431),x63432))) % 186.01/186.03 [6346]~P7(x63462)+~P7(x63461)+E(f335(f318(a927,a1,f107(a1)),f311(a927,f335(a111,x63461),f335(a111,x63462))),f311(a1,x63461,x63462)) % 186.01/186.03 [6352]P1(f335(x63521,x63522))+~P1(f335(f335(f243(a1),f2(a1)),x63522))+~P1(f335(x63521,f335(f107(a1),f434(x63521)))) % 186.01/186.03 [6382]E(f335(f335(f86(a927),f335(f110(a927),x63821)),f335(f110(a927),x63822)),f335(f110(a927),x63821))+P1(f335(f335(f244(a1),x63821),a89))+~P1(f335(f335(f244(a1),x63822),a89)) % 186.01/186.03 [6386]~P113(x63861)+P1(f335(f335(f244(x63861),f2(x63861)),f88(x63861,x63862)))+~P1(f335(f335(f244(x63861),f2(x63861)),x63862)) % 186.01/186.03 [6398]~P79(x63981)+~P1(f335(f335(f243(x63981),x63982),f2(x63981)))+P1(f335(f335(f243(x63981),f2(x63981)),f335(f85(x63981),x63982))) % 186.01/186.03 [6399]~P79(x63991)+~P1(f335(f335(f244(x63991),x63992),f2(x63991)))+P1(f335(f335(f244(x63991),f2(x63991)),f335(f85(x63991),x63992))) % 186.01/186.03 [6402]E(x64021,f250(f934(x64022,a922)))+~E(f335(f41(x64022),x64021),f335(f41(x64022),f250(f934(x64022,a922))))+~P1(f335(f67(x64022),f250(f934(x64022,a922)))) % 186.01/186.03 [6434]~P78(x64341)+P1(f335(f335(f243(x64341),x64342),f2(x64341)))+~P1(f335(f335(f243(x64341),x64342),f335(f85(x64341),x64342))) % 186.01/186.03 [6435]~P113(x64351)+P1(f335(f335(f244(x64351),x64352),f2(x64351)))+~P1(f335(f335(f244(x64351),x64352),f335(f85(x64351),x64352))) % 186.01/186.03 [6444]~P94(x64441)+P1(f335(f335(f337(x64441),f335(f110(x64441),x64442)),f193(x64441)))+~P1(f335(f335(f243(a1),a89),x64442)) % 186.01/186.03 [6473]E(x64731,f2(a927))+~P1(f335(f335(f244(a927),x64731),f335(a119,x64732)))+P1(f335(f335(f244(a927),f385(x64732,x64731)),x64732)) % 186.01/186.03 [6495]~P113(x64951)+~P1(f335(f335(f244(x64951),f2(x64951)),f88(x64951,x64952)))+P1(f335(f335(f244(x64951),f2(x64951)),x64952)) % 186.01/186.03 [6497]~E(f335(f110(a927),x64972),f335(f110(a927),x64971))+P1(f335(f335(f243(a1),f335(f110(a1),x64971)),f2(a1)))+~P1(f335(a200,f335(f110(a1),x64972))) % 186.01/186.03 [6526]E(f335(f259(a1,a1),f56(x65261,x65262)),f335(f335(f42(a1),x65261),x65262))+~P1(f335(f335(f244(a1),x65261),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x65262)) % 186.01/186.03 [6563]E(f335(f264(a1,a1),f56(x65631,x65632)),f51(a1,x65631,x65632))+~P1(f335(f335(f244(a1),x65631),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x65632)) % 186.01/186.03 [6566]~P113(x65662)+~P1(f335(f335(f243(x65662),f2(x65662)),f335(f109(x65662),x65661)))+P1(f335(f335(f243(a1),f2(a1)),x65661)) % 186.01/186.03 [6567]~P125(x65672)+~P1(f335(f335(f244(x65672),f2(x65672)),f335(f107(x65672),x65671)))+P1(f335(f335(f244(a927),f2(a927)),x65671)) % 186.01/186.03 [6568]~P113(x65682)+~P1(f335(f335(f244(x65682),f2(x65682)),f335(f109(x65682),x65681)))+P1(f335(f335(f244(a1),f2(a1)),x65681)) % 186.01/186.03 [6571]E(f335(f259(a1,a1),f53(x65711,x65712)),f335(f335(f42(a1),x65711),x65712))+~P1(f335(f335(f243(a1),f2(a1)),x65712))+~P1(f335(f335(f244(a1),f2(a1)),x65711)) % 186.01/186.03 [6585]E(f335(f264(a1,a1),f53(x65851,x65852)),f51(a1,x65851,x65852))+~P1(f335(f335(f243(a1),f2(a1)),x65852))+~P1(f335(f335(f244(a1),f2(a1)),x65851)) % 186.01/186.03 [6600]~P79(x66001)+P1(f335(f335(f243(x66001),x66002),f2(x66001)))+~P1(f335(f335(f243(x66001),f2(x66001)),f335(f85(x66001),x66002))) % 186.01/186.03 [6601]~P79(x66011)+P1(f335(f335(f244(x66011),x66012),f2(x66011)))+~P1(f335(f335(f244(x66011),f2(x66011)),f335(f85(x66011),x66012))) % 186.01/186.03 [6628]P1(f335(f55(x66281,x66282),f56(x66281,x66282)))+~P1(f335(f335(f244(a1),x66281),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x66282)) % 186.01/186.03 [6652]P1(f335(f55(x66521,x66522),f53(x66521,x66522)))+~P1(f335(f335(f243(a1),f2(a1)),x66521))+~P1(f335(f335(f244(a1),f2(a1)),x66522)) % 186.01/186.03 [6696]~P79(x66961)+P1(f335(f335(f243(x66961),f335(f85(x66961),x66962)),f2(x66961)))+~P1(f335(f335(f243(x66961),f2(x66961)),x66962)) % 186.01/186.03 [6697]~P79(x66971)+P1(f335(f335(f244(x66971),f335(f85(x66971),x66972)),f2(x66971)))+~P1(f335(f335(f244(x66971),f2(x66971)),x66972)) % 186.01/186.03 [6713]E(f335(f335(f23(a927),f335(a111,x67131)),f335(a111,x67132)),f335(a111,f201(x67131,x67132)))+~P1(f335(f335(f243(a1),f2(a1)),x67132))+~P1(f335(f335(f243(a1),f2(a1)),x67131)) % 186.01/186.03 [6731]P1(f335(f335(f243(a1),f2(a1)),f201(x67311,x67312)))+~P1(f335(f335(f243(a1),f2(a1)),x67312))+~P1(f335(f335(f243(a1),f2(a1)),x67311)) % 186.01/186.03 [6768]~P1(f335(x67681,x67682))+P1(f335(x67681,f2(a927)))+P1(f335(x67681,f335(f335(f86(a927),f536(x67682,x67681)),f84(a927)))) % 186.01/186.03 [6851]E(f335(f110(a927),x68511),f335(f110(a927),x68512))+~P1(f335(f335(f243(a1),f335(f110(a1),x68512)),f2(a1)))+~P1(f335(a200,f335(f110(a1),x68511))) % 186.01/186.03 [6863]~E(x68631,f2(a927))+~E(f699(x68632,x68631),f2(a927))+E(f335(f149(a927,a927,f86(a927),x68631),x68632),f2(a927)) % 186.01/186.03 [6887]~P1(f335(f67(x68871),f579(x68872,x68871)))+~P1(f335(f67(f934(x68871,a922)),x68872))+P1(f335(f67(x68871),f43(f934(x68871,a922),x68872))) % 186.01/186.03 [6893]E(x68931,x68932)+P1(f335(f335(f244(a1),x68931),x68932))+~P1(f335(f335(f244(a1),x68931),f335(f335(f86(a1),x68932),f84(a1)))) % 186.01/186.03 [6894]P1(f335(f335(f243(a927),f335(a111,x68941)),f335(a111,x68942)))+~P1(f335(f335(f243(a1),f2(a1)),x68942))+~P1(f335(f335(f243(a1),x68941),x68942)) % 186.01/186.03 [6895]P1(f335(f335(f243(a927),f335(a111,x68951)),f335(a111,x68952)))+~P1(f335(f335(f244(a1),f2(a1)),x68951))+~P1(f335(f335(f243(a1),x68951),x68952)) % 186.01/186.03 [6897]P1(f335(f335(f244(a927),f335(a111,x68971)),f335(a111,x68972)))+~P1(f335(f335(f243(a1),f2(a1)),x68971))+~P1(f335(f335(f244(a1),x68971),x68972)) % 186.01/186.03 [6898]P1(f335(f335(f244(a927),f335(a111,x68981)),f335(a111,x68982)))+~P1(f335(f335(f244(a1),f2(a1)),x68982))+~P1(f335(f335(f244(a1),x68981),x68982)) % 186.01/186.03 [6909]E(f51(a927,f335(a111,x69091),f335(a111,x69092)),f335(a111,f51(a1,x69091,x69092)))+~P1(f335(f335(f243(a1),f2(a1)),x69092))+~P1(f335(f335(f243(a1),f2(a1)),x69091)) % 186.01/186.03 [6933]~P79(x69331)+~P1(f335(f335(f243(x69331),f335(f85(x69331),x69332)),f2(x69331)))+P1(f335(f335(f243(x69331),f2(x69331)),x69332)) % 186.01/186.03 [6934]~P79(x69341)+~P1(f335(f335(f244(x69341),f335(f85(x69341),x69342)),f2(x69341)))+P1(f335(f335(f244(x69341),f2(x69341)),x69342)) % 186.01/186.03 [6948]~P1(f335(f335(f244(a1),a89),x69482))+~P1(f335(f335(f244(a1),x69481),x69482))+P1(f335(f335(f244(a927),f335(f110(a927),x69481)),f335(f110(a927),x69482))) % 186.01/186.03 [7038]~P1(f335(f335(f243(a1),f2(a1)),x70381))+P1(f335(f335(f244(a927),f335(a111,x70381)),x70382))+~P1(f335(f335(f244(a1),x70381),f335(f107(a1),x70382))) % 186.01/186.03 [7043]P1(f335(x70431,x70432))+~P1(f335(x70431,f335(a20,f839(x70431,x70432))))+~P1(f335(f335(f337(a927),x70432),f250(f934(a927,a922)))) % 186.01/186.03 [7054]E(x70541,f2(a1))+E(f51(a1,x70542,x70541),f2(a1))+E(f335(f335(f23(a1),f335(f85(a1),f335(f335(f42(a1),x70542),x70541))),f84(a1)),f335(f335(f42(a1),x70542),f335(f85(a1),x70541))) % 186.01/186.03 [7068]~P1(f335(f335(f243(a1),f2(a1)),x70681))+~P1(f335(f335(f244(a927),f335(a111,x70681)),x70682))+P1(f335(f335(f244(a1),x70681),f335(f107(a1),x70682))) % 186.01/186.03 [7102]~P1(f335(f335(f243(a927),f335(a111,x71021)),f335(a111,x71022)))+~P1(f335(f335(f243(a1),f2(a1)),x71022))+P1(f335(f335(f243(a1),x71021),x71022)) % 186.01/186.03 [7103]~P1(f335(f335(f243(a927),f335(a111,x71031)),f335(a111,x71032)))+~P1(f335(f335(f244(a1),f2(a1)),x71031))+P1(f335(f335(f243(a1),x71031),x71032)) % 186.01/186.03 [7131]P1(f335(f335(f243(a1),x71311),x71312))+~P1(f335(f335(f243(a927),f335(f110(a927),x71311)),f335(f110(a927),x71312)))+P1(f335(f335(f243(a1),x71311),a89)) % 186.01/186.03 [7156]P1(f335(f335(f243(a1),f2(a1)),f51(a1,x71561,x71562)))+~P1(f335(f335(f243(a1),f2(a1)),x71562))+~P1(f335(f335(f243(a1),f2(a1)),x71561)) % 186.01/186.03 [7253]P1(f335(f335(f244(a1),a89),x72531))+~P1(f335(f335(f244(a1),x72532),x72531))+~P1(f335(f335(f244(a927),f335(f110(a927),x72532)),f335(f110(a927),x72531))) % 186.01/186.03 [7306]E(f335(f335(f260(a1,a1),f335(f335(f42(a1),x73061),x73062)),f51(a1,x73061,x73062)),f56(x73061,x73062))+~P1(f335(f335(f244(a1),x73061),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x73062)) % 186.01/186.03 [7326]E(f335(f335(f260(a1,a1),f335(f335(f42(a1),x73261),x73262)),f51(a1,x73261,x73262)),f53(x73261,x73262))+~P1(f335(f335(f243(a1),f2(a1)),x73262))+~P1(f335(f335(f243(a1),f2(a1)),x73261)) % 186.01/186.03 [7378]~P96(x73782)+E(x73781,f120(x73782))+E(f335(f149(x73782,x73782,f87(x73782),f335(f148(x73782),x73781)),f335(f178(x73782),x73781)),f335(f69(x73782,f87(x73782)),f335(f179(x73782),x73781))) % 186.01/186.03 [7494]~E(x74941,f2(a927))+E(f335(f149(a927,a927,f86(a927),x74941),x74942),f2(a927))+P1(f335(f335(f337(a927),f699(x74942,x74941)),f335(f179(a927),x74942))) % 186.01/186.03 [7549]~P1(f335(f335(f243(a1),x75491),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x75491),x75492)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x75492)) % 186.01/186.03 [7550]~P1(f335(f335(f244(a1),x75502),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x75501),x75502)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x75501)) % 186.01/186.03 [7551]~P1(f335(f335(f244(a1),x75512),f2(a1)))+P1(f335(f335(f244(a1),f335(f335(f42(a1),x75511),x75512)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x75511)) % 186.01/186.03 [7553]~P1(f335(f335(f244(a1),x75531),f2(a1)))+P1(f335(f335(f244(a1),f335(f335(f42(a1),x75531),x75532)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x75532)) % 186.01/186.03 [7560]P1(f335(f335(f337(f934(x75601,a922)),f579(x75602,x75601)),x75602))+~P1(f335(f67(f934(x75601,a922)),x75602))+P1(f335(f67(x75601),f43(f934(x75601,a922),x75602))) % 186.01/186.03 [7648]P26(x76481,x76481,x76482,f250(f934(x76481,a922)))+~E(f335(f318(x76481,x76481,x76482),f250(f934(x76481,a922))),f250(f934(x76481,a922)))+~P1(f335(f67(x76481),f250(f934(x76481,a922)))) % 186.01/186.03 [7766]~P26(x77661,x77661,x77662,f250(f934(x77661,a922)))+E(f335(f318(x77661,x77661,x77662),f250(f934(x77661,a922))),f250(f934(x77661,a922)))+~P1(f335(f67(x77661),f250(f934(x77661,a922)))) % 186.01/186.03 [7903]E(f335(f335(f42(a1),x79031),x79032),f335(f110(a1),a104))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x79031),x79032)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x79031)) % 186.01/186.03 [7959]~P1(f335(f335(f244(a1),x79592),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f42(a1),x79591),x79592)),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x79591)) % 186.01/186.03 [7964]E(f335(f335(f86(a1),x79641),x79642),f51(a1,x79641,x79642))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),x79641),x79642)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x79641)) % 186.01/186.03 [7967]P1(f335(f335(f244(a1),x79671),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f42(a1),x79671),x79672)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x79672)) % 186.01/186.03 [8655]~P109(x86551)+P14(x86551,x86552)+~P1(f335(f335(f243(x86551),f335(f335(f171(x86551),x86552),f732(x86552,x86551))),f335(f335(f171(x86551),x86552),f733(x86552,x86551)))) % 186.01/186.03 [8656]~P109(x86561)+P14(x86561,x86562)+~P1(f335(f335(f243(x86561),f335(f335(f171(x86561),x86562),f739(x86562,x86561))),f335(f335(f171(x86561),x86562),f744(x86562,x86561)))) % 186.01/186.03 [5926]E(x59261,f2(a1))+~E(f51(a1,x59262,x59261),f2(a1))+E(f335(f335(f42(a1),x59262),f335(f85(a1),x59261)),f335(f85(a1),f335(f335(f42(a1),x59262),x59261))) % 186.01/186.03 [5944]~P41(x59442)+~P41(x59441)+P41(f335(f335(f108(f934(a1,a922)),x59441),x59442)) % 186.01/186.03 [5945]~P41(x59452)+~P41(x59451)+P41(f335(f335(f117(f934(a1,a922)),x59451),x59452)) % 186.01/186.03 [5963]~P94(x59631)+~P66(x59631)+E(f335(f85(x59631),f335(f335(f299(x59631),f84(x59631)),x59632)),f335(f335(f299(x59631),f335(f110(x59631),a104)),x59632)) % 186.01/186.03 [6081]E(x60811,f2(a1))+~E(f51(a1,x60812,x60811),f2(a1))+E(f335(f335(f42(a1),f335(f85(a1),x60812)),x60811),f335(f85(a1),f335(f335(f42(a1),x60812),x60811))) % 186.01/186.03 [6217]~P109(x62171)+P14(x62171,x62172)+P1(f335(f335(f244(a927),f733(x62172,x62171)),f335(f196(f928(x62171)),x62172))) % 186.01/186.03 [6218]~P109(x62181)+P14(x62181,x62182)+P1(f335(f335(f244(a927),f744(x62182,x62181)),f335(f196(f928(x62181)),x62182))) % 186.01/186.03 [6376]~P94(x63761)+~E(f335(f110(x63761),x63762),f2(x63761))+P29(x63761,f335(f110(x63761),f335(f335(f86(a1),x63762),f335(f85(a1),a89)))) % 186.01/186.03 [6377]~P94(x63771)+~E(f335(f110(x63771),x63772),f2(x63771))+P29(x63771,f335(f110(x63771),f335(f335(f86(a1),a89),f335(f85(a1),x63772)))) % 186.01/186.03 [6379]E(f335(a57,f53(f335(f85(a1),x63791),f335(f85(a1),x63792))),f52(x63791,x63792))+P1(f335(f335(f243(a1),f2(a1)),x63791))+P1(f335(f335(f244(a1),f2(a1)),x63792)) % 186.01/186.03 [6503]~E(x65032,f2(a927))+~E(x65031,f2(a927))+P1(f335(f335(f243(a1),f335(f107(a1),x65031)),f335(f85(a1),f335(f107(a1),x65032)))) % 186.01/186.03 [6532]E(f335(f335(f86(a927),f335(f110(a927),x65321)),f335(f110(a927),x65322)),f335(f110(a927),f335(f335(f86(a1),x65321),x65322)))+P1(f335(f335(f244(a1),x65321),a89))+P1(f335(f335(f244(a1),x65322),a89)) % 186.01/186.03 [6662]~P78(x66621)+~P1(f335(f335(f243(x66621),f2(x66621)),x66622))+P1(f335(f335(f243(x66621),f335(f85(x66621),x66622)),x66622)) % 186.01/186.03 [6663]~P78(x66631)+~P1(f335(f335(f244(x66631),f2(x66631)),x66632))+P1(f335(f335(f244(x66631),f335(f85(x66631),x66632)),x66632)) % 186.01/186.03 [6837]E(f335(f335(f23(a927),f335(a111,x68371)),f335(a111,x68372)),f335(a111,f335(f335(f23(a1),x68371),x68372)))+~P1(f335(f335(f243(a1),f2(a1)),x68372))+~P1(f335(f335(f243(a1),x68372),x68371)) % 186.01/186.03 [6871]E(f335(a111,f51(a1,f335(f110(a1),x68711),f335(f110(a1),x68712))),f51(a927,f335(f110(a927),x68711),f335(f110(a927),x68712)))+P1(f335(a200,f335(f110(a1),x68711)))+P1(f335(a200,f335(f110(a1),x68712))) % 186.01/186.03 [6888]~P78(x68881)+P1(f335(f335(f243(x68881),f2(x68881)),x68882))+~P1(f335(f335(f243(x68881),f335(f85(x68881),x68882)),x68882)) % 186.01/186.03 [6889]~P78(x68891)+P1(f335(f335(f244(x68891),f2(x68891)),x68892))+~P1(f335(f335(f244(x68891),f335(f85(x68891),x68892)),x68892)) % 186.01/186.03 [6901]~P78(x69011)+~P1(f335(f335(f243(x69011),f2(x69011)),x69012))+P1(f335(f335(f243(x69011),f2(x69011)),f335(f335(f86(x69011),x69012),x69012))) % 186.01/186.03 [6903]~P78(x69031)+~P1(f335(f335(f244(x69031),f2(x69031)),x69032))+P1(f335(f335(f244(x69031),f2(x69031)),f335(f335(f86(x69031),x69032),x69032))) % 186.01/186.03 [6916]E(f335(f335(f86(a927),f335(a111,x69161)),f335(a111,x69162)),f335(a111,f335(f335(f86(a1),x69161),x69162)))+~P1(f335(f335(f243(a1),f2(a1)),x69162))+~P1(f335(f335(f243(a1),f2(a1)),x69161)) % 186.01/186.03 [6927]E(x69271,f2(a927))+P1(f335(f335(f244(a927),f2(a927)),x69272))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f252(a927),x69272),x69271))) % 186.01/186.03 [6960]~P94(x69601)+E(f335(f110(x69601),x69602),f2(x69601))+~P29(x69601,f335(f110(x69601),f335(f335(f86(a1),a89),f335(f85(a1),x69602)))) % 186.01/186.03 [6961]~P94(x69611)+E(f335(f110(x69611),x69612),f2(x69611))+~P29(x69611,f335(f110(x69611),f335(f335(f86(a1),x69612),f335(f85(a1),a89)))) % 186.01/186.03 [7016]~P1(f335(f67(x70161),x70162))+~P1(f335(f67(x70161),f250(f934(x70161,a922))))+P1(f335(f67(x70161),f335(f85(f934(x70161,a922)),x70162))) % 186.01/186.03 [7039]~P1(f335(f335(f244(a1),f2(a1)),x70392))+~P1(f335(f335(f243(a1),x70392),x70391))+P1(f335(f335(f244(a1),f2(a1)),f335(f335(f42(a1),x70391),x70392))) % 186.01/186.03 [7040]~P1(f335(f335(f243(a1),x70401),f2(a1)))+~P1(f335(f335(f244(a1),x70402),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f42(a1),x70401),x70402))) % 186.01/186.03 [7076]~P1(f335(f335(f243(a1),f2(a1)),x70762))+~P1(f335(f335(f243(a1),f2(a1)),x70761))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f87(a1),x70761),x70762))) % 186.01/186.03 [7077]~P1(f335(f335(f243(a1),f2(a1)),x70772))+~P1(f335(f335(f243(a1),f2(a1)),x70771))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),x70771),x70772))) % 186.01/186.03 [7078]~P1(f335(f335(f243(a1),f2(a1)),x70782))+~P1(f335(f335(f243(a1),f2(a1)),x70781))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f42(a1),x70781),x70782))) % 186.01/186.03 [7079]~P1(f335(f335(f243(a1),f2(a1)),x70791))+~P1(f335(f335(f244(a1),f2(a1)),x70792))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f42(a1),x70791),x70792))) % 186.01/186.03 [7080]~P1(f335(f335(f244(a927),f2(a927)),x70802))+~P1(f335(f335(f244(a927),f2(a927)),x70801))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f87(a927),x70801),x70802))) % 186.01/186.03 [7143]E(x71431,f2(a1))+E(f51(a1,x71432,x71431),f2(a1))+E(f335(f335(f23(a1),f335(f85(a1),f335(f335(f42(a1),x71432),x71431))),f84(a1)),f335(f335(f42(a1),f335(f85(a1),x71432)),x71431)) % 186.01/186.03 [7199]P1(f335(f335(f244(a927),f2(a927)),x71991))+P1(f335(f335(f244(a927),f2(a927)),x71992))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f86(a927),x71992),x71991))) % 186.01/186.03 [7203]~P78(x72031)+P1(f335(f335(f243(x72031),f2(x72031)),x72032))+~P1(f335(f335(f243(x72031),f2(x72031)),f335(f335(f86(x72031),x72032),x72032))) % 186.01/186.03 [7204]~P78(x72041)+P1(f335(f335(f244(x72041),f2(x72041)),x72042))+~P1(f335(f335(f244(x72041),f2(x72041)),f335(f335(f86(x72041),x72042),x72042))) % 186.01/186.03 [7254]~P1(f335(f67(x72541),x72542))+P1(f335(f67(x72541),f250(f934(x72541,a922))))+~P1(f335(f67(x72541),f335(f85(f934(x72541,a922)),x72542))) % 186.01/186.03 [7318]P1(f335(f335(f243(a1),x73181),f2(a1)))+~P1(f335(f335(f244(a1),x73182),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f42(a1),x73181),x73182))) % 186.01/186.03 [7324]~P1(f335(f335(f244(a1),f2(a1)),x73241))+P1(f335(f335(f243(a1),x73241),x73242))+~P1(f335(f335(f244(a1),f2(a1)),f335(f335(f42(a1),x73242),x73241))) % 186.01/186.03 [7325]~P1(f335(f335(f243(a1),f2(a1)),x73252))+P1(f335(f335(f243(a1),x73251),x73252))+~P1(f335(f335(f244(a1),f2(a1)),f335(f335(f42(a1),x73252),x73251))) % 186.01/186.03 [7355]P1(f335(f335(f243(a1),f2(a1)),x73551))+~P1(f335(f335(f244(a1),f2(a1)),x73552))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f42(a1),x73551),x73552))) % 186.01/186.03 [7356]P1(f335(f335(f244(a1),f2(a1)),x73561))+~P1(f335(f335(f243(a1),f2(a1)),x73562))+~P1(f335(f335(f244(a1),f2(a1)),f335(f335(f42(a1),x73562),x73561))) % 186.01/186.03 [7797]~P1(f335(f67(x77972),f250(f934(x77972,a922))))+~P1(f335(f67(x77971),f250(f934(x77971,a922))))+P1(f335(f67(f933(x77971,x77972)),f250(f934(f933(x77971,x77972),a922)))) % 186.01/186.03 [7798]~P1(f335(f67(x77982),f250(f934(x77982,a922))))+~P1(f335(f67(x77981),f250(f934(x77981,a922))))+P1(f335(f67(f935(x77981,x77982)),f250(f934(f935(x77981,x77982),a922)))) % 186.01/186.03 [7868]~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x78681))+~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x78682))+P1(f335(f335(f244(a927),x78681),f335(f335(f87(a927),x78682),x78681))) % 186.01/186.03 [7869]~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x78691))+~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x78692))+P1(f335(f335(f244(a927),x78691),f335(f335(f87(a927),x78691),x78692))) % 186.01/186.03 [7902]E(f335(f41(x79021),f250(f934(x79021,a922))),f335(a119,f2(a927)))+P1(f335(f67(x79022),f250(f934(x79022,a922))))+~P1(f335(f67(f934(x79022,x79021)),f250(f934(f934(x79022,x79021),a922)))) % 186.01/186.03 [8027]~P1(f335(f335(f243(a927),f335(a119,f2(a927))),x80271))+~P1(f335(f335(f243(a927),f335(a119,f2(a927))),x80272))+P1(f335(f335(f243(a927),f335(a119,f2(a927))),f335(f335(f87(a927),x80271),x80272))) % 186.01/186.03 [8028]~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x80282))+~P1(f335(f335(f244(a927),f335(a119,f2(a927))),x80281))+P1(f335(f335(f244(a927),f335(a119,f2(a927))),f335(f335(f87(a927),x80281),x80282))) % 186.01/186.03 [8702]E(x87021,f120(x87022))+~P1(f335(f144(x87022),x87021))+E(f184(x87022,f335(f335(f8(a922,a922,x87022),a330),f335(f335(f7(x87022,x87022,a922),a332),f151(x87022,x87021))),x87021),f121(x87022,x87021)) % 186.01/186.03 [8797]~P41(x87972)+~P41(x87971)+E(f335(f318(a927,a1,f107(a1)),f335(f335(f108(f934(a927,a922)),f335(f318(a1,a927,a111),x87971)),f335(f318(a1,a927,a111),x87972))),f335(f335(f108(f934(a1,a922)),x87971),x87972)) % 186.01/186.03 [8798]~P41(x87982)+~P41(x87981)+E(f335(f318(a927,a1,f107(a1)),f335(f335(f117(f934(a927,a922)),f335(f318(a1,a927,a111),x87981)),f335(f318(a1,a927,a111),x87982))),f335(f335(f117(f934(a1,a922)),x87981),x87982)) % 186.01/186.03 [9464]~P94(x94641)+~E(f335(f110(x94641),x94642),f84(x94641))+P29(x94641,f335(f110(x94641),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f85(a1),x94642)))) % 186.01/186.03 [9703]~P94(x97031)+E(f335(f110(x97031),x97032),f84(x97031))+~P29(x97031,f335(f110(x97031),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f85(a1),x97032)))) % 186.01/186.03 [10470]E(x104701,f2(a1))+E(x104702,f2(a1))+E(f335(f266(a1,a1,a1,a1,f25(a1),f335(f87(a1),f88(a1,x104702))),f335(f335(f335(f103(f933(a1,a1)),f335(f335(a332,f88(a1,x104701)),f88(a1,x104702))),f59(x104701,x104702)),f335(f335(f265(a1,a1,f933(a1,a1)),f335(f335(f18(a1,f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f934(f933(a1,a1),f933(a1,a1))),f934(f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),a1),f18(a1,f933(a1,a1),f933(a1,a1))),f335(f335(f8(f933(a1,a1),f934(a1,f934(f933(a1,a1),f933(a1,a1))),a1),f335(f7(a1,f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),f335(f335(f8(a922,f934(f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),a1),f103(f933(a1,a1))),f335(f335(f7(a1,a1,a922),a332),f2(a1))))),f335(f335(f7(a1,a1,f933(a1,a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f335(f335(f7(a1,f934(a1,a1),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f933(a1,a1)),f934(f934(a1,a1),f934(a1,f933(a1,a1))),a1),f8(a1,f933(a1,a1),a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f934(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f335(f23(a1),f335(f81(a1),x104702))))),f59(x104701,x104702)))),f52(x104701,x104702)) % 186.01/186.03 [10471]E(x104711,f2(a1))+E(x104712,f2(a1))+E(f335(f266(a1,a1,a1,a1,f25(a1),f335(f87(a1),f88(a1,x104712))),f335(f335(f335(f103(f933(a1,a1)),f335(f335(a334,f335(f335(a333,f335(f335(f244(a1),f2(a1)),x104712)),f335(f335(f243(a1),f2(a1)),x104711))),f335(f335(a333,f335(f335(f244(a1),x104712),f2(a1))),f335(f335(f244(a1),x104711),f2(a1))))),f59(x104711,x104712)),f335(f335(f265(a1,a1,f933(a1,a1)),f335(f335(f18(a1,f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f934(f933(a1,a1),f933(a1,a1))),f934(f934(a1,f933(a1,a1)),f934(a1,f933(a1,a1))),a1),f18(a1,f933(a1,a1),f933(a1,a1))),f335(f335(f8(f933(a1,a1),f934(a1,f934(f933(a1,a1),f933(a1,a1))),a1),f335(f7(a1,f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),f335(f335(f8(a922,f934(f933(a1,a1),f934(f933(a1,a1),f933(a1,a1))),a1),f103(f933(a1,a1))),f335(f335(f7(a1,a1,a922),a332),f2(a1))))),f335(f335(f7(a1,a1,f933(a1,a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f85(a1))),f2(a1))))),f335(f335(f7(a1,f934(a1,a1),f934(a1,f933(a1,a1))),f335(f335(f8(f934(a1,f933(a1,a1)),f934(f934(a1,a1),f934(a1,f933(a1,a1))),a1),f8(a1,f933(a1,a1),a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f335(f335(f7(a1,a1,a1),f335(f335(f8(a1,f934(a1,a1),a1),f23(a1)),f85(a1))),f84(a1))))),f335(f23(a1),f335(f81(a1),x104712))))),f59(x104711,x104712)))),f52(x104711,x104712)) % 186.01/186.03 [5952]~P113(x59521)+~P94(x59521)+E(f335(f81(x59521),f335(f335(f252(x59521),f335(f110(x59521),a104)),x59522)),f84(x59521)) % 186.01/186.03 [6445]~P140(x64451)+~P1(f335(f335(f244(a1),x64452),f2(a1)))+E(f335(f85(x64451),f335(f107(x64451),f335(a111,f335(f85(a1),x64452)))),f335(f109(x64451),x64452)) % 186.01/186.03 [6645]P1(f335(f335(f243(a106),x66451),f84(a106)))+E(f335(f335(f86(a106),f84(a106)),f280(x66451,f335(f335(f42(a106),x66452),x66451))),f280(x66451,x66452))+P1(f335(f335(f244(a106),x66452),x66451)) % 186.01/186.03 [7243]~P93(x72431)+~P1(f335(f335(f337(x72431),x72432),f116(x72431)))+~E(f335(f335(f86(x72431),f335(f335(f86(x72431),f84(x72431)),x72432)),x72432),f2(x72431)) % 186.01/186.03 [7357]~P1(f335(f335(f243(a1),x73572),f2(a1)))+~P1(f335(f335(f244(a1),x73571),f2(a1)))+E(f335(f259(a1,a1),f335(a57,f53(f335(f85(a1),x73571),f335(f85(a1),x73572)))),f335(f335(f42(a1),x73571),x73572)) % 186.01/186.03 [7374]~P1(f335(f335(f243(a1),x73742),f2(a1)))+~P1(f335(f335(f244(a1),x73741),f2(a1)))+E(f335(f264(a1,a1),f335(a57,f53(f335(f85(a1),x73741),f335(f85(a1),x73742)))),f51(a1,x73741,x73742)) % 186.01/186.03 [7380]~P1(f335(f335(f244(a1),x73802),f2(a1)))+E(f335(f259(a1,a1),f335(a57,f56(f335(f85(a1),x73801),f335(f85(a1),x73802)))),f335(f335(f42(a1),x73801),x73802))+~P1(f335(f335(f244(a1),f2(a1)),x73801)) % 186.01/186.03 [7398]~P1(f335(f335(f244(a1),x73982),f2(a1)))+E(f335(f264(a1,a1),f335(a57,f56(f335(f85(a1),x73981),f335(f85(a1),x73982)))),f51(a1,x73981,x73982))+~P1(f335(f335(f244(a1),f2(a1)),x73981)) % 186.01/186.03 [7450]E(f335(f335(f42(a1),f335(f335(f252(a1),x74501),x74502)),x74501),f335(f335(f252(a1),x74501),f335(f335(f23(a927),x74502),f335(a119,f2(a927)))))+~P1(f335(f335(f244(a927),f2(a927)),x74502))+~P1(f335(f335(f244(a1),f2(a1)),x74501)) % 186.01/186.03 [7556]~P1(f335(f335(f244(a927),f2(a927)),x75561))+~P1(f335(f335(f244(a927),f2(a927)),x75562))+P1(f335(f335(f244(a927),f335(f335(f23(a927),x75561),x75562)),x75561)) % 186.01/186.03 [7557]~P1(f335(f335(f244(a927),f2(a927)),x75571))+~P1(f335(f335(f244(a927),f84(a927)),x75572))+P1(f335(f335(f244(a927),f335(f335(f42(a927),x75571),x75572)),x75571)) % 186.01/186.03 [7558]~P1(f335(f335(f244(a1),f2(a1)),x75581))+~P1(f335(f335(f244(a1),f84(a1)),x75582))+P1(f335(f335(f244(a1),f335(f335(f42(a1),x75581),x75582)),x75581)) % 186.01/186.03 [7694]E(x76941,f2(a927))+~E(x76942,f2(a1))+~P1(f335(f335(f244(a1),f2(a1)),f335(f335(f252(a1),f335(f81(a1),x76942)),x76941))) % 186.01/186.03 [8104]~E(x81042,f120(f928(x81041)))+E(f335(f196(f928(f928(x81041))),f186(x81041,x81042)),f2(a927))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x81041),a927),f196(f928(x81041))),x81042))) % 186.01/186.03 [8352]P1(f335(x83521,x83522))+~P1(f335(x83521,f335(a113,f567(x83521,x83522))))+~P1(f335(f335(f337(f934(f933(a927,a927),a922)),x83522),a105)) % 186.01/186.03 [8368]E(x83681,f120(f928(x83682)))+E(f335(f196(f928(x83682)),f335(f335(f171(f928(x83682)),x83681),f2(a927))),f335(f196(f928(f928(x83682))),f186(x83682,x83681)))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x83682),a927),f196(f928(x83682))),x83681))) % 186.01/186.03 [8510]~P39(x85101,x85102)+~P40(x85101,x85102)+P39(x85101,f335(f335(f23(f934(f933(x85101,x85101),a922)),x85102),f315(x85101,f195(f934(f933(x85101,x85101),a922))))) % 186.01/186.03 [9082]~P1(f335(f67(x90821),f335(f270(x90821),x90822)))+~P1(f335(f67(x90821),f250(f934(x90821,a922))))+P1(f335(f67(x90821),f335(f270(x90821),f335(f335(f8(a922,a922,x90821),a330),x90822)))) % 186.01/186.03 [9148]E(f335(f335(f260(a927,a927),f335(a119,f335(f335(f42(a927),f335(f335(f23(a927),x91481),x91482)),x91482))),f51(a927,f335(f335(f23(a927),x91481),x91482),x91482)),f91(f933(a927,a927),f54(x91481,x91482)))+~P1(f335(f335(f244(a927),f2(a927)),x91482))+~P1(f335(f335(f243(a927),x91482),x91481)) % 186.01/186.03 [9430]~P1(f335(f67(x94301),f335(f270(x94301),x94302)))+P1(f335(f67(x94301),f250(f934(x94301,a922))))+~P1(f335(f67(x94301),f335(f270(x94301),f335(f335(f8(a922,a922,x94301),a330),x94302)))) % 186.01/186.03 [10148]P28(x101481,x101482)+~P38(x101481,f335(f259(f934(f933(x101481,x101481),a922),f934(f933(x101481,x101481),a922)),x101482))+~P1(f335(f335(f243(f934(f933(x101481,x101481),a922)),f335(f335(f297(x101481,x101481,x101481),f335(f259(f934(f933(x101481,x101481),a922),f934(f933(x101481,x101481),a922)),x101482)),f335(f264(f934(f933(x101481,x101481),a922),f934(f933(x101481,x101481),a922)),x101482))),f335(f259(f934(f933(x101481,x101481),a922),f934(f933(x101481,x101481),a922)),x101482))) % 186.01/186.03 [10245]~E(f308(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x102452,x102451),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x102452),x102451))+P1(f335(f335(f295(a927),x102451),x102452)) % 186.01/186.03 [10246]~E(f305(a927,f295(a927),f335(f335(f18(a927,f934(a927,a922),f934(a927,a922)),f335(f335(f8(f934(a927,f934(a922,a922)),f934(f934(a927,a922),f934(a927,a922)),a927),f18(a927,a922,a922)),f335(f335(f8(f934(a927,a922),f934(a927,f934(a922,a922)),a927),f335(f8(a922,f934(a922,a922),a927),a333)),f295(a927)))),f335(f335(f8(f934(a927,a922),f934(a927,a922),a927),f335(f8(a922,a922,a927),a330)),f335(f7(a927,a927,a922),f295(a927)))),x102462,x102461),f195(f934(a927,a922)))+~P1(f335(f335(f295(a927),x102462),x102461))+P1(f335(f335(f295(a927),x102461),x102462)) % 186.01/186.03 [7480]~P1(f335(f335(f244(a927),f2(a927)),x74802))+P1(f335(f335(f244(a927),x74801),x74802))+E(f335(a119,f335(f335(f42(a927),f335(f335(f23(a927),x74801),x74802)),x74802)),f335(f335(f42(a927),x74801),x74802)) % 186.01/186.03 [7620]~P1(f335(f335(f244(a927),f2(a927)),x76202))+~P1(f335(f335(f243(a927),x76202),x76201))+E(f335(a119,f335(f335(f42(a927),f335(f335(f23(a927),x76201),x76202)),x76202)),f335(f335(f42(a927),x76201),x76202)) % 186.01/186.03 [8573]~P94(x85731)+~P93(x85731)+~P29(x85731,f335(f110(x85731),f335(f335(f23(a1),f335(f335(f86(a1),x85732),x85732)),a104))) % 186.01/186.03 [9340]E(x93401,f2(a927))+E(f335(f335(f265(a927,a927,f933(a927,a927)),f335(f335(f8(a927,f934(a927,f933(a927,a927)),a927),f260(a927,a927)),a119)),f91(f933(a927,a927),f54(f335(f335(f23(a927),x93402),x93401),x93401))),f91(f933(a927,a927),f54(x93402,x93401)))+P1(f335(f335(f244(a927),x93402),x93401)) % 186.01/186.03 [9516]~P39(x95161,x95162)+~P53(x95161,x95162)+P1(f335(f335(f243(f934(f933(x95161,x95161),a922)),f335(f335(f297(x95161,x95161,x95161),f335(f294(x95161,x95161),x95162)),x95162)),x95162)) % 186.01/186.03 [9767]P1(f335(x97672,f662(x97672,x97671)))+P1(f335(x97671,f662(x97672,x97671)))+E(f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97671)),f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97672))) % 186.01/186.03 [9771]~P1(f335(x97712,f662(x97712,x97711)))+~P1(f335(x97711,f662(x97712,x97711)))+E(f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97711)),f335(f270(a1),f335(f335(f18(a1,a922,a922),f335(f335(f8(a922,f934(a922,a922),a1),a333),f335(f243(a1),f2(a1)))),x97712))) % 186.01/186.03 [7826]~P94(x78261)+~P67(x78261)+E(f335(f335(f299(x78261),x78262),f335(f110(x78261),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))),x78262) % 186.01/186.03 [9463]~P94(x94631)+~E(f335(f110(x94631),x94632),f84(x94631))+P29(x94631,f335(f110(x94631),f335(f335(f86(a1),x94632),f335(f85(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.03 [9645]~P139(x96451)+~E(x96452,f84(x96451))+E(f335(f335(f252(x96451),x96452),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(x96451)) % 186.01/186.03 [9646]~P139(x96461)+~E(x96462,f2(x96461))+E(f335(f335(f252(x96461),x96462),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f2(x96461)) % 186.01/186.03 [9661]~P139(x96611)+~E(x96612,f335(f85(x96611),f84(x96611)))+E(f335(f335(f252(x96611),x96612),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(x96611)) % 186.01/186.03 [9704]~P94(x97041)+E(f335(f110(x97041),x97042),f84(x97041))+~P29(x97041,f335(f110(x97041),f335(f335(f86(a1),x97042),f335(f85(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.03 [10089]~P113(x100892)+E(x100891,f2(x100892))+P1(f335(f335(f244(x100892),f2(x100892)),f335(f335(f252(x100892),x100891),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.03 [10147]~P113(x101472)+~E(x101471,f2(x101472))+~P1(f335(f335(f244(x101472),f2(x101472)),f335(f335(f252(x101472),x101471),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.03 [10184]P1(f335(f335(f243(a1),x101841),f2(a1)))+P1(f335(f335(f244(a1),x101842),x101841))+E(f335(f49(x101841),f53(x101842,f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101841))),f53(x101842,x101841)) % 186.01/186.03 [10185]~P1(f335(f335(f244(a1),f2(a1)),x101851))+P1(f335(f335(f244(a1),x101852),x101851))+E(f335(f49(x101851),f53(x101852,f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101851))),f53(x101852,x101851)) % 186.01/186.03 [10186]P1(f335(f335(f243(a1),x101861),f2(a1)))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),x101862),x101861)))+E(f335(f49(x101861),f56(x101862,f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101861))),f56(x101862,x101861)) % 186.01/186.03 [10187]~P1(f335(f335(f244(a1),f2(a1)),x101871))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),x101872),x101871)))+E(f335(f49(x101871),f56(x101872,f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101871))),f56(x101872,x101871)) % 186.01/186.03 [10188]~P146(x101881)+~P1(f335(f335(f243(a1),f2(a1)),x101882))+E(f335(f107(x101881),f335(a111,f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x101882))),f335(f335(f86(x101881),f335(f107(x101881),f335(a111,x101882))),f335(f107(x101881),f335(a111,x101882)))) % 186.01/186.03 [5287]~P147(x52871,x52873,x52872)+~E(x52873,f2(a1))+P1(f335(x52871,x52872)) % 186.01/186.03 [5411]~P109(x54111)+~P14(x54111,x54113)+P14(x54111,f177(x54111,x54112,x54113)) % 186.01/186.03 [5412]~P109(x54121)+~P14(x54121,x54123)+P14(x54121,f184(x54121,x54122,x54123)) % 186.01/186.03 [4980]~P4(x49802)+~E(x49803,f335(f85(x49802),x49801))+E(x49801,f335(f85(x49802),x49803)) % 186.01/186.03 [4982]~P4(x49821)+~E(f335(f85(x49821),x49823),x49822)+E(f335(f85(x49821),x49822),x49823) % 186.01/186.03 [5061]~P83(x50613)+E(x50611,x50612)+~E(f335(f85(x50613),x50611),f335(f85(x50613),x50612)) % 186.01/186.03 [5062]~P4(x50623)+E(x50621,x50622)+~E(f335(f85(x50623),x50621),f335(f85(x50623),x50622)) % 186.01/186.03 [5063]~P109(x50633)+E(x50631,x50632)+~E(f335(f290(x50633),x50631),f335(f290(x50633),x50632)) % 186.01/186.03 [5064]~P104(x50643)+E(x50641,x50642)+~E(f335(f107(x50643),x50641),f335(f107(x50643),x50642)) % 186.01/186.03 [5065]~P93(x50653)+E(x50651,x50652)+~E(f335(f109(x50653),x50651),f335(f109(x50653),x50652)) % 186.01/186.03 [5066]~P109(x50663)+E(x50661,x50662)+~E(f335(f312(x50663),x50661),f335(f312(x50663),x50662)) % 186.01/186.03 [5067]~P109(x50673)+E(x50671,x50672)+~E(f335(f291(x50673),x50671),f335(f291(x50673),x50672)) % 186.01/186.03 [5068]~P109(x50683)+E(x50681,x50682)+~E(f335(f309(x50683),x50681),f335(f309(x50683),x50682)) % 186.01/186.03 [5170]~P65(x51701)+~P1(f335(x51702,x51703))+P1(f335(f62(x51701),x51702)) % 186.01/186.03 [5206]~P65(x52063)+P1(f335(x52061,x52062))+~P1(f335(f63(x52063),x52061)) % 186.01/186.03 [5307]~P148(x53071,x53072,x53073)+~E(x53072,f2(a1))+P1(f335(x53071,f2(a1))) % 186.01/186.03 [5347]~E(x53471,f2(a927))+E(f400(x53471,x53472,x53473),f195(f934(x53473,a922)))+~E(f335(f41(x53473),x53472),f335(a119,x53471)) % 186.01/186.03 [5495]~E(x54952,f2(a927))+E(f335(f259(a927,a927),x54951),f2(a927))+~P1(f335(f54(x54953,x54952),x54951)) % 186.01/186.03 [5538]P1(f335(x55381,x55382))+~E(x55383,f335(f107(a1),x55382))+~P1(f335(x55381,f335(a111,x55383))) % 186.01/186.03 [6016]~E(x60163,f2(a927))+~P1(f335(x60161,x60162))+P1(f335(x60161,f51(a927,x60162,x60163))) % 186.01/186.03 [6246]~P105(x62462)+~P105(x62461)+E(f138(x62461,x62462,f139(x62461,x62463),f139(x62462,x62463)),f139(f933(x62461,x62462),x62463)) % 186.01/186.03 [6427]~E(x64273,f2(a927))+P1(f335(x64271,x64272))+~P1(f335(x64271,f51(a927,x64272,x64273))) % 186.01/186.03 [6913]E(x69131,f195(f934(x69132,a922)))+~P1(f335(f67(x69132),x69131))+P1(f335(f68(x69132,x69133,x69131),f870(x69133,x69131,x69132))) % 186.01/186.03 [7101]E(x71011,f2(a927))+~P1(f335(x71012,f468(x71011,x71013,x71012)))+P1(f335(x71012,f51(a927,x71013,x71011))) % 186.01/186.03 [7209]~P6(x72091)+~P1(f335(f335(f243(x72091),x72092),f892(x72093,x72092,x72091)))+P1(f335(f335(f243(x72091),x72092),f44(x72091,x72093))) % 186.01/186.03 [7211]~P1(f335(x72111,x72112))+~P1(f335(x72111,f468(x72113,x72112,x72111)))+P1(f335(x72111,f51(a927,x72112,x72113))) % 186.01/186.03 [7312]E(x73121,f120(x73122))+E(f335(f335(f158(x73122),f713(x73123,x73121,x73122)),f716(x73123,x73121,x73122)),x73121)+~P1(f335(f335(f337(f928(x73122)),x73121),f168(x73122,x73123))) % 186.01/186.03 [7343]~P140(x73431)+~P1(f335(f335(f337(x73431),x73432),f116(x73431)))+P1(f335(f335(f337(x73431),f335(f335(f252(x73431),x73432),x73433)),f116(x73431))) % 186.01/186.03 [7666]P38(x76661,x76662)+~P1(f335(f335(f337(x76661),x76663),f913(x76662,x76661)))+P1(f335(f335(f337(x76661),f344(x76662,x76661,x76663)),f913(x76662,x76661))) % 186.01/186.03 [7929]E(x79291,f120(x79292))+~P1(f335(f335(f337(f928(x79292)),x79291),f168(x79292,x79293)))+P1(f335(f335(f337(f928(x79292)),f716(x79293,x79291,x79292)),f168(x79292,x79293))) % 186.01/186.03 [7981]E(x79811,f2(a927))+E(f335(f335(f86(a927),f335(f335(f87(a927),x79811),f469(x79811,x79812,x79813))),f468(x79811,x79812,x79813)),x79812)+P1(f335(x79813,f51(a927,x79812,x79811))) % 186.01/186.03 [8022]~P1(f335(x80223,x80222))+E(f335(f335(f86(a927),f335(f335(f87(a927),x80221),f469(x80221,x80222,x80223))),f468(x80221,x80222,x80223)),x80222)+P1(f335(x80223,f51(a927,x80222,x80221))) % 186.01/186.03 [8159]P1(f335(f335(f244(a1),x81591),f471(x81592,x81593,x81591)))+P1(f335(f335(x81593,f335(f335(f42(a1),x81592),x81591)),f51(a1,x81592,x81591)))+~P1(f335(f335(f244(a1),x81591),f2(a1))) % 186.01/186.03 [8423]P1(f335(f335(x84232,f335(f335(f42(a1),x84231),x84233)),f51(a1,x84231,x84233)))+~P1(f335(f335(f244(a1),x84233),f2(a1)))+P1(f335(f335(f243(a1),f471(x84231,x84232,x84233)),f2(a1))) % 186.01/186.03 [8608]E(f335(f335(f86(a1),f335(f335(f87(a1),x86081),f472(x86082,x86083,x86081))),f471(x86082,x86083,x86081)),x86082)+P1(f335(f335(x86083,f335(f335(f42(a1),x86082),x86081)),f51(a1,x86082,x86081)))+~P1(f335(f335(f244(a1),x86081),f2(a1))) % 186.01/186.03 [8845]~P1(f335(f335(x88451,f472(x88452,x88451,x88453)),f471(x88452,x88451,x88453)))+P1(f335(f335(x88451,f335(f335(f42(a1),x88452),x88453)),f51(a1,x88452,x88453)))+~P1(f335(f335(f244(a1),x88453),f2(a1))) % 186.01/186.03 [9095]~P109(x90951)+~P14(x90951,x90953)+P14(x90951,f156(x90951,x90951,f5(x90951),x90952,x90953)) % 186.01/186.03 [9593]~P127(x95932)+E(x95931,f2(x95932))+~P1(f335(f335(f243(x95932),f335(f335(f86(x95932),f335(f335(f87(x95932),x95933),x95933)),f335(f335(f87(x95932),x95931),x95931))),f2(x95932))) % 186.01/186.03 [9594]~P127(x95942)+E(x95941,f2(x95942))+~P1(f335(f335(f243(x95942),f335(f335(f86(x95942),f335(f335(f87(x95942),x95941),x95941)),f335(f335(f87(x95942),x95943),x95943))),f2(x95942))) % 186.01/186.03 [10402]~P113(x104021)+~P1(f335(f335(f244(x104021),x104022),f2(x104021)))+P1(f335(f335(f244(x104021),f335(f335(f252(x104021),x104022),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x104023)))),f2(x104021))) % 186.01/186.03 [10412]~P113(x104122)+E(x104121,f2(x104122))+~P1(f335(f335(f243(x104122),f335(f335(f86(x104122),f335(f335(f252(x104122),x104123),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x104122),x104121),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f2(x104122))) % 186.01/186.03 [10413]~P113(x104132)+E(x104131,f2(x104132))+~P1(f335(f335(f243(x104132),f335(f335(f86(x104132),f335(f335(f252(x104132),x104131),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x104132),x104133),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f2(x104132))) % 186.01/186.03 [5016]~E(x50162,x50163)+~P4(x50161)+E(f335(f335(f23(x50161),x50162),x50163),f2(x50161)) % 186.01/186.03 [5017]~E(x50172,x50173)+~P5(x50171)+E(f335(f335(f23(x50171),x50172),x50173),f2(x50171)) % 186.01/186.03 [5030]~P143(x50301)+~E(x50303,f2(x50301))+E(f335(f335(f86(x50301),x50302),x50303),x50302) % 186.01/186.03 [5047]~P142(x50471)+~E(x50473,f2(x50471))+E(f335(f335(f87(x50471),x50472),x50473),f2(x50471)) % 186.01/186.03 [5048]~P142(x50481)+~E(x50482,f2(x50481))+E(f335(f335(f87(x50481),x50482),x50483),f2(x50481)) % 186.01/186.03 [5070]~E(x50703,f120(x50701))+~E(x50702,f120(x50701))+E(f335(f335(f141(x50701),x50702),x50703),f120(x50701)) % 186.01/186.03 [5160]~P143(x51602)+E(x51601,f2(x51602))+~E(f335(f335(f86(x51602),x51603),x51601),x51603) % 186.01/186.03 [5161]~P4(x51611)+~E(x51612,f335(f85(x51611),x51613))+E(f335(f335(f86(x51611),x51612),x51613),f2(x51611)) % 186.01/186.03 [5168]E(x51681,f120(x51682))+E(x51683,f2(a927))+~E(f335(f335(f182(x51682),x51683),x51681),f120(x51682)) % 186.01/186.03 [5174]~P4(x51743)+E(x51741,x51742)+~E(f335(f335(f23(x51743),x51741),x51742),f2(x51743)) % 186.01/186.03 [5175]~P5(x51753)+E(x51751,x51752)+~E(f335(f335(f23(x51753),x51751),x51752),f2(x51753)) % 186.01/186.03 [5188]~P139(x51882)+E(x51881,f2(x51882))+~E(f335(f335(f252(x51882),x51881),x51883),f2(x51882)) % 186.01/186.03 [5189]~P99(x51892)+E(x51891,f195(x51892))+~E(f335(f335(f117(x51892),x51893),x51891),f195(x51892)) % 186.01/186.03 [5190]~P99(x51902)+E(x51901,f195(x51902))+~E(f335(f335(f117(x51902),x51901),x51903),f195(x51902)) % 186.01/186.03 [5191]~P101(x51912)+E(x51911,f250(x51912))+~E(f335(f335(f108(x51912),x51913),x51911),f250(x51912)) % 186.01/186.03 [5192]~P101(x51922)+E(x51921,f250(x51922))+~E(f335(f335(f108(x51922),x51921),x51923),f250(x51922)) % 186.01/186.03 [5261]~P4(x52612)+E(x52611,f335(f85(x52612),x52613))+~E(f335(f335(f86(x52612),x52611),x52613),f2(x52612)) % 186.01/186.03 [5262]~P4(x52621)+E(f335(f85(x52621),x52622),x52623)+~E(f335(f335(f86(x52621),x52622),x52623),f2(x52621)) % 186.01/186.03 [5264]~E(x52642,x52643)+~P107(x52641)+P1(f335(f335(f243(x52641),x52642),x52643)) % 186.01/186.03 [5266]~E(x52662,x52663)+~P110(x52661)+P1(f335(f335(f243(x52661),x52662),x52663)) % 186.01/186.03 [5364]~P114(x53641)+~E(x53642,f335(f85(x53641),x53643))+E(f335(f335(f87(x53641),x53642),x53642),f335(f335(f87(x53641),x53643),x53643)) % 186.01/186.03 [5372]~P109(x53721)+~P14(x53721,x53723)+P14(x53721,f335(f335(f182(x53721),x53722),x53723)) % 186.01/186.03 [5373]~P109(x53731)+~P14(x53731,x53733)+P14(x53731,f335(f335(f145(x53731),x53732),x53733)) % 186.01/186.03 [5409]E(x54091,x54092)+E(x54093,f2(a927))+~E(f335(f335(f87(a927),x54093),x54091),f335(f335(f87(a927),x54093),x54092)) % 186.01/186.03 [5410]E(x54101,x54102)+E(x54103,f2(a927))+~E(f335(f335(f87(a927),x54101),x54103),f335(f335(f87(a927),x54102),x54103)) % 186.01/186.03 [5488]~E(x54882,x54883)+~P110(x54881)+E(f311(x54881,x54882,x54883),f335(f335(f317(x54881),x54882),f195(f934(x54881,a922)))) % 186.01/186.03 [5536]~E(x55361,x55362)+~P109(x55363)+~P1(f335(f335(f244(x55363),x55361),x55362)) % 186.01/186.03 [5537]~E(x55371,x55372)+~P110(x55373)+~P1(f335(f335(f244(x55373),x55371),x55372)) % 186.01/186.03 [5549]~P110(x55491)+E(f335(f310(x55491,x55492),x55493),f195(f934(x55491,a922)))+P1(f335(f335(f244(x55491),x55492),x55493)) % 186.01/186.03 [5597]~P110(x55971)+E(f313(x55971,x55972,x55973),f195(f934(x55971,a922)))+P1(f335(f335(f244(x55971),x55972),x55973)) % 186.01/186.03 [5598]~P110(x55981)+E(f311(x55981,x55982,x55983),f195(f934(x55981,a922)))+P1(f335(f335(f243(x55981),x55982),x55983)) % 186.01/186.03 [5599]~P110(x55991)+E(f195(f934(x55991,a922)),f313(x55991,x55992,x55993))+P1(f335(f335(f244(x55991),x55992),x55993)) % 186.01/186.03 [5600]~P110(x56001)+E(f195(f934(x56001,a922)),f311(x56001,x56002,x56003))+P1(f335(f335(f243(x56001),x56002),x56003)) % 186.01/186.03 [5607]~P97(x56071)+~E(f335(f335(f108(x56071),x56072),x56073),x56072)+P1(f335(f335(f243(x56071),x56072),x56073)) % 186.01/186.03 [5608]~P103(x56081)+~E(f335(f335(f117(x56081),x56082),x56083),x56083)+P1(f335(f335(f243(x56081),x56082),x56083)) % 186.01/186.03 [5609]~P109(x56091)+~E(f335(f335(f241(x56091),x56092),x56093),x56092)+P1(f335(f335(f243(x56091),x56092),x56093)) % 186.01/186.03 [5610]~P109(x56101)+~E(f335(f335(f242(x56101),x56102),x56103),x56103)+P1(f335(f335(f243(x56101),x56102),x56103)) % 186.01/186.03 [5629]~P109(x56291)+P14(x56291,x56292)+~P14(x56291,f335(f335(f158(x56291),x56293),x56292)) % 186.01/186.03 [5630]~P109(x56301)+P14(x56301,x56302)+~P14(x56301,f335(f335(f141(x56301),x56303),x56302)) % 186.01/186.03 [5631]~P109(x56311)+P14(x56311,x56312)+~P14(x56311,f335(f335(f141(x56311),x56312),x56313)) % 186.01/186.03 [5697]~P109(x56971)+P1(f335(f335(f243(x56971),x56973),x56972))+P1(f335(f335(f243(x56971),x56972),x56973)) % 186.01/186.03 [5702]~P109(x57021)+P1(f335(f335(f244(x57021),x57023),x57022))+P1(f335(f335(f243(x57021),x57022),x57023)) % 186.01/186.03 [5740]~P97(x57401)+E(f335(f335(f108(x57401),x57402),x57403),x57403)+~P1(f335(f335(f243(x57401),x57403),x57402)) % 186.01/186.03 [5742]~P97(x57421)+E(f335(f335(f108(x57421),x57422),x57423),x57422)+~P1(f335(f335(f243(x57421),x57422),x57423)) % 186.01/186.03 [5743]~P103(x57431)+E(f335(f335(f117(x57431),x57432),x57433),x57432)+~P1(f335(f335(f243(x57431),x57433),x57432)) % 186.01/186.03 [5745]~P103(x57451)+E(f335(f335(f117(x57451),x57452),x57453),x57453)+~P1(f335(f335(f243(x57451),x57452),x57453)) % 186.01/186.03 [5746]~P109(x57461)+E(f335(f335(f241(x57461),x57462),x57463),x57463)+~P1(f335(f335(f243(x57461),x57463),x57462)) % 186.01/186.03 [5748]~P109(x57481)+E(f335(f335(f241(x57481),x57482),x57483),x57482)+~P1(f335(f335(f243(x57481),x57482),x57483)) % 186.01/186.03 [5749]~P109(x57491)+E(f335(f335(f242(x57491),x57492),x57493),x57492)+~P1(f335(f335(f243(x57491),x57493),x57492)) % 186.01/186.03 [5751]~P109(x57511)+E(f335(f335(f242(x57511),x57512),x57513),x57513)+~P1(f335(f335(f243(x57511),x57512),x57513)) % 186.01/186.03 [5758]~P121(x57582)+E(x57581,f2(x57582))+E(f335(f335(f299(x57582),f335(f85(x57582),x57583)),f335(f85(x57582),x57581)),f335(f335(f299(x57582),x57583),x57581)) % 186.01/186.03 [5809]~P110(x58091)+E(f335(f310(x58091,x58092),x58093),f195(f934(x58091,a922)))+~P1(f335(f335(f243(x58091),x58093),x58092)) % 186.01/186.03 [5841]~P110(x58411)+E(f314(x58411,x58412,x58413),f195(f934(x58411,a922)))+~P1(f335(f335(f243(x58411),x58413),x58412)) % 186.01/186.03 [5842]~P110(x58421)+E(f313(x58421,x58422,x58423),f195(f934(x58421,a922)))+~P1(f335(f335(f243(x58421),x58423),x58422)) % 186.01/186.03 [5843]~P110(x58431)+E(f311(x58431,x58432,x58433),f195(f934(x58431,a922)))+~P1(f335(f335(f244(x58431),x58433),x58432)) % 186.01/186.03 [5895]~E(f335(f335(f23(a927),x58951),x58953),x58952)+E(x58951,f335(f335(f86(a927),x58952),x58953))+~P1(f335(f335(f243(a927),x58953),x58951)) % 186.01/186.03 [5896]~E(x58961,f335(f335(f86(a927),x58963),x58962))+E(f335(f335(f23(a927),x58961),x58962),x58963)+~P1(f335(f335(f243(a927),x58962),x58961)) % 186.01/186.03 [5941]~P1(f335(x59411,x59413))+P1(f335(x59411,f445(x59411,x59412)))+~P1(f335(f335(f244(a927),x59413),x59412)) % 186.01/186.03 [5942]~P1(f335(x59421,x59423))+P1(f335(x59421,f466(x59421,x59422)))+~P1(f335(f335(f243(a927),x59423),x59422)) % 186.01/186.03 [5950]~P110(x59501)+~E(f335(f310(x59501,x59502),x59503),f195(f934(x59501,a922)))+~P1(f335(f335(f244(x59501),x59502),x59503)) % 186.01/186.03 [5955]~P107(x59551)+~P1(f335(f335(f244(x59551),x59552),x59553))+P1(f335(f335(f243(x59551),x59552),x59553)) % 186.01/186.03 [5957]~P110(x59571)+~P1(f335(f335(f244(x59571),x59572),x59573))+P1(f335(f335(f243(x59571),x59572),x59573)) % 186.01/186.03 [6066]~P110(x60661)+~E(f313(x60661,x60662,x60663),f195(f934(x60661,a922)))+~P1(f335(f335(f244(x60661),x60662),x60663)) % 186.01/186.03 [6067]~P110(x60671)+~E(f311(x60671,x60672,x60673),f195(f934(x60671,a922)))+~P1(f335(f335(f243(x60671),x60672),x60673)) % 186.01/186.03 [6068]~P110(x60681)+~E(f195(f934(x60681,a922)),f313(x60681,x60682,x60683))+~P1(f335(f335(f244(x60681),x60682),x60683)) % 186.01/186.03 [6069]~P110(x60691)+~E(f195(f934(x60691,a922)),f311(x60691,x60692,x60693))+~P1(f335(f335(f243(x60691),x60692),x60693)) % 186.01/186.03 [6079]P1(f335(x60791,x60792))+~P1(f335(x60791,f452(x60791,x60793)))+~P1(f335(f335(f244(a927),x60792),x60793)) % 186.01/186.03 [6080]P1(f335(x60801,x60802))+~P1(f335(x60801,f497(x60801,x60803)))+~P1(f335(f335(f243(a927),x60802),x60803)) % 186.01/186.03 [6088]~E(x60881,f335(a119,x60883))+P1(f335(f335(f244(a927),x60881),f335(a119,x60882)))+~P1(f335(f335(f244(a927),x60883),x60882)) % 186.01/186.03 [6107]E(x61071,x61072)+~E(f335(f335(f87(a927),x61073),x61071),f335(f335(f87(a927),x61073),x61072))+~P1(f335(f335(f244(a927),f2(a927)),x61073)) % 186.01/186.03 [6163]E(f335(x61631,f401(x61631,x61632,x61633)),f84(a927))+~E(f335(f335(f6(x61633,a927),x61631),x61632),f84(a927))+~P1(f335(f67(x61633),x61632)) % 186.01/186.03 [6179]~P6(x61791)+P1(f335(f335(f243(x61791),x61792),f43(x61791,x61793)))+~P1(f335(f335(f337(x61791),x61792),x61793)) % 186.01/186.03 [6202]~P107(x62021)+~P1(f335(f335(f244(x62021),x62023),x62022))+~P1(f335(f335(f243(x62021),x62022),x62023)) % 186.01/186.03 [6206]~P107(x62061)+~P1(f335(f335(f244(x62061),x62063),x62062))+~P1(f335(f335(f244(x62061),x62062),x62063)) % 186.01/186.03 [6209]~P109(x62091)+~P1(f335(f335(f244(x62091),x62093),x62092))+~P1(f335(f335(f243(x62091),x62092),x62093)) % 186.01/186.03 [6210]~P109(x62101)+~P1(f335(f335(f244(x62101),x62103),x62102))+~P1(f335(f335(f244(x62101),x62102),x62103)) % 186.01/186.03 [6211]~P110(x62111)+~P1(f335(f335(f244(x62111),x62113),x62112))+~P1(f335(f335(f244(x62111),x62112),x62113)) % 186.01/186.03 [6231]~E(x62312,x62313)+~E(x62311,x62312)+E(f298(a927,f295(a927),x62311,x62312),f335(f335(f317(a927),x62313),f195(f934(a927,a922)))) % 186.01/186.03 [6238]~E(f335(x62382,f402(x62382,x62383,x62381)),f2(a927))+E(f335(f335(f6(x62381,a927),x62382),x62383),f2(a927))+~P1(f335(f67(x62381),x62383)) % 186.01/186.03 [6239]~E(f335(x62392,f467(x62392,x62393,x62391)),f84(a927))+E(f335(f335(f9(x62391,a927),x62392),x62393),f84(a927))+~P1(f335(f67(x62391),x62393)) % 186.01/186.03 [6255]~P108(x62551)+~P1(f335(f335(f244(x62551),x62553),x62552))+P1(f335(f335(f337(x62551),x62552),f335(f312(x62551),x62553))) % 186.01/186.03 [6256]~P108(x62561)+~P1(f335(f335(f243(x62561),x62563),x62562))+P1(f335(f335(f337(x62561),x62562),f335(f291(x62561),x62563))) % 186.01/186.03 [6257]~P108(x62571)+~P1(f335(f335(f244(x62571),x62572),x62573))+P1(f335(f335(f337(x62571),x62572),f335(f290(x62571),x62573))) % 186.01/186.03 [6258]~P108(x62581)+~P1(f335(f335(f243(x62581),x62582),x62583))+P1(f335(f335(f337(x62581),x62582),f335(f309(x62581),x62583))) % 186.01/186.03 [6270]E(f335(x62701,f404(x62701,x62702,x62703)),f335(a119,f2(a927)))+~E(f335(f335(f6(x62703,a927),x62701),x62702),f335(a119,f2(a927)))+~P1(f335(f67(x62703),x62702)) % 186.01/186.03 [6353]~P6(x63531)+~P1(f335(f335(f337(x63531),x63533),x63532))+P1(f335(f335(f243(x63531),f44(x63531,x63532)),x63533)) % 186.01/186.03 [6373]~P1(f335(f335(f243(a927),x63731),x63733))+P1(f335(f335(f243(a927),x63731),x63732))+~P1(f335(f335(f243(a927),x63733),x63732)) % 186.01/186.03 [6374]~P1(f335(f335(f243(a1),x63741),x63743))+P1(f335(f335(f243(a1),x63741),x63742))+~P1(f335(f335(f243(a1),x63743),x63742)) % 186.01/186.03 [6394]~P108(x63941)+~P1(f335(f335(f337(x63941),x63943),f335(f291(x63941),x63942)))+P1(f335(f335(f243(x63941),x63942),x63943)) % 186.01/186.03 [6395]~P108(x63951)+~P1(f335(f335(f337(x63951),x63952),f335(f309(x63951),x63953)))+P1(f335(f335(f243(x63951),x63952),x63953)) % 186.01/186.03 [6396]~P108(x63961)+~P1(f335(f335(f337(x63961),x63963),f335(f312(x63961),x63962)))+P1(f335(f335(f244(x63961),x63962),x63963)) % 186.01/186.03 [6397]~P108(x63971)+~P1(f335(f335(f337(x63971),x63972),f335(f290(x63971),x63973)))+P1(f335(f335(f244(x63971),x63972),x63973)) % 186.01/186.03 [6470]~P1(f335(x64701,x64702))+P1(f335(x64701,f804(x64701)))+~P1(f335(f335(f337(x64703),x64702),f250(f934(x64703,a922)))) % 186.01/186.03 [6610]~P68(x66101)+P1(f335(f335(f244(x66101),f2(x66101)),f545(x66103,x66102,x66101)))+P1(f335(f335(f243(x66101),x66102),x66103)) % 186.01/186.03 [6611]~P69(x66111)+P1(f335(f335(f244(x66111),f2(x66111)),f794(x66113,x66112,x66111)))+P1(f335(f335(f243(x66111),x66112),x66113)) % 186.01/186.03 [6679]~P79(x66791)+~P1(f335(f335(f243(x66791),x66793),f335(f85(x66791),x66792)))+P1(f335(f335(f243(x66791),x66792),f335(f85(x66791),x66793))) % 186.01/186.03 [6681]~P79(x66811)+~P1(f335(f335(f244(x66811),x66813),f335(f85(x66811),x66812)))+P1(f335(f335(f244(x66811),x66812),f335(f85(x66811),x66813))) % 186.01/186.03 [6693]~P1(f335(f335(f244(a927),x66931),x66933))+~P1(f335(f335(f244(a927),x66933),x66932))+P1(f335(f335(f244(a927),f335(a119,x66931)),x66932)) % 186.01/186.03 [6719]~P125(x67191)+P1(f335(f335(f243(x67191),f335(f107(x67191),x67192)),f335(f107(x67191),x67193)))+~P1(f335(f335(f243(a927),x67192),x67193)) % 186.01/186.03 [6720]~P113(x67201)+P1(f335(f335(f243(x67201),f335(f109(x67201),x67202)),f335(f109(x67201),x67203)))+~P1(f335(f335(f243(a1),x67202),x67203)) % 186.01/186.03 [6722]~P113(x67221)+P1(f335(f335(f244(x67221),f335(f109(x67221),x67222)),f335(f109(x67221),x67223)))+~P1(f335(f335(f244(a1),x67222),x67223)) % 186.01/186.03 [6723]~P125(x67231)+P1(f335(f335(f244(x67231),f335(f107(x67231),x67232)),f335(f107(x67231),x67233)))+~P1(f335(f335(f244(a927),x67232),x67233)) % 186.01/186.03 [6729]~P109(x67291)+E(f335(f335(f117(f934(x67291,a922)),f335(f290(x67291),x67292)),f335(f310(x67291,x67292),x67293)),f335(f290(x67291),x67293))+~P1(f335(f335(f243(x67291),x67292),x67293)) % 186.01/186.03 [6759]~P79(x67591)+~P1(f335(f335(f243(x67591),x67593),x67592))+P1(f335(f335(f243(x67591),f335(f85(x67591),x67592)),f335(f85(x67591),x67593))) % 186.01/186.03 [6761]~P83(x67611)+~P1(f335(f335(f243(x67611),x67613),x67612))+P1(f335(f335(f243(x67611),f335(f85(x67611),x67612)),f335(f85(x67611),x67613))) % 186.01/186.03 [6762]~P79(x67621)+~P1(f335(f335(f244(x67621),x67623),x67622))+P1(f335(f335(f244(x67621),f335(f85(x67621),x67622)),f335(f85(x67621),x67623))) % 186.01/186.03 [6797]~P109(x67971)+E(f335(f335(f117(f934(x67971,a922)),f335(f290(x67971),x67972)),f311(x67971,x67972,x67973)),f335(f309(x67971),x67973))+~P1(f335(f335(f243(x67971),x67972),x67973)) % 186.01/186.03 [6798]~P109(x67981)+E(f335(f335(f117(f934(x67981,a922)),f335(f309(x67981),x67982)),f314(x67981,x67982,x67983)),f335(f290(x67981),x67983))+~P1(f335(f335(f244(x67981),x67982),x67983)) % 186.01/186.03 [6799]~P109(x67991)+E(f335(f335(f117(f934(x67991,a922)),f335(f309(x67991),x67992)),f313(x67991,x67992,x67993)),f335(f309(x67991),x67993))+~P1(f335(f335(f243(x67991),x67992),x67993)) % 186.01/186.03 [6832]~P109(x68321)+E(f335(f335(f117(f934(x68321,a922)),f335(f310(x68321,x68322),x68323)),f335(f291(x68321),x68323)),f335(f291(x68321),x68322))+~P1(f335(f335(f243(x68321),x68322),x68323)) % 186.01/186.03 [6986]~P109(x69861)+E(f335(f335(f117(f934(x69861,a922)),f314(x69861,x69862,x69863)),f335(f291(x69861),x69863)),f335(f312(x69861),x69862))+~P1(f335(f335(f244(x69861),x69862),x69863)) % 186.01/186.03 [6987]~P109(x69871)+E(f335(f335(f117(f934(x69871,a922)),f313(x69871,x69872,x69873)),f335(f312(x69871),x69873)),f335(f312(x69871),x69872))+~P1(f335(f335(f243(x69871),x69872),x69873)) % 186.01/186.03 [6988]~P109(x69881)+E(f335(f335(f117(f934(x69881,a922)),f311(x69881,x69882,x69883)),f335(f312(x69881),x69883)),f335(f291(x69881),x69882))+~P1(f335(f335(f243(x69881),x69882),x69883)) % 186.01/186.03 [7007]P1(f335(x70071,x70072))+~P1(f335(f335(f243(a927),x70072),x70073))+P1(f335(f335(f337(a927),f497(x70071,x70073)),f311(a927,f2(a927),x70073))) % 186.01/186.03 [7041]E(x70411,x70412)+~E(f335(f335(f171(x70413),x70411),f630(x70413,x70412,x70411)),f335(f335(f171(x70413),x70412),f630(x70413,x70412,x70411)))+~E(f335(f196(f928(x70413)),x70411),f335(f196(f928(x70413)),x70412)) % 186.01/186.03 [7046]~E(x70463,f335(f335(f42(a927),x70461),x70462))+~P1(f335(f335(f244(a927),f2(a927)),x70462))+P1(f335(f335(f244(a927),x70461),f335(f335(f87(a927),x70462),f335(a119,x70463)))) % 186.01/186.03 [7062]~P1(f335(x70621,x70623))+~P1(f335(f335(f243(a927),x70623),x70622))+P1(f335(f335(f337(a927),f466(x70621,x70622)),f311(a927,f2(a927),x70622))) % 186.01/186.03 [7099]~P1(f335(x70991,x70993))+P1(f335(x70991,f498(x70991,x70992)))+~P1(f335(f335(f337(a927),x70993),f311(a927,f2(a927),x70992))) % 186.01/186.03 [7117]~P125(x71173)+~P1(f335(f335(f243(x71173),f335(f107(x71173),x71171)),f335(f107(x71173),x71172)))+P1(f335(f335(f243(a927),x71171),x71172)) % 186.01/186.03 [7118]~P113(x71183)+~P1(f335(f335(f243(x71183),f335(f109(x71183),x71181)),f335(f109(x71183),x71182)))+P1(f335(f335(f243(a1),x71181),x71182)) % 186.01/186.03 [7120]~P125(x71203)+~P1(f335(f335(f244(x71203),f335(f107(x71203),x71201)),f335(f107(x71203),x71202)))+P1(f335(f335(f244(a927),x71201),x71202)) % 186.01/186.03 [7121]~P113(x71213)+~P1(f335(f335(f244(x71213),f335(f109(x71213),x71211)),f335(f109(x71213),x71212)))+P1(f335(f335(f244(a1),x71211),x71212)) % 186.01/186.03 [7137]~P125(x71371)+~P1(f335(f335(f244(x71371),f84(x71371)),x71372))+P1(f335(f335(f244(x71371),f84(x71371)),f335(f335(f252(x71371),x71372),f335(a119,x71373)))) % 186.01/186.03 [7139]~P79(x71391)+~P1(f335(f335(f243(x71391),f335(f85(x71391),x71393)),f335(f85(x71391),x71392)))+P1(f335(f335(f243(x71391),x71392),x71393)) % 186.01/186.03 [7140]~P83(x71401)+~P1(f335(f335(f243(x71401),f335(f85(x71401),x71403)),f335(f85(x71401),x71402)))+P1(f335(f335(f243(x71401),x71402),x71403)) % 186.01/186.03 [7141]~P79(x71411)+~P1(f335(f335(f244(x71411),f335(f85(x71411),x71413)),f335(f85(x71411),x71412)))+P1(f335(f335(f244(x71411),x71412),x71413)) % 186.01/186.03 [7165]P1(f335(x71651,x71652))+~P1(f335(x71651,f499(x71651,x71653)))+~P1(f335(f335(f337(a927),x71652),f311(a927,f2(a927),x71653))) % 186.01/186.03 [7185]~P68(x71851)+P1(f335(f335(f244(x71851),f545(x71853,x71852,x71851)),f84(x71851)))+P1(f335(f335(f243(x71851),x71852),x71853)) % 186.01/186.03 [7206]~E(f51(a927,x72063,x72062),f51(a927,x72061,x72062))+E(f335(f335(f86(a927),x72061),f335(f335(f87(a927),x72062),f587(x72061,x72062,x72063))),x72063)+~P1(f335(f335(f243(a927),x72061),x72063)) % 186.01/186.03 [7260]E(f335(f335(f6(x72601,a927),x72602),x72603),f2(a927))+~P1(f335(f67(x72601),x72603))+P1(f335(f335(f337(x72601),f402(x72602,x72603,x72601)),x72603)) % 186.01/186.03 [7261]E(f335(f335(f9(x72611,a927),x72612),x72613),f84(a927))+~P1(f335(f67(x72611),x72613))+P1(f335(f335(f337(x72611),f467(x72612,x72613,x72611)),x72613)) % 186.01/186.03 [7283]~P109(x72831)+~P1(f335(f335(f243(x72831),x72832),x72833))+P1(f335(f335(f243(f934(x72831,a922)),f335(f290(x72831),x72832)),f335(f290(x72831),x72833))) % 186.01/186.03 [7284]~P109(x72841)+~P1(f335(f335(f243(x72841),x72843),x72842))+P1(f335(f335(f243(f934(x72841,a922)),f335(f312(x72841),x72842)),f335(f312(x72841),x72843))) % 186.01/186.03 [7285]~P110(x72851)+~P1(f335(f335(f243(x72851),x72853),x72852))+P1(f335(f335(f243(f934(x72851,a922)),f335(f291(x72851),x72852)),f335(f291(x72851),x72853))) % 186.01/186.03 [7286]~P110(x72861)+~P1(f335(f335(f243(x72861),x72862),x72863))+P1(f335(f335(f243(f934(x72861,a922)),f335(f309(x72861),x72862)),f335(f309(x72861),x72863))) % 186.01/186.03 [7287]~P109(x72871)+~P1(f335(f335(f244(x72871),x72872),x72873))+P1(f335(f335(f244(f934(x72871,a922)),f335(f290(x72871),x72872)),f335(f290(x72871),x72873))) % 186.01/186.03 [7298]~P6(x72981)+P1(f335(f335(f243(x72981),x72982),f44(x72981,x72983)))+P1(f335(f335(f337(x72981),f892(x72983,x72982,x72981)),x72983)) % 186.01/186.03 [7304]~P79(x73041)+P1(f335(f335(f243(x73041),f335(f335(f23(x73041),x73042),x73043)),f2(x73041)))+~P1(f335(f335(f243(x73041),x73042),x73043)) % 186.01/186.03 [7305]~P79(x73051)+P1(f335(f335(f244(x73051),f335(f335(f23(x73051),x73052),x73053)),f2(x73051)))+~P1(f335(f335(f244(x73051),x73052),x73053)) % 186.01/186.03 [7347]P1(f335(x73471,x73472))+P1(f335(f335(f243(a927),f499(x73471,x73473)),x73473))+~P1(f335(f335(f337(a927),x73472),f311(a927,f2(a927),x73473))) % 186.01/186.03 [7387]~E(f335(f335(f6(x73871,a927),x73872),x73873),f84(a927))+~P1(f335(f67(x73871),x73873))+P1(f335(f335(f337(x73871),f401(x73872,x73873,x73871)),x73873)) % 186.01/186.03 [7388]~P1(f335(x73881,x73883))+P1(f335(f335(f243(a927),f498(x73881,x73882)),x73882))+~P1(f335(f335(f337(a927),x73883),f311(a927,f2(a927),x73882))) % 186.01/186.03 [7427]~P6(x74271)+P1(f335(f335(f337(x74271),f582(x74273,x74272,x74271)),x74272))+P1(f335(f335(f243(x74271),f43(x74271,x74272)),x74273)) % 186.01/186.03 [7461]~E(f335(f335(f6(x74611,a927),x74612),x74613),f335(a119,f2(a927)))+~P1(f335(f67(x74611),x74613))+P1(f335(f335(f337(x74611),f404(x74612,x74613,x74611)),x74613)) % 186.01/186.03 [7472]E(x74721,f2(a927))+P1(f335(x74722,f51(a927,x74723,x74721)))+P1(f335(f335(f244(a927),f468(x74721,x74723,x74722)),x74721)) % 186.01/186.03 [7586]~P1(f335(x75861,x75862))+P1(f335(x75861,f51(a927,x75862,x75863)))+P1(f335(f335(f244(a927),f468(x75863,x75862,x75861)),x75863)) % 186.01/186.03 [7698]E(x76981,f120(x76982))+~P1(f335(f335(f337(f928(x76982)),x76981),f168(x76982,x76983)))+P1(f335(f335(f337(x76982),f713(x76983,x76981,x76982)),x76983)) % 186.01/186.03 [7720]~P109(x77201)+E(f335(f335(f117(f934(x77201,a922)),f335(f335(f317(x77201),x77202),f195(f934(x77201,a922)))),f314(x77201,x77202,x77203)),f335(f310(x77201,x77202),x77203))+~P1(f335(f335(f244(x77201),x77202),x77203)) % 186.01/186.03 [7742]~P109(x77421)+E(f335(f335(f117(f934(x77421,a922)),f335(f335(f317(x77421),x77422),f195(f934(x77421,a922)))),f313(x77421,x77422,x77423)),f311(x77421,x77422,x77423))+~P1(f335(f335(f243(x77421),x77422),x77423)) % 186.01/186.03 [7848]~P109(x78481)+P1(f335(f335(f243(x78481),x78482),x78483))+~P1(f335(f335(f243(f934(x78481,a922)),f335(f312(x78481),x78483)),f335(f312(x78481),x78482))) % 186.01/186.03 [7849]~P110(x78491)+P1(f335(f335(f243(x78491),x78492),x78493))+~P1(f335(f335(f243(f934(x78491,a922)),f335(f291(x78491),x78493)),f335(f291(x78491),x78492))) % 186.01/186.03 [7850]~P109(x78501)+P1(f335(f335(f243(x78501),x78502),x78503))+~P1(f335(f335(f243(f934(x78501,a922)),f335(f290(x78501),x78502)),f335(f290(x78501),x78503))) % 186.01/186.03 [7851]~P110(x78511)+P1(f335(f335(f243(x78511),x78512),x78513))+~P1(f335(f335(f243(f934(x78511,a922)),f335(f309(x78511),x78512)),f335(f309(x78511),x78513))) % 186.01/186.03 [7852]~P109(x78521)+P1(f335(f335(f244(x78521),x78522),x78523))+~P1(f335(f335(f244(f934(x78521,a922)),f335(f290(x78521),x78522)),f335(f290(x78521),x78523))) % 186.01/186.03 [7875]~P79(x78751)+~P1(f335(f335(f243(x78751),f335(f335(f23(x78751),x78752),x78753)),f2(x78751)))+P1(f335(f335(f243(x78751),x78752),x78753)) % 186.01/186.03 [7876]~P79(x78761)+~P1(f335(f335(f244(x78761),f335(f335(f23(x78761),x78762),x78763)),f2(x78761)))+P1(f335(f335(f244(x78761),x78762),x78763)) % 186.01/186.03 [8029]E(x80291,f2(a927))+~E(f335(f149(a927,a927,f86(a927),x80292),x80293),f2(a927))+~P1(f335(f335(f337(a927),x80291),f335(f179(a927),x80293))) % 186.01/186.03 [8033]~P6(x80331)+~P1(f335(f335(f243(x80331),f582(x80333,x80332,x80331)),x80333))+P1(f335(f335(f243(x80331),f43(x80331,x80332)),x80333)) % 186.01/186.03 [8185]P1(f335(f335(f243(a1),f2(a1)),f473(x81851,x81852,x81853)))+P1(f335(f335(x81852,f335(f335(f42(a1),x81851),x81853)),f51(a1,x81851,x81853)))+~P1(f335(f335(f244(a1),f2(a1)),x81853)) % 186.01/186.03 [8273]E(x82731,x82732)+~E(f335(f196(f928(x82733)),x82731),f335(f196(f928(x82733)),x82732))+~P1(f335(f335(f265(x82733,x82733,a922),a332),f687(x82733,x82731,x82732))) % 186.01/186.03 [8341]~P38(x83412,x83413)+E(x83411,f195(f934(x83412,a922)))+~P1(f335(f335(f243(f934(x83412,a922)),x83411),f335(f293(x83412,x83412,x83413),x83411))) % 186.01/186.03 [8370]~P69(x83701)+~P1(f335(f335(f243(x83701),x83702),f335(f335(f86(x83701),x83703),f794(x83703,x83702,x83701))))+P1(f335(f335(f243(x83701),x83702),x83703)) % 186.01/186.03 [8405]P54(x84051,x84052,x84053)+P1(f335(f335(f337(x84051),f568(x84053,x84052,x84051)),x84052))+P1(f335(f335(f337(f933(x84051,x84051)),f569(x84053,x84052,x84051)),x84053)) % 186.01/186.03 [8426]P1(f335(f335(x84262,f335(f335(f42(a1),x84261),x84263)),f51(a1,x84261,x84263)))+~P1(f335(f335(f244(a1),f2(a1)),x84263))+P1(f335(f335(f244(a1),f473(x84261,x84262,x84263)),x84263)) % 186.01/186.03 [8450]E(f335(f318(a927,a927,f335(f335(f7(a927,a927,a927),f23(a927)),x84501)),f335(f310(a927,x84502),x84503)),f195(f934(a927,a922)))+P1(f335(f335(f244(a927),x84501),x84503))+P1(f335(f335(f244(a927),x84502),x84503)) % 186.01/186.03 [8562]E(f335(f318(a927,a927,f335(f335(f7(a927,a927,a927),f23(a927)),x85621)),f335(f310(a927,x85622),x85623)),f335(f335(f317(a927),f2(a927)),f195(f934(a927,a922))))+P1(f335(f335(f244(a927),x85621),x85623))+~P1(f335(f335(f244(a927),x85622),x85623)) % 186.01/186.03 [8576]~P109(x85761)+E(f156(x85761,x85761,f5(x85761),x85762,x85763),x85763)+~P1(f335(f335(f337(x85761),x85762),f335(f179(x85761),x85763))) % 186.01/186.03 [8589]P26(x85891,x85891,x85892,x85893)+~P1(f335(f67(x85891),x85893))+~P1(f335(f335(f243(f934(x85891,a922)),x85893),f335(f318(x85891,x85891,x85892),x85893))) % 186.01/186.03 [8615]E(f335(f335(f86(a1),f335(f335(f87(a1),x86151),f474(x86152,x86153,x86151))),f473(x86152,x86153,x86151)),x86152)+P1(f335(f335(x86153,f335(f335(f42(a1),x86152),x86151)),f51(a1,x86152,x86151)))+~P1(f335(f335(f244(a1),f2(a1)),x86151)) % 186.01/186.03 [8852]~P1(f335(f335(x88521,f474(x88522,x88521,x88523)),f473(x88522,x88521,x88523)))+P1(f335(f335(x88521,f335(f335(f42(a1),x88522),x88523)),f51(a1,x88522,x88523)))+~P1(f335(f335(f244(a1),f2(a1)),x88523)) % 186.01/186.03 [9735]~P1(f335(f67(x97351),x97352))+~P1(f335(f335(f337(x97351),x97353),x97352))+P1(f335(f335(f244(a927),f335(f41(x97351),f335(f335(f23(f934(x97351,a922)),x97352),f335(f335(f317(x97351),x97353),f195(f934(x97351,a922)))))),f335(f41(x97351),x97352))) % 186.01/186.03 [10344]P54(x103441,x103442,x103443)+~P1(f335(f335(f265(x103441,x103441,a922),f335(f335(f7(x103441,f934(x103441,a922),f934(x103441,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x103441,a922),f934(x103441,a922)),x103441),f8(a922,a922,x103441)),f335(f335(f8(a922,f934(a922,a922),x103441),a333),f335(f335(f7(x103441,f934(x103441,a922),a922),f337(x103441)),x103442)))),f335(f335(f7(x103441,f934(x103441,a922),a922),f337(x103441)),x103442))),f569(x103443,x103442,x103441)))+P1(f335(f335(f337(x103441),f568(x103443,x103442,x103441)),x103442)) % 186.01/186.03 [5719]~P121(x57192)+E(x57191,f2(x57192))+E(f335(f335(f299(x57192),x57193),f335(f85(x57192),x57191)),f335(f85(x57192),f335(f335(f299(x57192),x57193),x57191))) % 186.01/186.03 [5857]~E(x58573,f195(f934(x58571,a922)))+~E(x58572,f195(f934(x58571,a922)))+E(f335(f335(f117(f934(x58571,a922)),x58572),x58573),f195(f934(x58571,a922))) % 186.01/186.03 [5915]~E(x59153,f2(a927))+~P1(f335(x59151,f2(a927)))+P1(f335(x59151,f335(f335(f42(a927),x59152),x59153))) % 186.01/186.03 [6058]~P69(x60582)+E(x60581,f2(x60582))+E(f335(f335(f299(x60582),f335(f81(x60582),x60583)),f335(f81(x60582),x60581)),f335(f81(x60582),f335(f335(f299(x60582),x60583),x60581))) % 186.01/186.03 [6227]~P1(f335(f67(x62271),x62273))+E(f335(f41(x62271),f335(f335(f317(x62271),x62272),x62273)),f335(a119,f335(f41(x62271),x62273)))+P1(f335(f335(f337(x62271),x62272),x62273)) % 186.01/186.03 [6302]~E(x63022,f2(a927))+P1(f335(x63021,f2(a927)))+~P1(f335(x63021,f335(f335(f42(a927),x63023),x63022))) % 186.01/186.03 [6319]~P1(f335(f67(x63191),x63193))+E(f335(f41(x63191),f335(f335(f317(x63191),x63192),x63193)),f335(f41(x63191),x63193))+~P1(f335(f335(f337(x63191),x63192),x63193)) % 186.01/186.03 [6355]~P1(f335(f67(x63551),x63553))+E(f335(f41(x63551),f335(f335(f317(x63551),x63552),x63553)),f335(f335(f86(a927),f84(a927)),f335(f41(x63551),x63553)))+P1(f335(f335(f337(x63551),x63552),x63553)) % 186.01/186.03 [6471]E(f335(f335(f86(a927),x64711),f392(x64711,x64712,x64713)),x64712)+~P1(f335(x64713,f2(a927)))+P1(f335(x64713,f335(f335(f23(a927),x64712),x64711))) % 186.01/186.03 [6472]E(f335(f335(f86(a927),x64721),f393(x64721,x64722,x64723)),x64722)+~P1(f335(x64723,f2(a927)))+P1(f335(x64723,f335(f335(f23(a927),x64722),x64721))) % 186.01/186.03 [6518]~P6(x65181)+~P1(f335(f67(x65181),x65183))+E(f335(f335(f70(x65181,x65181,f108(x65181)),x65182),x65183),f335(f335(f108(x65181),x65182),f44(x65181,x65183))) % 186.01/186.03 [6519]~P6(x65191)+~P1(f335(f67(x65191),x65193))+E(f335(f335(f70(x65191,x65191,f117(x65191)),x65192),x65193),f335(f335(f117(x65191),x65192),f43(x65191,x65193))) % 186.01/186.03 [6525]~P94(x65251)+~E(f335(f110(x65251),x65252),f335(f110(x65251),x65253))+P29(x65251,f335(f110(x65251),f335(f335(f86(a1),x65252),f335(f85(a1),x65253)))) % 186.01/186.03 [6534]~P140(x65341)+E(f335(f335(f23(x65341),f335(f107(x65341),x65342)),f335(f107(x65341),x65343)),f335(f107(x65341),f335(f335(f23(a927),x65342),x65343)))+~P1(f335(f335(f243(a927),x65343),x65342)) % 186.01/186.03 [6621]E(f335(f335(f86(a927),x66211),f392(x66211,x66212,x66213)),x66212)+P1(f335(f335(f244(a927),x66212),x66211))+P1(f335(x66213,f335(f335(f23(a927),x66212),x66211))) % 186.01/186.03 [6622]E(f335(f335(f86(a927),x66221),f393(x66221,x66222,x66223)),x66222)+P1(f335(f335(f244(a927),x66222),x66221))+P1(f335(x66223,f335(f335(f23(a927),x66222),x66221))) % 186.01/186.03 [6637]~P113(x66371)+E(f335(f335(f87(x66371),f335(f81(x66371),x66372)),x66373),f335(f81(x66371),f335(f335(f87(x66371),x66372),x66373)))+~P1(f335(f335(f243(x66371),f2(x66371)),x66373)) % 186.01/186.03 [6638]~P68(x66381)+E(f335(f335(f299(x66381),f335(f81(x66381),x66382)),x66383),f335(f81(x66381),f335(f335(f299(x66381),x66382),x66383)))+~P1(f335(f335(f244(x66381),f2(x66381)),x66383)) % 186.01/186.03 [6646]~P98(x66461)+~P1(f335(f67(x66461),x66463))+E(f335(f335(f70(x66461,x66461,f117(x66461)),x66462),x66463),f13(x66461,f335(f335(f317(x66461),x66462),x66463))) % 186.01/186.03 [6647]~P98(x66471)+~P1(f335(f67(x66471),x66473))+E(f335(f335(f70(x66471,x66471,f108(x66471)),x66472),x66473),f10(x66471,f335(f335(f317(x66471),x66472),x66473))) % 186.01/186.03 [6648]~P109(x66481)+~P1(f335(f67(x66481),x66483))+E(f335(f335(f70(x66481,x66481,f242(x66481)),x66482),x66483),f14(x66481,f335(f335(f317(x66481),x66482),x66483))) % 186.01/186.03 [6649]~P109(x66491)+~P1(f335(f67(x66491),x66493))+E(f335(f335(f70(x66491,x66491,f241(x66491)),x66492),x66493),f15(x66491,f335(f335(f317(x66491),x66492),x66493))) % 186.01/186.03 [6695]E(x66951,f120(x66952))+~E(f186(x66952,x66953),f120(f928(x66952)))+~P1(f335(f335(f337(f928(x66952)),x66951),f335(f179(f928(x66952)),x66953))) % 186.01/186.03 [6737]~P1(f335(f144(x67371),x67373))+P1(f335(f335(f337(x67371),x67372),f335(f179(x67371),x67373)))+P1(f335(f144(x67371),f335(f335(f158(x67371),x67372),x67373))) % 186.01/186.03 [6748]~P96(x67481)+~P1(f335(f67(x67481),x67483))+E(f335(f69(x67481,f87(x67481)),f335(f335(f317(x67481),x67482),x67483)),f335(f335(f70(x67481,x67481,f87(x67481)),x67482),x67483)) % 186.01/186.03 [6770]~P109(x67701)+~P1(f335(f67(x67701),x67703))+E(f11(x67701,f242(x67701),f335(f335(f317(x67701),x67702),x67703)),f335(f335(f70(x67701,x67701,f242(x67701)),x67702),x67703)) % 186.01/186.03 [6771]~P109(x67711)+~P1(f335(f67(x67711),x67713))+E(f12(x67711,f241(x67711),f335(f335(f317(x67711),x67712),x67713)),f335(f335(f70(x67711,x67711,f241(x67711)),x67712),x67713)) % 186.01/186.03 [6773]P1(f335(x67731,f2(a927)))+~P1(f335(f335(f244(a927),x67732),x67733))+~P1(f335(x67731,f335(f335(f23(a927),x67732),x67733))) % 186.01/186.03 [6795]~P87(x67951)+P1(f335(f335(f243(x67951),x67952),x67953))+~P1(f335(f335(f243(x67951),f335(f81(x67951),x67952)),x67953)) % 186.01/186.03 [6796]~P113(x67961)+P1(f335(f335(f244(x67961),x67962),x67963))+~P1(f335(f335(f244(x67961),f335(f81(x67961),x67962)),x67963)) % 186.01/186.03 [6813]E(x68131,f120(x68132))+E(f335(f148(x68132),f335(f335(f145(x68132),x68133),x68131)),f335(f335(f171(x68132),x68131),x68133))+~P1(f335(f335(f244(a927),x68133),f335(f196(f928(x68132)),x68131))) % 186.01/186.03 [6865]~P1(f335(x68651,x68653))+P1(f335(x68651,f447(x68651,x68652)))+~P1(f335(f335(f337(a927),x68653),f335(f310(a927,f2(a927)),x68652))) % 186.01/186.03 [6885]P1(f335(x68851,x68852))+~P1(f335(f335(f244(a927),x68852),x68853))+P1(f335(f335(f337(a927),f452(x68851,x68853)),f335(f310(a927,f2(a927)),x68853))) % 186.01/186.03 [6900]~P125(x69001)+~P1(f335(f335(f243(x69001),f84(x69001)),x69002))+P1(f335(f335(f243(x69001),f84(x69001)),f335(f335(f252(x69001),x69002),x69003))) % 186.01/186.03 [6902]~P125(x69021)+~P1(f335(f335(f243(x69021),f2(x69021)),x69022))+P1(f335(f335(f243(x69021),f2(x69021)),f335(f335(f252(x69021),x69022),x69023))) % 186.01/186.03 [6904]~P125(x69041)+~P1(f335(f335(f244(x69041),f2(x69041)),x69042))+P1(f335(f335(f244(x69041),f2(x69041)),f335(f335(f252(x69041),x69042),x69043))) % 186.01/186.03 [6929]~P1(f335(x69291,x69293))+~P1(f335(f335(f244(a927),x69293),x69292))+P1(f335(f335(f337(a927),f445(x69291,x69292)),f335(f310(a927,f2(a927)),x69292))) % 186.01/186.03 [6937]P1(f335(f67(x69371),x69372))+~P1(f335(f67(x69371),x69373))+~P1(f335(f335(f243(f934(x69371,a922)),x69372),x69373)) % 186.01/186.03 [6944]P1(f335(x69441,x69442))+~P1(f335(x69441,f448(x69441,x69443)))+~P1(f335(f335(f337(a927),x69442),f335(f310(a927,f2(a927)),x69443))) % 186.01/186.03 [6957]E(x69571,f2(a927))+P1(f335(x69572,f454(x69571,x69573,x69572)))+~P1(f335(x69572,f335(f335(f42(a927),x69573),x69571))) % 186.01/186.03 [6964]~P127(x69642)+E(x69641,f2(x69642))+~E(f335(f335(f86(x69642),f335(f335(f87(x69642),x69643),x69643)),f335(f335(f87(x69642),x69641),x69641)),f2(x69642)) % 186.01/186.03 [6965]~P127(x69652)+E(x69651,f2(x69652))+~E(f335(f335(f86(x69652),f335(f335(f87(x69652),x69651),x69651)),f335(f335(f87(x69652),x69653),x69653)),f2(x69652)) % 186.01/186.03 [7008]E(x70081,f2(a927))+~P1(f335(x70082,f455(x70081,x70083,x70082)))+P1(f335(x70082,f335(f335(f42(a927),x70083),x70081))) % 186.01/186.03 [7013]~P109(x70131)+~P14(x70131,x70133)+P14(x70131,f335(f335(f155(x70131,x70131,f5(x70131)),x70132),x70133)) % 186.01/186.03 [7055]P1(f335(x70551,f454(x70552,x70553,x70551)))+P1(f335(x70551,f2(a927)))+~P1(f335(x70551,f335(f335(f42(a927),x70553),x70552))) % 186.01/186.03 [7061]~P94(x70611)+E(f335(f110(x70611),x70612),f335(f110(x70611),x70613))+~P29(x70611,f335(f110(x70611),f335(f335(f86(a1),x70612),f335(f85(a1),x70613)))) % 186.01/186.03 [7124]E(x71241,f2(a1))+E(x71242,f2(a1))+~P1(f335(f55(x71242,x71242),f335(f335(f260(a1,a1),x71243),x71241))) % 186.01/186.03 [7125]E(x71251,f84(a1))+E(x71252,f2(a1))+~P1(f335(f55(x71252,x71252),f335(f335(f260(a1,a1),x71251),x71253))) % 186.01/186.03 [7138]P1(f335(x71381,x71382))+P1(f335(f335(f244(a927),f448(x71381,x71383)),x71383))+~P1(f335(f335(f337(a927),x71382),f335(f310(a927,f2(a927)),x71383))) % 186.01/186.03 [7161]~P1(f335(x71611,f392(x71613,x71612,x71611)))+~P1(f335(x71611,f2(a927)))+P1(f335(x71611,f335(f335(f23(a927),x71612),x71613))) % 186.01/186.03 [7162]~P1(f335(x71621,f393(x71623,x71622,x71621)))+~P1(f335(x71621,f2(a927)))+P1(f335(x71621,f335(f335(f23(a927),x71622),x71623))) % 186.01/186.03 [7163]~P1(f335(x71631,f455(x71633,x71632,x71631)))+~P1(f335(x71631,f2(a927)))+P1(f335(x71631,f335(f335(f42(a927),x71632),x71633))) % 186.01/186.03 [7181]~P1(f335(x71811,x71813))+P1(f335(f335(f244(a927),f447(x71811,x71812)),x71812))+~P1(f335(f335(f337(a927),x71813),f335(f310(a927,f2(a927)),x71812))) % 186.01/186.03 [7182]E(f335(f335(f23(a927),f335(f335(f23(a927),x71821),x71822)),f335(f335(f23(a927),x71823),x71822)),f335(f335(f23(a927),x71821),x71823))+~P1(f335(f335(f243(a927),x71822),x71821))+~P1(f335(f335(f243(a927),x71822),x71823)) % 186.01/186.03 [7219]~P79(x72191)+~P1(f335(f335(f243(x72191),f335(f85(x72191),x72193)),x72192))+P1(f335(f335(f243(x72191),f335(f85(x72191),x72192)),x72193)) % 186.01/186.03 [7221]~P87(x72211)+~P1(f335(f335(f243(x72211),f335(f81(x72211),x72212)),x72213))+P1(f335(f335(f243(x72211),f335(f85(x72211),x72212)),x72213)) % 186.01/186.03 [7223]~P79(x72231)+~P1(f335(f335(f244(x72231),f335(f85(x72231),x72233)),x72232))+P1(f335(f335(f244(x72231),f335(f85(x72231),x72232)),x72233)) % 186.01/186.03 [7224]~P113(x72241)+~P1(f335(f335(f244(x72241),f335(f81(x72241),x72242)),x72243))+P1(f335(f335(f244(x72241),f335(f85(x72241),x72242)),x72243)) % 186.01/186.03 [7255]~P1(f335(x72553,f392(x72552,x72551,x72553)))+P1(f335(f335(f244(a927),x72551),x72552))+P1(f335(x72553,f335(f335(f23(a927),x72551),x72552))) % 186.01/186.03 [7256]~P1(f335(x72563,f393(x72562,x72561,x72563)))+P1(f335(f335(f244(a927),x72561),x72562))+P1(f335(x72563,f335(f335(f23(a927),x72561),x72562))) % 186.01/186.03 [7308]~E(f588(x73083,x73082,x73081),f589(x73083,x73082,x73081))+E(f335(f335(f108(f934(x73081,a922)),x73082),f43(f934(x73081,a922),x73083)),f195(f934(x73081,a922)))+P1(f335(f335(f337(f934(x73081,a922)),x73082),x73083)) % 186.01/186.03 [7316]~P1(f335(f67(x73161),x73163))+P1(f335(f67(x73161),f44(f934(x73161,a922),x73162)))+~P1(f335(f335(f337(f934(x73161,a922)),x73163),x73162)) % 186.01/186.03 [7376]~P109(x73761)+E(f335(f335(f117(f934(x73761,a922)),f335(f310(x73761,x73762),x73763)),f335(f335(f317(x73761),x73763),f195(f934(x73761,a922)))),f311(x73761,x73762,x73763))+~P1(f335(f335(f243(x73761),x73762),x73763)) % 186.01/186.03 [7377]E(x73771,f2(a927))+P1(f335(f335(f244(a927),f460(x73771,x73773,x73772)),x73771))+P1(f335(x73772,f335(f335(f42(a927),x73773),x73771))) % 186.01/186.03 [7406]P1(f335(f335(f244(a927),f335(f196(f928(x74061)),x74062)),f806(x74063,x74061)))+~P1(f335(f67(f928(x74061)),x74063))+~P1(f335(f335(f337(f928(x74061)),x74062),x74063)) % 186.01/186.03 [7412]E(x74121,x74122)+~P1(f335(f335(f243(f934(x74123,a922)),x74121),x74122))+P1(f335(f335(f244(f934(x74123,a922)),x74121),x74122)) % 186.01/186.03 [7424]E(x74241,x74242)+~E(f335(f196(f928(x74243)),x74241),f335(f196(f928(x74243)),x74242))+P1(f335(f335(f244(a927),f630(x74243,x74241,x74242)),f335(f196(f928(x74243)),x74242))) % 186.01/186.03 [7473]P9(x74731,x74732,x74733)+~E(f335(f272(x74731,x74731),x74733),x74732)+~E(f335(f335(f297(x74731,x74731,x74731),f335(f294(x74731,x74731),x74733)),x74733),x74733) % 186.01/186.03 [7555]~P1(f335(x75551,f2(a927)))+P1(f335(f335(f244(a927),f460(x75553,x75552,x75551)),x75553))+P1(f335(x75551,f335(f335(f42(a927),x75552),x75553))) % 186.01/186.03 [7565]~P109(x75651)+E(f335(f335(f117(f934(x75651,a922)),f314(x75651,x75652,x75653)),f335(f335(f317(x75651),x75653),f195(f934(x75651,a922)))),f313(x75651,x75652,x75653))+~P1(f335(f335(f244(x75651),x75652),x75653)) % 186.01/186.03 [7655]~P1(f335(f67(x76551),x76553))+P1(f335(f335(f243(a927),f335(f41(x76551),x76552)),f335(f41(x76551),x76553)))+~P1(f335(f335(f243(f934(x76551,a922)),x76552),x76553)) % 186.01/186.03 [7656]~P1(f335(f67(x76561),x76563))+P1(f335(f335(f244(a927),f335(f41(x76561),x76562)),f335(f41(x76561),x76563)))+~P1(f335(f335(f244(f934(x76561,a922)),x76562),x76563)) % 186.01/186.03 [7785]E(x77851,x77852)+~P1(f335(f335(f243(f934(x77853,a922)),x77852),x77851))+~P1(f335(f335(f243(f934(x77853,a922)),x77851),x77852)) % 186.01/186.03 [7788]~P109(x77881)+P14(x77881,x77882)+~P14(x77881,f335(f335(f155(x77881,x77881,f5(x77881)),x77883),x77882)) % 186.01/186.03 [7857]~P1(f335(f335(f244(a927),x78573),x78572))+~P1(f335(f335(f244(a927),x78573),x78571))+P1(f335(f335(f244(a927),f335(f335(f23(a927),x78571),x78572)),f335(f335(f23(a927),x78571),x78573))) % 186.01/186.03 [7858]~P1(f335(f335(f243(a927),x78582),x78581))+~P1(f335(f335(f244(a927),x78581),x78583))+P1(f335(f335(f244(a927),f335(f335(f23(a927),x78581),x78582)),f335(f335(f23(a927),x78583),x78582))) % 186.01/186.03 [7873]~P1(f335(f335(f244(a1),x78732),f2(a1)))+~P1(f335(f335(f243(a1),x78733),x78731))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x78731),x78732)),f335(f335(f42(a1),x78733),x78732))) % 186.01/186.03 [7890]~P1(f335(f335(f244(a927),f2(a927)),x78903))+~P1(f335(f335(f243(a927),x78903),x78902))+P1(f335(f335(f243(a927),f335(f335(f42(a927),x78901),x78902)),f335(f335(f42(a927),x78901),x78903))) % 186.01/186.03 [7891]~P1(f335(f335(f244(a1),f2(a1)),x78912))+~P1(f335(f335(f243(a1),x78911),x78913))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x78911),x78912)),f335(f335(f42(a1),x78913),x78912))) % 186.01/186.03 [7895]~P1(f335(f335(f244(a927),f2(a927)),x78952))+~P1(f335(f335(f244(a927),x78951),x78953))+P1(f335(f335(f244(a927),f335(f335(f87(a927),x78951),x78952)),f335(f335(f87(a927),x78953),x78952))) % 186.01/186.03 [7896]~P1(f335(f335(f244(a927),f2(a927)),x78961))+~P1(f335(f335(f244(a927),x78962),x78963))+P1(f335(f335(f244(a927),f335(f335(f87(a927),x78961),x78962)),f335(f335(f87(a927),x78961),x78963))) % 186.01/186.03 [7897]~P1(f335(f335(f244(a1),f2(a1)),x78971))+~P1(f335(f335(f244(a1),x78972),x78973))+P1(f335(f335(f244(a1),f335(f335(f87(a1),x78971),x78972)),f335(f335(f87(a1),x78971),x78973))) % 186.01/186.03 [7944]E(x79441,f2(a927))+E(f335(f335(f86(a927),f335(f335(f87(a927),x79441),f455(x79441,x79442,x79443))),f460(x79441,x79442,x79443)),x79442)+P1(f335(x79443,f335(f335(f42(a927),x79442),x79441))) % 186.01/186.03 [8003]E(f335(f335(f86(a927),f335(f335(f87(a927),x80031),f455(x80031,x80032,x80033))),f460(x80031,x80032,x80033)),x80032)+~P1(f335(x80033,f2(a927)))+P1(f335(x80033,f335(f335(f42(a927),x80032),x80031))) % 186.01/186.03 [8020]~P1(f335(f67(x80201),x80203))+P1(f335(f335(f337(x80201),f478(x80202,x80203,x80201)),x80203))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f9(x80201,a927),x80202),x80203))) % 186.01/186.03 [8021]~P1(f335(f67(x80211),x80213))+P1(f335(f335(f337(x80211),f557(x80212,x80213,x80211)),x80213))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f9(x80211,a927),x80212),x80213))) % 186.01/186.03 [8309]E(x83091,f195(f934(x83092,a922)))+E(x83091,f335(f335(f317(x83092),x83093),f195(f934(x83092,a922))))+~P1(f335(f335(f243(f934(x83092,a922)),x83091),f335(f335(f317(x83092),x83093),f195(f934(x83092,a922))))) % 186.01/186.03 [8342]~P1(f335(f335(f244(a927),f84(a927)),x83423))+P1(f335(f335(f243(a927),x83421),x83422))+~P1(f335(f335(f295(a927),f335(f335(f252(a927),x83423),x83421)),f335(f335(f252(a927),x83423),x83422))) % 186.01/186.03 [8344]~P1(f335(f335(f244(a927),f2(a927)),x83443))+P1(f335(f335(f243(a927),x83441),x83442))+~P1(f335(f335(f243(a927),f335(f335(f87(a927),x83443),x83441)),f335(f335(f87(a927),x83443),x83442))) % 186.01/186.03 [8345]~P1(f335(f335(f244(a927),f2(a927)),x83453))+P1(f335(f335(f243(a927),x83451),x83452))+~P1(f335(f335(f243(a927),f335(f335(f87(a927),x83451),x83453)),f335(f335(f87(a927),x83452),x83453))) % 186.01/186.03 [8347]~P1(f335(f335(f244(a927),f2(a927)),x83473))+P1(f335(f335(f244(a927),x83471),x83472))+~P1(f335(f335(f244(a927),f335(f335(f252(a927),x83473),x83471)),f335(f335(f252(a927),x83473),x83472))) % 186.01/186.03 [8386]~E(f335(f335(f108(f934(x83861,a922)),f589(x83863,x83862,x83861)),f588(x83863,x83862,x83861)),f195(f934(x83861,a922)))+E(f335(f335(f108(f934(x83861,a922)),x83862),f43(f934(x83861,a922),x83863)),f195(f934(x83861,a922)))+P1(f335(f335(f337(f934(x83861,a922)),x83862),x83863)) % 186.01/186.03 [8400]E(x84001,f120(x84002))+~E(f335(f149(f928(x84002),f928(x84002),f141(x84002),f120(x84002)),x84003),f120(x84002))+~P1(f335(f335(f337(f928(x84002)),x84001),f335(f179(f928(x84002)),x84003))) % 186.01/186.03 [8455]E(x84551,f195(f934(f934(x84552,a922),a922)))+P1(f335(f335(f337(f934(x84552,a922)),f904(x84553,x84551,x84552)),x84551))+P1(f335(f335(f243(f934(x84552,a922)),f44(f934(x84552,a922),x84551)),x84553)) % 186.01/186.03 [8462]~P72(x84621)+~P76(x84621)+E(f335(f335(f6(a1,x84621),f335(f335(f8(a927,x84621,a1),x84622),a111)),f335(f318(a927,a1,f107(a1)),x84623)),f335(f335(f6(a927,x84621),x84622),x84623)) % 186.01/186.03 [8463]~P72(x84631)+~P76(x84631)+E(f335(f335(f9(a1,x84631),f335(f335(f8(a927,x84631,a1),x84632),a111)),f335(f318(a927,a1,f107(a1)),x84633)),f335(f335(f9(a927,x84631),x84632),x84633)) % 186.01/186.03 [8506]~P1(f335(f67(x85061),x85063))+~P1(f335(f335(f244(a927),f2(a927)),f335(x85062,f478(x85062,x85063,x85061))))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f9(x85061,a927),x85062),x85063))) % 186.01/186.03 [8507]~P1(f335(f67(x85071),x85073))+~P1(f335(f335(f244(a927),f2(a927)),f335(x85072,f557(x85072,x85073,x85071))))+P1(f335(f335(f244(a927),f2(a927)),f335(f335(f9(x85071,a927),x85072),x85073))) % 186.01/186.03 [8543]~P67(x85432)+E(x85431,f84(x85432))+E(f335(f335(f299(x85432),f335(f335(f23(x85432),f335(f335(f252(x85432),x85431),x85433)),f84(x85432))),f335(f335(f23(x85432),x85431),f84(x85432))),f335(f335(f6(a927,x85432),f335(f252(x85432),x85431)),f335(f310(a927,f2(a927)),x85433))) % 186.01/186.03 [8600]E(x86001,f2(a927))+~P1(f335(x86003,f335(f335(f42(a927),x86002),x86001)))+P1(f335(f335(f244(a927),x86002),f335(f335(f87(a927),x86001),f335(a119,f454(x86001,x86002,x86003))))) % 186.01/186.03 [8619]P1(f335(x86191,f2(a927)))+~P1(f335(x86191,f335(f335(f42(a927),x86192),x86193)))+P1(f335(f335(f244(a927),x86192),f335(f335(f87(a927),x86193),f335(a119,f454(x86193,x86192,x86191))))) % 186.01/186.03 [8657]E(x86571,f2(a927))+~P1(f335(x86573,f335(f335(f42(a927),x86572),x86571)))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x86571),f454(x86571,x86572,x86573))),x86572)) % 186.01/186.03 [8688]P1(f335(x86881,f2(a927)))+~P1(f335(x86881,f335(f335(f42(a927),x86883),x86882)))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x86882),f454(x86882,x86883,x86881))),x86883)) % 186.01/186.03 [8696]~P109(x86961)+E(f335(f335(f155(x86961,x86961,f5(x86961)),x86962),x86963),f156(x86961,x86961,f5(x86961),x86962,x86963))+P1(f335(f335(f337(x86961),x86962),f335(f179(x86961),x86963))) % 186.01/186.03 [8731]~E(f335(x87313,f917(x87312,x87313,x87311)),f335(x87313,f919(x87312,x87313,x87311)))+~P61(x87311,f335(x87313,f918(x87312,x87313,x87311)))+P61(x87311,f335(f335(f45(x87312,f934(x87311,f934(x87311,a922))),f250(f934(x87312,a922))),x87313)) % 186.01/186.03 [8740]E(x87401,f195(f934(f934(x87402,a922),a922)))+~P1(f335(f335(f243(f934(x87402,a922)),f904(x87403,x87401,x87402)),x87403))+P1(f335(f335(f243(f934(x87402,a922)),f44(f934(x87402,a922),x87401)),x87403)) % 186.01/186.03 [8800]~P69(x88001)+~P1(f335(f335(f244(x88001),x88002),x88003))+P1(f335(f335(f244(x88001),x88002),f335(f335(f299(x88001),f335(f335(f86(x88001),x88002),x88003)),f335(f335(f86(x88001),f84(x88001)),f84(x88001))))) % 186.01/186.03 [8858]~P1(f335(f335(x88581,f475(x88581,x88583,x88582)),f476(x88581,x88583,x88582)))+P1(f335(f335(x88581,x88582),x88583))+~P1(f335(f323(f933(a1,a1),a230),f335(f335(f260(a1,a1),x88582),x88583))) % 186.01/186.03 [8859]~P1(f335(f335(x88591,f479(x88591,x88593,x88592)),f487(x88591,x88593,x88592)))+P1(f335(f335(x88591,x88592),x88593))+~P1(f335(f323(f933(a1,a1),a64),f335(f335(f260(a1,a1),x88592),x88593))) % 186.01/186.03 [8860]~P1(f335(f335(x88601,f488(x88601,x88603,x88602)),f489(x88601,x88603,x88602)))+P1(f335(f335(x88601,x88602),x88603))+~P1(f335(f323(f933(a1,a1),a58),f335(f335(f260(a1,a1),x88602),x88603))) % 186.01/186.03 [8861]~P1(f335(f335(x88611,f552(x88611,x88613,x88612)),f554(x88611,x88613,x88612)))+P1(f335(f335(x88611,x88612),x88613))+~P1(f335(f323(f933(a927,a927),a228),f335(f335(f260(a927,a927),x88612),x88613))) % 186.01/186.03 [8862]~P1(f335(f335(x88621,f701(x88621,x88623,x88622)),f703(x88621,x88623,x88622)))+P1(f335(f335(x88621,x88622),x88623))+~P1(f335(f323(f933(a1,a1),a189),f335(f335(f260(a1,a1),x88622),x88623))) % 186.01/186.03 [8863]~P1(f335(f335(x88631,f798(x88631,x88633,x88632)),f800(x88631,x88633,x88632)))+P1(f335(f335(x88631,x88632),x88633))+~P1(f335(f323(f933(a1,a1),a140),f335(f335(f260(a1,a1),x88632),x88633))) % 186.01/186.03 [9138]P1(f335(f335(x91381,x91382),x91383))+P1(f335(f323(f933(a927,a927),a228),f335(f335(f260(a927,a927),f552(x91381,x91383,x91382)),f554(x91381,x91383,x91382))))+~P1(f335(f323(f933(a927,a927),a228),f335(f335(f260(a927,a927),x91382),x91383))) % 186.01/186.03 [9139]P1(f335(f335(x91391,x91392),x91393))+P1(f335(f323(f933(a1,a1),a230),f335(f335(f260(a1,a1),f475(x91391,x91393,x91392)),f476(x91391,x91393,x91392))))+~P1(f335(f323(f933(a1,a1),a230),f335(f335(f260(a1,a1),x91392),x91393))) % 186.01/186.03 [9140]P1(f335(f335(x91401,x91402),x91403))+P1(f335(f323(f933(a1,a1),a64),f335(f335(f260(a1,a1),f479(x91401,x91403,x91402)),f487(x91401,x91403,x91402))))+~P1(f335(f323(f933(a1,a1),a64),f335(f335(f260(a1,a1),x91402),x91403))) % 186.01/186.03 [9141]P1(f335(f335(x91411,x91412),x91413))+P1(f335(f323(f933(a1,a1),a58),f335(f335(f260(a1,a1),f488(x91411,x91413,x91412)),f489(x91411,x91413,x91412))))+~P1(f335(f323(f933(a1,a1),a58),f335(f335(f260(a1,a1),x91412),x91413))) % 186.01/186.03 [9142]P1(f335(f335(x91421,x91422),x91423))+P1(f335(f323(f933(a1,a1),a189),f335(f335(f260(a1,a1),f701(x91421,x91423,x91422)),f703(x91421,x91423,x91422))))+~P1(f335(f323(f933(a1,a1),a189),f335(f335(f260(a1,a1),x91422),x91423))) % 186.01/186.03 [9143]P1(f335(f335(x91431,x91432),x91433))+P1(f335(f323(f933(a1,a1),a140),f335(f335(f260(a1,a1),f798(x91431,x91433,x91432)),f800(x91431,x91433,x91432))))+~P1(f335(f323(f933(a1,a1),a140),f335(f335(f260(a1,a1),x91432),x91433))) % 186.01/186.03 [9476]~P1(f335(f67(x94761),x94763))+P1(f335(f335(f337(f933(f934(x94761,a922),f934(x94761,a922))),f335(f335(f260(f934(x94761,a922),f934(x94761,a922)),x94762),x94763)),f322(x94761)))+~P1(f335(f335(f244(f934(x94761,a922)),x94762),x94763)) % 186.01/186.03 [9549]~P61(x95491,f335(x95493,f918(x95492,x95493,x95491)))+P61(x95491,f335(f335(f45(x95492,f934(x95491,f934(x95491,a922))),f250(f934(x95492,a922))),x95493))+~E(f335(f335(f108(f934(x95491,a922)),f257(x95491,x95491,f335(x95493,f917(x95492,x95493,x95491)))),f258(x95491,x95491,f335(x95493,f919(x95492,x95493,x95491)))),f195(f934(x95491,a922))) % 186.01/186.03 [9748]P54(x97481,x97482,x97483)+P1(f335(f335(f337(f933(x97481,x97481)),f569(x97483,x97482,x97481)),x97483))+~P1(f335(f335(f337(f933(x97481,x97481)),f335(f335(f260(x97481,x97481),f568(x97483,x97482,x97481)),f568(x97483,x97482,x97481))),x97483)) % 186.01/186.03 [10347]P54(x103471,x103472,x103473)+~P1(f335(f335(f265(x103471,x103471,a922),f335(f335(f7(x103471,f934(x103471,a922),f934(x103471,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x103471,a922),f934(x103471,a922)),x103471),f8(a922,a922,x103471)),f335(f335(f8(a922,f934(a922,a922),x103471),a333),f335(f335(f7(x103471,f934(x103471,a922),a922),f337(x103471)),x103472)))),f335(f335(f7(x103471,f934(x103471,a922),a922),f337(x103471)),x103472))),f569(x103473,x103472,x103471)))+~P1(f335(f335(f337(f933(x103471,x103471)),f335(f335(f260(x103471,x103471),f568(x103473,x103472,x103471)),f568(x103473,x103472,x103471))),x103473)) % 186.01/186.03 [5897]~P63(x58972)+E(x58971,f2(x58972))+E(f335(f335(f42(x58972),f335(f335(f87(x58972),x58973),x58971)),x58971),x58973) % 186.01/186.03 [5898]~P63(x58982)+E(x58981,f2(x58982))+E(f335(f335(f42(x58982),f335(f335(f87(x58982),x58981),x58983)),x58981),x58983) % 186.01/186.03 [6694]~P76(x66941)+~E(f335(x66942,f2(a927)),f2(x66941))+E(f335(f335(f6(a927,x66941),x66942),f335(f310(a927,f335(a119,f2(a927))),x66943)),f335(f335(f6(a927,x66941),x66942),f335(f310(a927,f2(a927)),x66943))) % 186.01/186.03 [6825]~P63(x68252)+E(x68251,f2(x68252))+E(f335(f335(f42(x68252),f335(f335(f86(x68252),x68253),x68251)),x68251),f335(f335(f86(x68252),f335(f335(f42(x68252),x68253),x68251)),f84(x68252))) % 186.01/186.03 [6826]~P63(x68262)+E(x68261,f2(x68262))+E(f335(f335(f42(x68262),f335(f335(f86(x68262),x68261),x68263)),x68261),f335(f335(f86(x68262),f335(f335(f42(x68262),x68263),x68261)),f84(x68262))) % 186.01/186.03 [7044]~P1(f335(x70443,f2(a1)))+P1(f335(f335(f243(a927),x70441),x70442))+P1(f335(x70443,f335(f107(a1),f335(f335(f23(a927),x70442),x70441)))) % 186.01/186.03 [7144]P1(f335(f335(f244(a927),x71442),x71441))+P1(f335(f335(f243(a927),x71441),x71442))+P1(f335(x71443,f335(f107(a1),f335(f335(f23(a927),x71442),x71441)))) % 186.01/186.03 [7217]E(f335(f335(f86(a927),f335(f110(a927),x72171)),f335(f335(f86(a927),f335(f110(a927),x72172)),x72173)),f335(f335(f86(a927),f335(f110(a927),x72171)),x72173))+P1(f335(a200,f335(f110(a1),x72171)))+~P1(f335(a200,f335(f110(a1),x72172))) % 186.01/186.03 [7295]~E(x72952,f335(f335(f42(a927),x72953),x72951))+~P1(f335(f335(f244(a927),f2(a927)),x72951))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x72951),x72952)),x72953)) % 186.01/186.03 [7410]~P1(f335(f67(x74101),x74103))+~P1(f335(f67(x74101),x74102))+P1(f335(f67(x74101),f335(f335(f117(f934(x74101,a922)),x74102),x74103))) % 186.01/186.03 [7458]~P39(x74581,x74583)+~P39(x74581,x74582)+P39(x74581,f335(f335(f108(f934(f933(x74581,x74581),a922)),x74582),x74583)) % 186.01/186.03 [7459]~P53(x74591,x74593)+~P53(x74591,x74592)+P53(x74591,f335(f335(f108(f934(f933(x74591,x74591),a922)),x74592),x74593)) % 186.01/186.03 [7460]~P53(x74601,x74603)+~P53(x74601,x74602)+P53(x74601,f335(f335(f117(f934(f933(x74601,x74601),a922)),x74602),x74603)) % 186.01/186.03 [7704]~P109(x77041)+~P1(f335(f67(x77041),x77042))+E(f146(x77041,f335(f335(f23(f934(x77041,a922)),x77042),f335(f335(f317(x77041),x77043),f195(f934(x77041,a922))))),f177(x77041,x77043,f146(x77041,x77042))) % 186.01/186.03 [7764]P1(f335(x77641,f2(a1)))+~P1(f335(f335(f244(a927),x77642),x77643))+~P1(f335(x77641,f335(f107(a1),f335(f335(f23(a927),x77642),x77643)))) % 186.01/186.03 [7782]~P1(f335(f67(x77821),x77822))+E(f335(f41(x77821),f335(f335(f23(f934(x77821,a922)),x77822),f335(f335(f317(x77821),x77823),f195(f934(x77821,a922))))),f335(f41(x77821),x77822))+P1(f335(f335(f337(x77821),x77823),x77822)) % 186.01/186.03 [7912]~P125(x79121)+~P1(f335(f335(f244(x79121),f84(x79121)),x79122))+P1(f335(f335(f244(x79121),f84(x79121)),f335(f335(f87(x79121),x79122),f335(f335(f252(x79121),x79122),x79123)))) % 186.01/186.03 [7954]~P1(f335(f67(x79541),x79543))+E(f335(f335(f23(a927),f335(f41(x79541),x79542)),f335(f41(x79541),x79543)),f335(f41(x79541),f335(f335(f23(f934(x79541,a922)),x79542),x79543)))+~P1(f335(f335(f243(f934(x79541,a922)),x79543),x79542)) % 186.01/186.03 [8011]~P1(f335(f335(f243(a927),x80112),x80113))+~P1(f335(f335(f243(a927),x80111),f335(f335(f23(a927),x80113),x80112)))+P1(f335(f335(f243(a927),f335(f335(f86(a927),x80111),x80112)),x80113)) % 186.01/186.03 [8062]P1(f335(f67(x80621),x80622))+~P1(f335(f67(x80621),x80623))+~P1(f335(f67(x80621),f335(f335(f23(f934(x80621,a922)),x80622),x80623))) % 186.01/186.03 [8068]~P1(f335(f67(x80681),x80682))+E(f335(f41(x80681),f335(f335(f23(f934(x80681,a922)),x80682),f335(f335(f317(x80681),x80683),f195(f934(x80681,a922))))),f335(f335(f23(a927),f335(f41(x80681),x80682)),f84(a927)))+~P1(f335(f335(f337(x80681),x80683),x80682)) % 186.01/186.03 [8143]P61(x81431,x81432)+~P61(x81431,x81433)+~P1(f335(f335(f243(f934(x81431,f934(x81431,a922))),x81432),x81433)) % 186.01/186.03 [8184]~P1(f335(f335(f243(a927),x81843),x81842))+P1(f335(f335(f243(a927),x81841),f335(f335(f23(a927),x81842),x81843)))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),x81841),x81843)),x81842)) % 186.01/186.03 [8202]P38(x82021,x82022)+~P38(x82021,x82023)+~P1(f335(f335(f243(f934(f933(x82021,x82021),a922)),x82022),x82023)) % 186.01/186.03 [8203]P59(x82031,x82032)+~P59(x82031,x82033)+~P1(f335(f335(f243(f934(f933(x82031,x82031),a922)),x82032),x82033)) % 186.01/186.03 [8204]P40(x82041,x82042)+~P40(x82041,x82043)+~P1(f335(f335(f243(f934(f933(x82041,x82041),a922)),x82042),x82043)) % 186.01/186.03 [8433]~P125(x84331)+~P1(f335(f335(f244(x84331),f84(x84331)),x84332))+P1(f335(f335(f244(x84331),f335(f335(f252(x84331),x84332),x84333)),f335(f335(f87(x84331),x84332),f335(f335(f252(x84331),x84332),x84333)))) % 186.01/186.03 [8525]~P1(f335(x85251,f2(a1)))+~P1(f335(x85251,f335(f335(f23(a1),f335(f107(a1),x85252)),f335(f107(a1),x85253))))+P1(f335(x85251,f335(f107(a1),f335(f335(f23(a927),x85252),x85253)))) % 186.01/186.03 [8540]~P1(f335(f335(f243(a927),x85403),x85402))+P1(f335(x85401,f335(f335(f23(a1),f335(f107(a1),x85402)),f335(f107(a1),x85403))))+~P1(f335(x85401,f335(f107(a1),f335(f335(f23(a927),x85402),x85403)))) % 186.01/186.03 [8559]P1(f335(f335(f244(a927),x85591),x85592))+~P1(f335(x85593,f335(f335(f23(a1),f335(f107(a1),x85591)),f335(f107(a1),x85592))))+P1(f335(x85593,f335(f107(a1),f335(f335(f23(a927),x85591),x85592)))) % 186.01/186.03 [8612]~P127(x86122)+E(x86121,f2(x86122))+P1(f335(f335(f244(x86122),f2(x86122)),f335(f335(f86(x86122),f335(f335(f87(x86122),x86123),x86123)),f335(f335(f87(x86122),x86121),x86121)))) % 186.01/186.03 [8613]~P127(x86132)+E(x86131,f2(x86132))+P1(f335(f335(f244(x86132),f2(x86132)),f335(f335(f86(x86132),f335(f335(f87(x86132),x86131),x86131)),f335(f335(f87(x86132),x86133),x86133)))) % 186.01/186.03 [8713]~P1(f335(f335(f244(a927),f2(a927)),x87131))+~P1(f335(f335(f244(a1),x87132),x87133))+P1(f335(f335(f244(a1),f335(f335(f87(a1),f335(f107(a1),x87131)),x87132)),f335(f335(f87(a1),f335(f107(a1),x87131)),x87133))) % 186.01/186.03 [8769]E(f335(f335(f108(f934(x87691,a922)),x87692),f43(f934(x87691,a922),x87693)),f195(f934(x87691,a922)))+P1(f335(f335(f337(f934(x87691,a922)),x87692),x87693))+P1(f335(f335(f337(f934(x87691,a922)),f589(x87693,x87692,x87691)),f335(f335(f317(f934(x87691,a922)),x87692),x87693))) % 186.01/186.03 [8770]E(f335(f335(f108(f934(x87701,a922)),x87702),f43(f934(x87701,a922),x87703)),f195(f934(x87701,a922)))+P1(f335(f335(f337(f934(x87701,a922)),x87702),x87703))+P1(f335(f335(f337(f934(x87701,a922)),f588(x87703,x87702,x87701)),f335(f335(f317(f934(x87701,a922)),x87702),x87703))) % 186.01/186.03 [8799]E(x87991,x87992)+~E(f335(f196(f928(x87993)),x87991),f335(f196(f928(x87993)),x87992))+P1(f335(f335(f337(f933(x87993,x87993)),f687(x87993,x87991,x87992)),f335(f179(f933(x87993,x87993)),f335(f335(f188(x87993,x87993),x87992),x87991)))) % 186.01/186.03 [9049]E(f315(x90491,x90492),f315(x90491,x90493))+~P1(f335(f335(f243(f934(f933(x90491,x90491),a922)),x90493),f315(x90491,x90492)))+~P1(f335(f335(f243(f934(f933(x90491,x90491),a922)),x90492),x90493)) % 186.01/186.03 [9116]~P54(x91161,f250(f934(x91161,a922)),x91163)+P1(f335(f335(f243(f934(f933(f928(x91161),f928(x91161)),a922)),f164(x91161,x91162)),f165(x91161,x91163)))+~P1(f335(f335(f243(f934(f933(x91161,x91161),a922)),x91162),x91163)) % 186.01/186.03 [9316]P38(x93161,x93162)+~P1(f335(f335(f337(x93161),x93163),f913(x93162,x93161)))+P1(f335(f335(f337(f933(x93161,x93161)),f335(f335(f260(x93161,x93161),f344(x93162,x93161,x93163)),x93163)),x93162)) % 186.01/186.03 [9351]~P1(f335(f67(x93511),x93512))+P1(f335(f67(f934(x93511,a922)),f335(f335(f66(x93511),x93512),x93513)))+~P1(f335(f335(f243(f934(f933(x93511,x93511),a922)),x93513),f335(f335(f262(x93511,x93511),x93512),f335(f16(f934(x93511,a922),x93511),x93512)))) % 186.01/186.03 [9387]P54(x93871,x93872,x93873)+P1(f335(f335(f337(x93871),f561(x93873,x93872,x93871)),x93872))+~P1(f335(f335(f243(f934(f933(x93871,x93871),a922)),x93873),f335(f335(f262(x93871,x93871),x93872),f335(f16(f934(x93871,a922),x93871),x93872)))) % 186.01/186.03 [9388]P54(x93881,x93882,x93883)+P1(f335(f335(f337(x93881),f566(x93882,x93883,x93881)),x93882))+~P1(f335(f335(f243(f934(f933(x93881,x93881),a922)),x93883),f335(f335(f262(x93881,x93881),x93882),f335(f16(f934(x93881,a922),x93881),x93882)))) % 186.01/186.03 [9420]~P69(x94201)+~P1(f335(f335(f244(x94201),x94202),x94203))+P1(f335(f335(f244(x94201),f335(f335(f299(x94201),f335(f335(f86(x94201),x94202),x94203)),f335(f335(f86(x94201),f84(x94201)),f84(x94201)))),x94203)) % 186.01/186.03 [9449]~P68(x94491)+P1(f335(f335(f243(x94491),x94492),x94493))+~P1(f335(f335(f243(x94491),f335(f335(f87(x94491),f545(x94493,x94492,x94491)),x94492)),x94493)) % 186.01/186.03 [9584]E(f335(f196(f928(f928(x95841))),f335(f143(f928(x95841),f335(f335(f8(a927,a922,f928(x95841)),f335(f244(a927),x95842)),f196(f928(x95841)))),f186(x95841,x95843))),f335(f196(f928(x95841)),f335(f335(f171(f928(x95841)),x95843),x95842)))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x95841),a927),f196(f928(x95841))),x95843)))+~P1(f335(f335(f244(a927),x95842),f335(f196(f928(f928(x95841))),x95843))) % 186.01/186.03 [9696]~P38(x96961,x96962)+P28(x96961,f335(f335(f260(f934(f933(x96961,x96961),a922),f934(f933(x96961,x96961),a922)),x96962),x96963))+~P1(f335(f335(f243(f934(f933(x96961,x96961),a922)),f335(f335(f297(x96961,x96961,x96961),x96962),x96963)),x96962)) % 186.01/186.03 [9701]E(f335(f335(f161(f928(x97011),x97011),f335(f335(f7(f928(x97011),a927,x97011),f171(x97011)),x97012)),f335(f143(f928(x97011),f335(f335(f8(a927,a922,f928(x97011)),f335(f244(a927),x97012)),f196(f928(x97011)))),f186(x97011,x97013))),f335(f335(f171(f928(x97011)),x97013),x97012))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x97011),a927),f196(f928(x97011))),x97013)))+~P1(f335(f335(f244(a927),x97012),f335(f196(f928(f928(x97011))),x97013))) % 186.01/186.03 [9836]P54(x98361,x98362,x98363)+~P1(f335(f335(f337(f933(x98361,x98361)),f335(f335(f260(x98361,x98361),f561(x98363,x98362,x98361)),f561(x98363,x98362,x98361))),x98363))+~P1(f335(f335(f243(f934(f933(x98361,x98361),a922)),x98363),f335(f335(f262(x98361,x98361),x98362),f335(f16(f934(x98361,a922),x98361),x98362)))) % 186.01/186.03 [9837]P54(x98371,x98372,x98373)+~P1(f335(f335(f337(f933(x98371,x98371)),f335(f335(f260(x98371,x98371),f566(x98372,x98373,x98371)),f566(x98372,x98373,x98371))),x98373))+~P1(f335(f335(f243(f934(f933(x98371,x98371),a922)),x98373),f335(f335(f262(x98371,x98371),x98372),f335(f16(f934(x98371,a922),x98371),x98372)))) % 186.01/186.03 [10008]~P140(x100081)+~P124(x100081)+E(f335(f335(f299(x100081),f335(f109(x100081),f335(f335(f78(f933(a1,a1),a1,x100082,f259(a1,a1)),f221(x100082)),x100083))),f335(f109(x100081),f335(f335(f78(f933(a1,a1),a1,x100082,f264(a1,a1)),f221(x100082)),x100083))),f231(x100082,x100081,x100083)) % 186.01/186.03 [10216]~E(x102163,f2(a927))+~E(f335(f196(f928(x102161)),f335(f335(f171(f928(x102161)),x102162),f735(x102163,x102161,x102162))),x102163)+E(f335(f335(f161(a927,f928(x102161)),f335(f335(f7(a927,f928(a927),f928(x102161)),f335(f335(f8(f934(a927,x102161),f934(f928(a927),f928(x102161)),a927),f161(a927,x102161)),f335(f7(a927,a927,x102161),f335(f335(f8(f928(x102161),f934(a927,x102161),a927),f171(x102161)),f335(f171(f928(x102161)),x102162))))),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(f928(x102161))),x102162))))),f146(a927,f335(f310(a927,f2(a927)),x102163))),f186(x102161,x102162)) % 186.01/186.03 [10217]E(x102171,f120(f928(x102172)))+~E(f335(f196(f928(x102172)),f335(f335(f171(f928(x102172)),x102171),f735(x102173,x102172,x102171))),x102173)+E(f335(f335(f161(a927,f928(x102172)),f335(f335(f7(a927,f928(a927),f928(x102172)),f335(f335(f8(f934(a927,x102172),f934(f928(a927),f928(x102172)),a927),f161(a927,x102172)),f335(f7(a927,a927,x102172),f335(f335(f8(f928(x102172),f934(a927,x102172),a927),f171(x102172)),f335(f171(f928(x102172)),x102171))))),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(f928(x102172))),x102171))))),f146(a927,f335(f310(a927,f2(a927)),x102173))),f186(x102172,x102171)) % 186.01/186.03 [10218]~E(x102183,f2(a927))+E(f335(f335(f161(a927,f928(x102181)),f335(f335(f7(a927,f928(a927),f928(x102181)),f335(f335(f8(f934(a927,x102181),f934(f928(a927),f928(x102181)),a927),f161(a927,x102181)),f335(f7(a927,a927,x102181),f335(f335(f8(f928(x102181),f934(a927,x102181),a927),f171(x102181)),f335(f171(f928(x102181)),x102182))))),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(f928(x102181))),x102182))))),f146(a927,f335(f310(a927,f2(a927)),x102183))),f186(x102181,x102182))+P1(f335(f335(f244(a927),f735(x102183,x102181,x102182)),f335(f196(f928(f928(x102181))),x102182))) % 186.01/186.03 [10219]E(x102191,f120(f928(x102192)))+E(f335(f335(f161(a927,f928(x102192)),f335(f335(f7(a927,f928(a927),f928(x102192)),f335(f335(f8(f934(a927,x102192),f934(f928(a927),f928(x102192)),a927),f161(a927,x102192)),f335(f7(a927,a927,x102192),f335(f335(f8(f928(x102192),f934(a927,x102192),a927),f171(x102192)),f335(f171(f928(x102192)),x102191))))),f146(a927,f335(f310(a927,f2(a927)),f335(f196(f928(f928(x102192))),x102191))))),f146(a927,f335(f310(a927,f2(a927)),x102193))),f186(x102192,x102191))+P1(f335(f335(f244(a927),f735(x102193,x102192,x102191)),f335(f196(f928(f928(x102192))),x102191))) % 186.01/186.03 [7951]E(f335(f335(f86(a927),f335(f110(a927),x79511)),f335(f335(f86(a927),f335(f110(a927),x79512)),x79513)),f335(f335(f86(a927),f335(f110(a927),f335(f335(f86(a1),x79511),x79512))),x79513))+P1(f335(a200,f335(f110(a1),x79511)))+P1(f335(a200,f335(f110(a1),x79512))) % 186.01/186.03 [8705]~P1(f335(f67(x87051),x87052))+~P1(f335(f335(f337(x87051),x87053),x87052))+E(f335(a119,f335(f41(x87051),f335(f335(f23(f934(x87051,a922)),x87052),f335(f335(f317(x87051),x87053),f195(f934(x87051,a922)))))),f335(f41(x87051),x87052)) % 186.01/186.03 [8721]~P1(f335(f67(x87211),x87212))+~P1(f335(f335(f337(x87211),x87213),x87212))+E(f335(f335(f86(a927),f84(a927)),f335(f41(x87211),f335(f335(f23(f934(x87211,a922)),x87212),f335(f335(f317(x87211),x87213),f195(f934(x87211,a922)))))),f335(f41(x87211),x87212)) % 186.01/186.03 [8808]~P109(x88081)+~P1(f335(f67(x88081),x88083))+E(f335(f335(f155(x88081,x88081,f5(x88081)),x88082),f146(x88081,f335(f335(f23(f934(x88081,a922)),x88083),f335(f335(f317(x88081),x88082),f195(f934(x88081,a922)))))),f146(x88081,f335(f335(f317(x88081),x88082),x88083))) % 186.01/186.03 [8974]~P1(f335(f67(x89741),x89743))+~P1(f335(f67(x89741),x89742))+E(f335(f335(f86(a927),f335(f41(x89741),f335(f335(f117(f934(x89741,a922)),x89742),x89743))),f335(f41(x89741),f335(f335(f108(f934(x89741,a922)),x89742),x89743))),f335(f335(f86(a927),f335(f41(x89741),x89742)),f335(f41(x89741),x89743))) % 186.01/186.03 [10164]~P26(x101641,f934(f934(x101641,a922),a922),f335(f335(f7(x101641,f934(f933(x101641,x101641),a922),f934(f934(x101641,a922),a922)),f335(f335(f8(f934(x101641,a922),f934(f934(f933(x101641,x101641),a922),f934(f934(x101641,a922),a922)),x101641),f66(x101641)),f335(f335(f7(x101641,f934(x101641,a922),f934(x101641,a922)),f317(x101641)),f195(f934(x101641,a922))))),x101643),x101642)+~P1(f335(f67(x101641),x101642))+E(f335(f41(f934(x101641,a922)),f335(f335(f66(x101641),x101642),x101643)),f335(f41(x101641),x101642)) % 186.01/186.03 [8216]~P94(x82161)+P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x82163)))+E(f335(f335(f252(x82161),x82162),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x82163),x82163)),a104))),f84(x82161)) % 186.01/186.03 [9681]~P94(x96811)+~P1(f335(f335(f243(a1),f2(a1)),f335(f110(a1),x96813)))+E(f335(f335(f252(x96811),x96812),f335(f110(a927),f335(f335(f23(a1),f335(f335(f86(a1),x96813),x96813)),a104))),f335(f335(f92(x96811,x96811),f335(f335(f252(x96811),x96812),f335(f110(a927),x96813))),f335(f335(f18(x96811,x96811,x96811),f335(f335(f8(x96811,f934(x96811,x96811),x96811),f87(x96811)),f335(f87(x96811),x96812))),f5(x96811)))) % 186.01/186.03 [10071]~P1(f335(f144(x100711),x100713))+~P1(f335(f335(f337(x100711),x100712),f335(f179(x100711),x100713)))+E(f335(f335(f145(x100711),f335(f196(f928(x100711)),f184(x100711,f335(f335(f8(a922,a922,x100711),a330),f335(f335(f7(x100711,x100711,a922),a332),x100712)),f335(f175(x100711),x100713)))),f335(f175(x100711),x100713)),f335(f335(f158(x100711),x100712),f335(f175(x100711),f184(x100711,f335(f335(f8(a922,a922,x100711),a330),f335(f335(f7(x100711,x100711,a922),a332),x100712)),x100713)))) % 186.01/186.03 [10132]P1(f335(f335(f243(f934(f933(x101321,x101321),a922)),f315(x101321,x101322)),x101323))+~P1(f335(f335(f243(f934(f933(x101321,x101321),a922)),f315(x101321,f195(f934(f933(x101321,x101321),a922)))),x101323))+~P1(f335(f335(f243(f934(f933(x101321,x101321),a922)),f335(f335(f297(x101321,x101321,x101321),f335(f335(f108(f934(f933(x101321,x101321),a922)),f315(x101321,x101322)),x101323)),x101322)),x101323)) % 186.01/186.03 [9988]~P1(f335(f67(x99881),f335(f270(x99881),x99883)))+~P1(f335(f67(x99881),f335(f270(x99881),x99882)))+P1(f335(f67(x99881),f335(f270(x99881),f335(f335(f18(x99881,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99881),a334),x99882)),x99883)))) % 186.01/186.03 [10282]P1(f335(f335(f243(f934(f933(x102821,x102821),a922)),f335(f335(f297(x102821,x102821,x102821),x102822),f315(x102821,x102822))),x102823))+~P1(f335(f335(f243(f934(f933(x102821,x102821),a922)),x102822),x102823))+~P1(f335(f335(f243(f934(f933(x102821,x102821),a922)),f335(f335(f297(x102821,x102821,x102821),f335(f335(f108(f934(f933(x102821,x102821),a922)),f335(f335(f297(x102821,x102821,x102821),x102822),f315(x102821,x102822))),x102823)),x102822)),x102823)) % 186.01/186.03 [10232]~P113(x102322)+E(x102321,f2(x102322))+~E(f335(f335(f86(x102322),f335(f335(f252(x102322),x102323),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x102322),x102321),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f2(x102322)) % 186.01/186.03 [10233]~P113(x102332)+E(x102331,f2(x102332))+~E(f335(f335(f86(x102332),f335(f335(f252(x102332),x102331),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x102332),x102333),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f2(x102332)) % 186.01/186.03 [10238]~P1(f335(f144(x102381),x102383))+~P1(f335(f335(f337(x102381),x102382),f335(f179(x102381),x102383)))+E(f335(f175(x102381),f335(f178(x102381),f335(f335(f145(x102381),f335(f196(f928(x102381)),f184(x102381,f335(f335(f8(a922,a922,x102381),a330),f335(f335(f7(x102381,x102381,a922),a332),x102382)),x102383))),x102383))),f184(x102381,f335(f335(f8(a922,a922,x102381),a330),f335(f335(f7(x102381,x102381,a922),a332),x102382)),f335(f175(x102381),x102383))) % 186.01/186.03 [10329]~P113(x103292)+E(x103291,f2(x103292))+P1(f335(f335(f244(x103292),f2(x103292)),f335(f335(f86(x103292),f335(f335(f252(x103292),x103293),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103292),x103291),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))) % 186.01/186.03 [10330]~P113(x103302)+E(x103301,f2(x103302))+P1(f335(f335(f244(x103302),f2(x103302)),f335(f335(f86(x103302),f335(f335(f252(x103302),x103301),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103302),x103303),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))) % 186.01/186.03 [10385]~P113(x103851)+P1(f335(f335(f243(x103851),f2(x103851)),x103852))+~P1(f335(f335(f243(x103851),f2(x103851)),f335(f335(f252(x103851),x103852),f335(a119,f335(f335(f87(a927),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),x103853))))) % 186.01/186.03 [5732]~P25(x57321,x57324,x57323)+P25(x57321,x57322,x57323)+~P25(x57321,x57322,x57324) % 186.01/186.03 [5198]~E(x51982,f96(x51983,x51981))+P1(f335(x51981,x51982))+~P1(f335(x51981,x51984)) % 186.01/186.03 [5443]E(f74(x54433,x54432,x54434),x54432)+E(x54431,f761(x54432,x54433,x54434))+~P1(f335(x54434,x54431)) % 186.01/186.03 [6749]E(f74(x67491,x67492,x67493),f91(x67491,x67493))+~E(f802(x67492,x67491,x67493,x67494),x67494)+~P1(f335(x67493,x67494)) % 186.01/186.03 [6958]~P38(x69582,x69584)+~P38(x69581,x69583)+P38(f933(x69581,x69582),f328(x69581,x69582,x69583,x69584)) % 186.01/186.03 [6959]~P39(x69592,x69594)+~P39(x69591,x69593)+P39(f933(x69591,x69592),f328(x69591,x69592,x69593,x69594)) % 186.01/186.03 [5383]~P8(x53834,x53831)+~E(f335(x53831,x53832),f335(x53831,x53833))+P1(f335(f335(x53831,x53832),x53833)) % 186.01/186.03 [5546]~P8(x55464,x55461)+E(f335(x55461,x55462),f335(x55461,x55463))+~P1(f335(f335(x55461,x55462),x55463)) % 186.01/186.03 [5547]~P16(x55474,x55471)+E(f335(x55471,x55472),f335(x55471,x55473))+~P1(f335(f335(x55471,x55472),x55473)) % 186.01/186.03 [5638]~P19(x56383,x56384,x56381)+E(f335(x56381,x56382),f335(f69(x56383,x56384),x56382))+~P1(f335(f67(x56383),x56382)) % 186.01/186.03 [5639]~P10(x56393,x56394,x56391)+E(f335(x56391,x56392),f335(f69(x56393,x56394),x56392))+~P1(f335(f67(x56393),x56392)) % 186.01/186.03 [5765]~P8(x57654,x57651)+~P1(f335(f335(x57651,x57653),x57652))+P1(f335(f335(x57651,x57652),x57653)) % 186.01/186.03 [5766]~P52(x57664,x57661)+~P1(f335(f335(x57661,x57663),x57662))+P1(f335(f335(x57661,x57662),x57663)) % 186.01/186.03 [5767]~P16(x57674,x57671)+~P1(f335(f335(x57671,x57673),x57672))+P1(f335(f335(x57671,x57672),x57673)) % 186.01/186.03 [5768]~P16(x57683,x57681)+P1(f335(f335(x57681,x57682),x57682))+~P1(f335(f335(x57681,x57684),x57682)) % 186.01/186.03 [5769]~P16(x57693,x57691)+P1(f335(f335(x57691,x57692),x57692))+~P1(f335(f335(x57691,x57692),x57694)) % 186.01/186.03 [5839]E(x58391,x58392)+~E(f335(f259(x58393,x58394),x58391),f335(f259(x58393,x58394),x58392))+~E(f335(f264(x58393,x58394),x58391),f335(f264(x58393,x58394),x58392)) % 186.01/186.03 [5866]E(x58661,x58662)+~P1(f335(f54(x58663,x58664),x58662))+~P1(f335(f54(x58663,x58664),x58661)) % 186.01/186.03 [6057]~P76(x60572)+E(f240(x60571,x60572,x60573,x60574),f2(x60572))+P1(f335(f67(x60571),x60574)) % 186.01/186.03 [6105]~P8(x61053,x61052)+~P1(f335(x61051,x61054))+P1(f335(x61051,f845(x61051,x61052,x61053))) % 186.01/186.03 [6197]~P1(f335(f323(x61971,x61972),x61974))+P1(f335(f323(x61971,x61972),x61973))+~P1(f335(f335(x61972,x61973),x61974)) % 186.01/186.03 [6625]P50(x66251,x66252,x66253,x66254)+P1(f335(f335(x66252,x66254),x66253))+~P1(f335(f335(x66252,x66253),x66254)) % 186.01/186.03 [6991]~P30(x69911,x69913,x69914)+P1(f335(x69911,x69912))+~P1(f335(f335(f337(a1),x69912),f311(a1,x69913,x69914))) % 186.01/186.03 [7178]~P8(x71781,x71783)+~P1(f335(x71782,x71784))+P1(f335(f335(f337(x71781),f845(x71782,x71783,x71781)),f278(x71781,x71783))) % 186.01/186.03 [8057]E(x80571,f2(a927))+~P1(f335(x80572,x80573))+P1(f335(x80572,f796(x80572,x80573,x80571,x80574))) % 186.01/186.03 [8138]~P109(x81382)+~P1(f335(f144(x81381),x81384))+P1(f335(f144(x81381),f157(x81381,x81382,x81383,x81384))) % 186.01/186.03 [8183]E(f74(x81831,x81832,x81833),f91(x81831,x81833))+~P1(f335(x81833,x81834))+P1(f335(x81833,f802(x81832,x81831,x81833,x81834))) % 186.01/186.03 [8360]~P1(f335(f67(x83602),x83604))+~P1(f335(f67(x83601),x83603))+P1(f335(f67(f935(x83601,x83602)),f321(x83601,x83602,x83603,x83604))) % 186.01/186.03 [8361]~P1(f335(f144(x83612),x83614))+~P1(f335(f144(x83611),x83613))+P1(f335(f144(f933(x83611,x83612)),f65(x83611,x83612,x83613,x83614))) % 186.01/186.03 [8364]P1(f335(f335(f337(f928(x83641)),f335(f335(f141(x83641),x83642),x83643)),f168(x83641,x83644)))+~P1(f335(f335(f337(f928(x83641)),x83643),f168(x83641,x83644)))+~P1(f335(f335(f337(f928(x83641)),x83642),f168(x83641,x83644))) % 186.01/186.03 [8643]E(x86431,f2(a927))+P1(f335(x86432,x86433))+~P1(f335(x86432,f797(x86432,x86433,x86431,x86434))) % 186.01/186.03 [8680]~P109(x86803)+~P1(f335(f144(x86801),f157(x86801,x86803,x86804,x86802)))+P1(f335(f144(x86801),x86802)) % 186.01/186.03 [8963]~P1(f335(f335(f337(f933(x89631,x89631)),f335(f335(f260(x89631,x89631),x89632),x89634)),f315(x89631,x89633)))+P1(f335(f335(f337(x89631),x89632),f324(x89631,x89633)))+~P1(f335(f335(f337(x89631),x89634),f324(x89631,x89633))) % 186.01/186.03 [5367]~P76(x53672)+E(f335(f335(f6(x53671,x53672),x53673),x53674),f2(x53672))+P1(f335(f67(x53671),x53674)) % 186.01/186.03 [5370]~P72(x53702)+E(f335(f335(f9(x53701,x53702),x53703),x53704),f84(x53702))+P1(f335(f67(x53701),x53704)) % 186.01/186.03 [5511]~P73(x55113)+E(x55111,x55112)+~E(f335(f335(f86(x55113),x55114),x55111),f335(f335(f86(x55113),x55114),x55112)) % 186.01/186.03 [5512]~P74(x55123)+E(x55121,x55122)+~E(f335(f335(f86(x55123),x55124),x55121),f335(f335(f86(x55123),x55124),x55122)) % 186.01/186.03 [5514]~P73(x55143)+E(x55141,x55142)+~E(f335(f335(f86(x55143),x55141),x55144),f335(f335(f86(x55143),x55142),x55144)) % 186.01/186.03 [5634]~P6(x56343)+E(x56341,f195(f934(x56342,a922)))+E(f335(f335(f45(x56342,x56343),x56341),f335(f16(x56343,x56342),x56344)),x56344) % 186.01/186.03 [5635]~P6(x56353)+E(x56351,f195(f934(x56352,a922)))+E(f335(f335(f46(x56352,x56353),x56351),f335(f16(x56353,x56352),x56354)),x56354) % 186.01/186.03 [5852]~P110(x58523)+E(x58521,x58522)+~E(f311(x58523,x58524,x58521),f335(f335(f317(x58523),x58522),f195(f934(x58523,a922)))) % 186.01/186.03 [5853]~P110(x58533)+E(x58531,x58532)+~E(f311(x58533,x58531,x58532),f335(f335(f317(x58533),x58534),f195(f934(x58533,a922)))) % 186.01/186.03 [5913]~P36(x59133,x59131,x59134)+P36(x59133,x59131,f335(f335(f158(x59133),x59132),x59134))+P1(f335(x59131,x59132)) % 186.01/186.03 [6015]~P32(x60151,x60152,x60154)+~P1(f335(x60152,x60153))+P32(x60151,x60152,f335(f335(f158(x60151),x60153),x60154)) % 186.01/186.03 [6153]P1(f335(x61531,x61532))+~P1(f335(f256(x61533,x61531),x61534))+~P1(f335(f335(f337(x61533),x61532),x61534)) % 186.01/186.03 [6162]~P32(x61621,x61622,x61624)+~P32(x61621,x61622,x61623)+P32(x61621,x61622,f335(f335(f141(x61621),x61623),x61624)) % 186.01/186.03 [6176]P34(x61761,x61762,x61763)+~P34(x61761,x61762,f335(f335(f158(x61761),x61764),x61763))+P1(f335(x61762,x61764)) % 186.01/186.03 [6177]P36(x61771,x61772,x61773)+~P36(x61771,x61772,f335(f335(f158(x61771),x61774),x61773))+P1(f335(x61772,x61774)) % 186.01/186.03 [6252]P34(x62521,x62522,x62523)+P34(x62521,x62522,x62524)+~P34(x62521,x62522,f335(f335(f141(x62521),x62524),x62523)) % 186.01/186.03 [6271]~P76(x62711)+E(f335(f335(f6(a927,x62711),x62712),f335(f310(a927,x62713),f335(a119,x62714))),f2(x62711))+~P1(f335(f335(f244(a927),x62714),x62713)) % 186.01/186.03 [6276]~P64(x62761)+~E(f51(x62761,x62762,x62763),f51(x62761,x62764,x62763))+E(f51(x62761,f335(f85(x62761),x62762),x62763),f51(x62761,f335(f85(x62761),x62764),x62763)) % 186.01/186.03 [6344]P1(f335(x63441,x63442))+~E(f335(f143(x63443,x63441),x63444),x63444)+~P1(f335(f335(f337(x63443),x63442),f335(f179(x63443),x63444))) % 186.01/186.03 [6363]~E(f335(f335(f86(a927),x63633),x63632),f335(f335(f86(a927),x63631),x63634))+~P1(f335(f335(f244(a927),x63633),x63634))+P1(f335(f335(f244(a927),x63631),x63632)) % 186.01/186.03 [6369]P34(x63691,x63692,x63693)+~P1(f335(x63692,x63694))+~P1(f335(f335(f337(x63691),x63694),f335(f179(x63691),x63693))) % 186.01/186.03 [6372]~P63(x63721)+E(f51(x63721,f51(x63721,x63722,x63723),x63724),f51(x63721,x63722,x63724))+~P1(f335(f335(f295(x63721),x63724),x63723)) % 186.01/186.03 [6409]~P32(x64093,x64091,x64094)+P1(f335(x64091,x64092))+~P1(f335(f335(f337(x64093),x64092),f335(f179(x64093),x64094))) % 186.01/186.03 [6411]~E(f335(f143(x64111,x64112),x64113),f120(x64111))+~P1(f335(x64112,x64114))+~P1(f335(f335(f337(x64111),x64114),f335(f179(x64111),x64113))) % 186.01/186.03 [6412]~E(f184(x64123,x64121,x64124),x64124)+P1(f335(x64121,x64122))+~P1(f335(f335(f337(x64123),x64122),f335(f179(x64123),x64124))) % 186.01/186.03 [6438]~E(x64384,f195(f934(x64382,a922)))+~E(x64383,f195(f934(x64381,a922)))+E(f321(x64381,x64382,x64383,x64384),f195(f934(f935(x64381,x64382),a922))) % 186.01/186.03 [6583]P1(f335(x65831,x65832))+~P1(f335(f167(x65833,x65831),x65834))+~P1(f335(f335(f337(x65833),x65832),f335(f179(x65833),x65834))) % 186.01/186.03 [6718]~P31(x67181,x67183,x67184)+P1(f335(x67181,x67182))+~P1(f335(f335(f337(a927),x67182),f335(f310(a927,x67183),x67184))) % 186.01/186.03 [6855]~P76(x68551)+E(f335(f335(f6(a927,x68551),x68552),f311(a927,x68553,f335(a119,x68554))),f2(x68551))+~P1(f335(f335(f244(a927),f335(a119,x68554)),x68553)) % 186.01/186.03 [6994]~P109(x69941)+E(f335(f335(f23(f934(x69941,a922)),f335(f310(x69941,x69942),x69943)),f335(f310(x69941,x69942),x69944)),f335(f310(x69941,x69944),x69943))+~P1(f335(f335(f243(x69941),x69942),x69944)) % 186.01/186.03 [7065]~E(x70653,x70654)+E(x70651,f2(a927))+P1(f335(f335(f337(x70652),x70653),f335(f179(x70652),f176(x70652,x70651,x70654)))) % 186.01/186.03 [7341]~P1(f335(f335(f337(f928(x73411)),x73414),f168(x73411,x73413)))+P1(f335(f335(f337(x73411),x73412),x73413))+~P1(f335(f335(f337(x73411),x73412),f335(f179(x73411),x73414))) % 186.01/186.03 [7348]~P38(x73481,x73482)+P1(f335(f335(f337(x73481),f914(x73482,x73481,x73483)),x73483))+~P1(f335(f335(f337(x73481),x73484),x73483)) % 186.01/186.03 [7403]~P76(x74031)+E(f335(f335(f335(f71(x74031,x74032,f86(x74031)),x74033),f2(x74031)),x74034),f335(f335(f6(x74032,x74031),x74033),x74034))+~P1(f335(f67(x74032),x74034)) % 186.01/186.03 [7405]~P72(x74051)+E(f335(f335(f335(f71(x74051,x74052,f87(x74051)),x74053),f84(x74051)),x74054),f335(f335(f9(x74052,x74051),x74053),x74054))+~P1(f335(f67(x74052),x74054)) % 186.01/186.03 [7433]P26(x74331,x74332,x74333,x74334)+~E(f335(f41(x74332),f335(f318(x74331,x74332,x74333),x74334)),f335(f41(x74331),x74334))+~P1(f335(f67(x74331),x74334)) % 186.01/186.03 [7626]~P76(x76261)+E(f335(f335(f86(x76261),f335(x76262,x76263)),f335(f335(f6(a927,x76261),x76262),f313(a927,x76263,x76264))),f335(f335(f6(a927,x76261),x76262),f311(a927,x76263,x76264)))+~P1(f335(f335(f243(a927),x76263),x76264)) % 186.01/186.03 [7636]~P76(x76361)+~P26(x76362,x76361,x76363,x76364)+E(f335(f335(f6(x76361,x76361),f25(x76361)),f335(f318(x76362,x76361,x76363),x76364)),f335(f335(f6(x76362,x76361),x76363),x76364)) % 186.01/186.03 [7637]~P72(x76371)+~P26(x76372,x76371,x76373,x76374)+E(f335(f335(f9(x76371,x76371),f25(x76371)),f335(f318(x76372,x76371,x76373),x76374)),f335(f335(f9(x76372,x76371),x76373),x76374)) % 186.01/186.03 [7686]E(f335(f41(f935(x76861,x76862)),f321(x76861,x76862,x76863,x76864)),f335(f335(f86(a927),f335(f41(x76861),x76863)),f335(f41(x76862),x76864)))+~P1(f335(f67(x76862),x76864))+~P1(f335(f67(x76861),x76863)) % 186.01/186.03 [7765]E(x77651,x77652)+P1(f335(f335(f337(x77653),x77651),f335(f179(x77653),f177(x77653,x77652,x77654))))+~P1(f335(f335(f337(x77653),x77651),f335(f179(x77653),x77654))) % 186.01/186.03 [7990]~P76(x79901)+E(f335(f335(f86(x79901),f335(f335(f6(a927,x79901),x79902),f335(f310(a927,x79903),x79904))),f335(x79902,x79904)),f335(f335(f6(a927,x79901),x79902),f335(f310(a927,x79903),f335(a119,x79904))))+P1(f335(f335(f244(a927),x79904),x79903)) % 186.01/186.03 [8039]~P26(x80391,x80392,x80393,f250(f934(x80391,a922)))+~P1(f335(f67(x80392),x80394))+P1(f335(f67(x80391),f335(f319(x80391,x80392,x80393),x80394))) % 186.01/186.03 [8153]P1(f335(f335(f337(f928(x81531)),f335(f335(f158(x81531),x81532),x81533)),f168(x81531,x81534)))+~P1(f335(f335(f337(f928(x81531)),x81533),f168(x81531,x81534)))+~P1(f335(f335(f337(x81531),x81532),x81534)) % 186.01/186.03 [8240]~E(f335(f318(x82403,x82401,x82404),f250(f934(x82403,a922))),f250(f934(x82401,a922)))+P1(f335(f67(x82401),x82402))+~P1(f335(f67(x82403),f335(f319(x82403,x82401,x82404),x82402))) % 186.01/186.03 [8332]~P26(x83321,x83323,x83324,x83322)+P1(f335(f67(x83321),x83322))+~P1(f335(f67(x83323),f335(f318(x83321,x83323,x83324),x83322))) % 186.01/186.03 [8354]~E(x83542,x83543)+P1(f335(f335(f337(f933(x83541,x83541)),f335(f335(f260(x83541,x83541),x83542),x83543)),f271(x83541,x83544)))+~P1(f335(f335(f337(x83541),x83542),x83544)) % 186.01/186.03 [8387]~P76(x83871)+E(f335(f335(f86(x83871),f335(f335(f6(a927,x83871),x83872),f311(a927,x83873,x83874))),f335(x83872,f335(a119,x83874))),f335(f335(f6(a927,x83871),x83872),f311(a927,x83873,f335(a119,x83874))))+P1(f335(f335(f244(a927),f335(a119,x83874)),x83873)) % 186.01/186.03 [8447]P1(f335(x84471,x84472))+~P1(f335(x84471,f335(f335(f171(x84473),x84474),f685(x84471,x84474,x84473))))+~P1(f335(f335(f337(x84473),x84472),f335(f179(x84473),x84474))) % 186.01/186.03 [8588]~P1(f335(f335(f337(x85881),x85882),f324(x85881,x85884)))+P1(f335(f335(f337(f928(x85881)),f335(f335(f158(x85881),x85882),x85883)),f324(f928(x85881),f164(x85881,x85884))))+~P1(f335(f335(f337(f928(x85881)),x85883),f324(f928(x85881),f164(x85881,x85884)))) % 186.01/186.03 [8603]~P26(x86032,x86033,x86034,f905(x86034,x86033,x86032,x86031))+P26(x86032,x86033,x86034,f44(f934(x86032,a922),x86031))+E(x86031,f195(f934(f934(x86032,a922),a922))) % 186.01/186.03 [8872]E(x88721,x88722)+~P1(f335(f335(f337(f933(x88723,x88723)),f335(f335(f260(x88723,x88723),x88721),x88722)),f315(x88723,x88724)))+P1(f335(f335(f337(x88723),x88721),f335(f272(x88723,x88723),x88724))) % 186.01/186.03 [9154]E(x91541,f2(a927))+P1(f335(x91542,x91543))+P1(f335(f335(f337(x91544),f797(x91542,x91543,x91541,x91544)),f335(f179(x91544),f176(x91544,x91541,x91543)))) % 186.01/186.03 [9166]E(x91661,f2(a927))+~P1(f335(x91663,x91664))+P1(f335(f335(f337(x91662),f796(x91663,x91664,x91661,x91662)),f335(f179(x91662),f176(x91662,x91661,x91664)))) % 186.01/186.03 [9168]~P27(x91681,x91682,x91683,f250(f934(x91681,a922)),f250(f934(x91682,a922)))+~P1(f335(f67(x91682),x91684))+P1(f335(f67(x91681),f335(f319(x91681,x91682,x91683),x91684))) % 186.01/186.03 [9171]P26(x91712,x91713,x91714,f44(f934(x91712,a922),x91711))+E(x91711,f195(f934(f934(x91712,a922),a922)))+P1(f335(f335(f337(f934(x91712,a922)),f905(x91714,x91713,x91712,x91711)),x91711)) % 186.01/186.03 [9286]~P27(x92863,x92861,x92864,f250(f934(x92863,a922)),f250(f934(x92861,a922)))+P1(f335(f67(x92861),x92862))+~P1(f335(f67(x92863),f335(f319(x92863,x92861,x92864),x92862))) % 186.01/186.03 [9303]P1(f335(f67(x93031),x93032))+~P1(f335(f67(x93034),f335(f318(x93031,x93034,x93033),x93032)))+P1(f335(f335(f337(x93031),f570(x93033,x93034,x93032,x93031)),x93032)) % 186.01/186.03 [9398]~P6(x93982)+E(f335(f335(f70(x93981,x93982,f335(f335(f8(x93982,f934(x93982,x93982),x93981),f117(x93982)),x93983)),f195(x93982)),x93984),f335(f335(f45(x93981,x93982),x93984),x93983))+~P1(f335(f67(x93981),x93984)) % 186.01/186.03 [9399]~P6(x93992)+E(f335(f335(f70(x93991,x93992,f335(f335(f8(x93992,f934(x93992,x93992),x93991),f108(x93992)),x93993)),f250(x93992)),x93994),f335(f335(f46(x93991,x93992),x93994),x93993))+~P1(f335(f67(x93991),x93994)) % 186.01/186.03 [9479]P1(f335(x94791,x94792))+~P1(f335(x94791,f335(f335(f171(x94793),x94794),f722(x94792,x94791,x94794,x94793))))+~P1(f335(f335(f337(x94793),x94792),f335(f179(x94793),x94794))) % 186.01/186.03 [9500]E(x95001,x95002)+~P1(f335(f335(f337(f933(x95003,x95003)),f335(f335(f260(x95003,x95003),x95001),x95002)),f315(x95003,x95004)))+P1(f335(f335(f337(f933(x95003,x95003)),f335(f335(f260(x95003,x95003),x95001),x95002)),f335(f335(f297(x95003,x95003,x95003),x95004),f315(x95003,x95004)))) % 186.01/186.03 [9550]~E(f335(f196(f928(x95501)),x95502),f335(f196(f928(x95501)),x95503))+~P1(f335(f335(f337(f933(f928(x95501),f928(x95501))),f335(f335(f260(f928(x95501),f928(x95501)),x95502),x95503)),f154(x95501,x95504)))+P1(f335(f335(f337(f933(f928(x95501),f928(x95501))),f335(f335(f260(f928(x95501),f928(x95501)),x95502),x95503)),f152(x95501,x95504))) % 186.01/186.03 [9784]P32(x97841,f335(f335(f18(x97841,a922,a922),f335(f335(f8(a922,f934(a922,a922),x97841),a334),f335(f335(f8(a922,a922,x97841),a330),x97842))),f335(a332,x97843)),x97844)+~P1(f335(x97842,x97843))+~P36(x97841,x97842,f335(f335(f158(x97841),x97843),x97844)) % 186.01/186.03 [9951]~P32(x99511,f335(f335(f18(x99511,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99511),a334),f335(f335(f8(a922,a922,x99511),a330),x99512))),f335(a332,x99513)),x99514)+~P1(f335(x99512,x99513))+P36(x99511,x99512,f335(f335(f158(x99511),x99513),x99514)) % 186.01/186.03 [9955]~P36(x99551,x99552,x99554)+~P32(x99551,f335(f335(f18(x99551,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99551),a334),f335(f335(f8(a922,a922,x99551),a330),x99552))),f335(a332,x99553)),x99554)+P36(x99551,x99552,f335(f335(f158(x99551),x99553),x99554)) % 186.01/186.03 [9989]~P5(x99891)+E(f335(f335(f6(a927,x99891),f335(f335(f18(a927,x99891,x99891),f335(f335(f8(x99891,f934(x99891,x99891),a927),f23(x99891)),x99892)),f335(f335(f8(a927,x99891,a927),x99892),f335(f335(f7(a927,a927,a927),f86(a927)),f84(a927))))),f311(a927,x99893,x99894)),f2(x99891))+P1(f335(f335(f243(a927),x99893),x99894)) % 186.01/186.03 [10231]~P38(x102312,x102314)+~P26(x102312,x102311,x102313,f250(f934(x102312,a922)))+P38(x102311,f335(f318(f933(x102312,x102312),f933(x102311,x102311),f266(x102312,x102311,x102312,x102311,x102313,x102313)),x102314)) % 186.01/186.03 [10425]~E(f335(f196(f928(x104251)),x104253),f335(f196(f928(x104251)),x104252))+P1(f335(f335(f337(f933(f928(x104251),f928(x104251))),f335(f335(f260(f928(x104251),f928(x104251)),x104252),x104253)),f165(x104251,x104254)))+~P1(f335(f335(f265(x104251,x104251,a922),f335(f335(f7(x104251,f934(f933(x104251,x104251),a922),f934(x104251,a922)),f335(f335(f8(f934(x104251,f934(f934(f933(x104251,x104251),a922),a922)),f934(f934(f933(x104251,x104251),a922),f934(x104251,a922)),x104251),f7(x104251,f934(f933(x104251,x104251),a922),a922)),f335(f335(f8(f934(x104251,f933(x104251,x104251)),f934(x104251,f934(f934(f933(x104251,x104251),a922),a922)),x104251),f335(f8(f933(x104251,x104251),f934(f934(f933(x104251,x104251),a922),a922),x104251),f337(f933(x104251,x104251)))),f260(x104251,x104251)))),x104254)),f688(x104254,x104253,x104252,x104251))) % 186.01/186.03 [6325]~P63(x63251)+~E(x63252,f2(x63251))+E(f335(f335(f42(x63251),f335(f335(f87(x63251),x63252),x63253)),f335(f335(f87(x63251),x63252),x63254)),f2(x63251)) % 186.01/186.03 [6366]E(x63661,f120(x63662))+E(x63663,f335(f335(f23(a927),f335(f196(f928(x63662)),x63661)),f84(a927)))+E(f151(x63662,f335(f335(f166(x63662,x63661),x63663),x63664)),f151(x63662,x63661)) % 186.01/186.03 [6400]E(x64001,x64002)+P1(f335(x64003,x64002))+~P1(f335(f335(f335(f317(x64004),x64001),x64003),x64002)) % 186.01/186.03 [6416]~P76(x64161)+~P1(f335(f144(x64162),x64164))+E(f335(f172(x64161),f335(f335(f161(x64162,x64161),x64163),x64164)),f335(f335(f6(x64162,x64161),x64163),f335(f179(x64162),x64164))) % 186.01/186.03 [6431]~P72(x64312)+~P1(f335(f67(x64311),x64314))+E(f335(f335(f9(x64311,x64312),f335(f16(x64312,x64311),x64313)),x64314),f335(f335(f252(x64312),x64313),f335(f41(x64311),x64314))) % 186.01/186.03 [6484]~P63(x64842)+E(x64841,f2(x64842))+E(f335(f335(f42(x64842),f335(f335(f87(x64842),x64843),x64841)),f335(f335(f87(x64842),x64844),x64841)),f335(f335(f42(x64842),x64843),x64844)) % 186.01/186.03 [6486]~P66(x64862)+E(x64861,f2(x64862))+E(f335(f335(f299(x64862),f335(f335(f87(x64862),x64863),x64861)),f335(f335(f87(x64862),x64864),x64861)),f335(f335(f299(x64862),x64863),x64864)) % 186.01/186.03 [6487]~P66(x64872)+E(x64871,f2(x64872))+E(f335(f335(f299(x64872),f335(f335(f87(x64872),x64871),x64873)),f335(f335(f87(x64872),x64871),x64874)),f335(f335(f299(x64872),x64873),x64874)) % 186.01/186.03 [6488]~P63(x64882)+E(x64881,f2(x64882))+E(f335(f335(f42(x64882),f335(f335(f87(x64882),x64881),x64883)),f335(f335(f87(x64882),x64881),x64884)),f335(f335(f42(x64882),x64883),x64884)) % 186.01/186.03 [6552]P1(f335(x65521,x65522))+~E(x65523,f335(f335(f86(a927),x65524),x65522))+~P1(f335(x65521,f335(f335(f23(a927),x65523),x65524))) % 186.01/186.03 [6636]~P1(f335(x66362,x66363))+~P1(f335(f167(x66361,x66362),x66364))+P1(f335(f167(x66361,x66362),f335(f335(f158(x66361),x66363),x66364))) % 186.01/186.03 [6677]E(x66771,f120(x66772))+~E(x66773,f335(f335(f23(a927),f335(f196(f928(x66772)),x66771)),f84(a927)))+E(f151(x66772,f335(f335(f166(x66772,x66771),x66773),x66774)),x66774) % 186.01/186.03 [6700]~P103(x67001)+~P1(f335(f335(f243(x67001),x67002),x67004))+P1(f335(f335(f243(x67001),x67002),f335(f335(f117(x67001),x67003),x67004))) % 186.01/186.03 [6701]~P103(x67011)+~P1(f335(f335(f243(x67011),x67012),x67013))+P1(f335(f335(f243(x67011),x67012),f335(f335(f117(x67011),x67013),x67014))) % 186.01/186.03 [6703]~P109(x67031)+~P1(f335(f335(f243(x67031),x67032),x67034))+P1(f335(f335(f243(x67031),x67032),f335(f335(f242(x67031),x67033),x67034))) % 186.01/186.03 [6705]~P109(x67051)+~P1(f335(f335(f243(x67051),x67052),x67053))+P1(f335(f335(f243(x67051),x67052),f335(f335(f242(x67051),x67053),x67054))) % 186.01/186.03 [6706]~P103(x67061)+~P1(f335(f335(f244(x67061),x67062),x67064))+P1(f335(f335(f244(x67061),x67062),f335(f335(f117(x67061),x67063),x67064))) % 186.01/186.03 [6707]~P103(x67071)+~P1(f335(f335(f244(x67071),x67072),x67073))+P1(f335(f335(f244(x67071),x67072),f335(f335(f117(x67071),x67073),x67074))) % 186.01/186.03 [6709]~P109(x67091)+~P1(f335(f335(f244(x67091),x67092),x67094))+P1(f335(f335(f244(x67091),x67092),f335(f335(f242(x67091),x67093),x67094))) % 186.01/186.03 [6711]~P109(x67111)+~P1(f335(f335(f244(x67111),x67112),x67113))+P1(f335(f335(f244(x67111),x67112),f335(f335(f242(x67111),x67113),x67114))) % 186.01/186.03 [6800]~E(f335(f335(f171(x68001),x68002),x68003),x68004)+E(f335(f335(f166(x68001,x68002),x68003),x68004),x68002)+~P1(f335(f335(f244(a927),x68003),f335(f196(f928(x68001)),x68002))) % 186.01/186.03 [6839]P1(f335(x68391,x68392))+~P1(f335(x68393,x68392))+~P1(f335(f335(f243(f934(x68394,a922)),x68393),x68391)) % 186.01/186.03 [6872]~E(f335(f335(f166(x68721,x68722),x68723),x68724),x68722)+E(f335(f335(f171(x68721),x68722),x68723),x68724)+~P1(f335(f335(f244(a927),x68723),f335(f196(f928(x68721)),x68722))) % 186.01/186.03 [6886]~P1(f335(f167(x68861,x68862),x68864))+~P1(f335(f167(x68861,x68862),x68863))+P1(f335(f167(x68861,x68862),f335(f335(f141(x68861),x68863),x68864))) % 186.01/186.03 [6990]E(x69901,f195(f934(x69902,a922)))+E(x69903,f195(f934(x69904,a922)))+~E(f335(f335(f262(x69904,x69902),x69903),f335(f16(f934(x69902,a922),x69904),x69901)),f195(f934(f933(x69904,x69902),a922))) % 186.01/186.03 [7010]E(x70101,x70102)+P1(f335(f335(f337(x70103),x70101),x70104))+~P1(f335(f335(f337(x70103),x70101),f335(f335(f317(x70103),x70102),x70104))) % 186.01/186.03 [7027]~P109(x70271)+P1(f335(f335(f243(x70271),x70272),x70273))+~P1(f335(f335(f243(x70271),x70272),f335(f335(f241(x70271),x70274),x70273))) % 186.01/186.03 [7029]~P109(x70291)+P1(f335(f335(f243(x70291),x70292),x70293))+~P1(f335(f335(f243(x70291),x70292),f335(f335(f241(x70291),x70293),x70294))) % 186.01/186.03 [7031]~P97(x70311)+P1(f335(f335(f243(x70311),x70312),x70313))+~P1(f335(f335(f243(x70311),x70312),f335(f335(f108(x70311),x70314),x70313))) % 186.01/186.03 [7033]~P97(x70331)+P1(f335(f335(f243(x70331),x70332),x70333))+~P1(f335(f335(f243(x70331),x70332),f335(f335(f108(x70331),x70333),x70334))) % 186.01/186.03 [7034]~P109(x70341)+P1(f335(f335(f244(x70341),x70342),x70343))+~P1(f335(f335(f244(x70341),x70342),f335(f335(f241(x70341),x70344),x70343))) % 186.01/186.03 [7035]~P109(x70351)+P1(f335(f335(f244(x70351),x70352),x70353))+~P1(f335(f335(f244(x70351),x70352),f335(f335(f241(x70351),x70353),x70354))) % 186.01/186.03 [7056]~E(f335(f335(f171(x70561),x70563),x70564),x70562)+P1(f335(f335(f337(x70561),x70562),f335(f179(x70561),x70563)))+~P1(f335(f335(f244(a927),x70564),f335(f196(f928(x70561)),x70563))) % 186.01/186.03 [7066]~P109(x70661)+~P14(x70661,f335(f335(f158(x70661),x70662),f335(f335(f158(x70661),x70663),x70664)))+P1(f335(f335(f243(x70661),x70662),x70663)) % 186.01/186.03 [7207]~P32(x72072,x72071,x72073)+P1(f335(x72071,f335(f335(f171(x72072),x72073),x72074)))+~P1(f335(f335(f244(a927),x72074),f335(f196(f928(x72072)),x72073))) % 186.01/186.03 [7225]E(x72251,f2(a1))+E(f335(f335(f42(a1),x72252),x72251),x72253)+~P1(f335(f55(x72252,x72251),f335(f335(f260(a1,a1),x72253),x72254))) % 186.01/186.03 [7246]E(f51(a1,x72462,x72461),x72463)+E(x72461,f2(a1))+~P1(f335(f55(x72462,x72461),f335(f335(f260(a1,a1),x72464),x72463))) % 186.01/186.03 [7365]P1(f335(f335(f337(x73651),x73652),x73653))+~P1(f335(f335(f337(x73651),x73652),x73654))+~P1(f335(f335(f244(f934(x73651,a922)),x73654),x73653)) % 186.01/186.03 [7366]P1(f335(f335(f337(x73661),x73662),x73663))+~P1(f335(f335(f337(x73661),x73662),x73664))+~P1(f335(f335(f243(f934(x73661,a922)),x73664),x73663)) % 186.01/186.03 [7477]P34(x74771,x74772,x74773)+~P1(f335(x74772,f335(f335(f171(x74771),x74773),x74774)))+~P1(f335(f335(f244(a927),x74774),f335(f196(f928(x74771)),x74773))) % 186.01/186.03 [7594]~P108(x75942)+~P1(f335(f335(f244(f934(x75941,x75942)),x75943),x75944))+P1(f335(f335(f243(f934(x75941,x75942)),x75943),x75944)) % 186.01/186.03 [7675]~P25(x76751,x76752,x76754)+P25(x76751,x76752,f335(f335(f317(f926(x76751)),x76753),x76754))+~P25(x76751,x76752,f335(f335(f317(f926(x76751)),x76753),f195(f934(f926(x76751),a922)))) % 186.01/186.03 [7717]~P1(f335(f335(f337(x77171),x77172),x77174))+P1(f335(f335(f337(x77171),x77172),f43(f934(x77171,a922),x77173)))+~P1(f335(f335(f337(f934(x77171,a922)),x77174),x77173)) % 186.01/186.03 [7745]~P85(x77451)+~P1(f335(f335(f243(x77451),x77453),x77454))+P1(f335(f335(f243(x77451),f335(f335(f86(x77451),x77452),x77453)),f335(f335(f86(x77451),x77452),x77454))) % 186.01/186.03 [7746]~P86(x77461)+~P1(f335(f335(f243(x77461),x77463),x77464))+P1(f335(f335(f243(x77461),f335(f335(f86(x77461),x77462),x77463)),f335(f335(f86(x77461),x77462),x77464))) % 186.01/186.03 [7747]~P85(x77471)+~P1(f335(f335(f243(x77471),x77472),x77474))+P1(f335(f335(f243(x77471),f335(f335(f86(x77471),x77472),x77473)),f335(f335(f86(x77471),x77474),x77473))) % 186.01/186.03 [7748]~P86(x77481)+~P1(f335(f335(f243(x77481),x77482),x77484))+P1(f335(f335(f243(x77481),f335(f335(f86(x77481),x77482),x77483)),f335(f335(f86(x77481),x77484),x77483))) % 186.01/186.03 [7749]~P85(x77491)+~P1(f335(f335(f244(x77491),x77493),x77494))+P1(f335(f335(f244(x77491),f335(f335(f86(x77491),x77492),x77493)),f335(f335(f86(x77491),x77492),x77494))) % 186.01/186.03 [7750]~P88(x77501)+~P1(f335(f335(f244(x77501),x77503),x77504))+P1(f335(f335(f244(x77501),f335(f335(f86(x77501),x77502),x77503)),f335(f335(f86(x77501),x77502),x77504))) % 186.01/186.03 [7751]~P85(x77511)+~P1(f335(f335(f244(x77511),x77512),x77514))+P1(f335(f335(f244(x77511),f335(f335(f86(x77511),x77512),x77513)),f335(f335(f86(x77511),x77514),x77513))) % 186.01/186.03 [7752]~P88(x77521)+~P1(f335(f335(f244(x77521),x77522),x77524))+P1(f335(f335(f244(x77521),f335(f335(f86(x77521),x77522),x77523)),f335(f335(f86(x77521),x77524),x77523))) % 186.01/186.03 [7759]~P112(x77591)+~P95(x77591)+E(f335(f335(f23(x77591),f335(f335(f87(x77591),x77592),f335(f110(x77591),x77593))),f335(f335(f87(x77591),x77594),f335(f110(x77591),x77593))),f335(f335(f87(x77591),f335(f335(f23(x77591),x77592),x77594)),f335(f110(x77591),x77593))) % 186.01/186.03 [7760]~P141(x77601)+~P95(x77601)+E(f335(f335(f86(x77601),f335(f335(f87(x77601),x77602),f335(f110(x77601),x77603))),f335(f335(f87(x77601),x77604),f335(f110(x77601),x77603))),f335(f335(f87(x77601),f335(f335(f86(x77601),x77602),x77604)),f335(f110(x77601),x77603))) % 186.01/186.03 [7796]~P76(x77961)+E(f335(f335(f86(x77961),f335(x77962,x77963)),f335(f335(f6(a927,x77961),x77962),f311(a927,f335(a119,x77963),x77964))),f335(f335(f6(a927,x77961),x77962),f311(a927,x77963,x77964)))+~P1(f335(f335(f243(a927),x77963),x77964)) % 186.01/186.03 [7808]~P26(x78082,x78081,x78083,f335(f179(x78082),x78084))+~P1(f335(f144(x78082),x78084))+P1(f335(f144(x78081),f335(f335(f161(x78082,x78081),x78083),x78084))) % 186.01/186.03 [7855]~P1(f335(f335(f243(a927),x78552),x78554))+~P1(f335(f335(f243(a927),x78551),x78553))+P1(f335(f335(f243(a927),f335(f335(f87(a927),x78551),x78552)),f335(f335(f87(a927),x78553),x78554))) % 186.01/186.03 [7856]~P1(f335(f335(f243(a927),x78562),x78564))+~P1(f335(f335(f243(a927),x78561),x78563))+P1(f335(f335(f243(a927),f335(f335(f86(a927),x78561),x78562)),f335(f335(f86(a927),x78563),x78564))) % 186.01/186.03 [7859]~P1(f335(f335(f244(a927),x78592),x78594))+~P1(f335(f335(f244(a927),x78591),x78593))+P1(f335(f335(f244(a927),f335(f335(f86(a927),x78591),x78592)),f335(f335(f86(a927),x78593),x78594))) % 186.01/186.03 [7860]~P1(f335(f335(f243(a1),x78602),x78604))+~P1(f335(f335(f244(a1),x78601),x78603))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x78601),x78602)),f335(f335(f86(a1),x78603),x78604))) % 186.01/186.03 [7907]P1(f335(f335(f337(x79071),x79072),x79073))+~P1(f335(f335(f337(x79071),x79072),f44(f934(x79071,a922),x79074)))+~P1(f335(f335(f337(f934(x79071,a922)),x79073),x79074)) % 186.01/186.03 [7923]~P1(f335(x79231,f683(x79231,x79233,x79232)))+P1(f335(x79231,f335(f335(f171(x79232),x79233),x79234)))+~P1(f335(f335(f244(a927),x79234),f335(f196(f928(x79232)),x79233))) % 186.01/186.03 [7928]P1(f335(x79281,x79282))+~P1(f335(f335(f337(x79284),x79282),f335(f179(x79284),x79283)))+P1(f335(f335(f244(a927),f685(x79281,x79283,x79284)),f335(f196(f928(x79284)),x79283))) % 186.01/186.03 [7975]~P108(x79751)+~P1(f335(f335(f244(f934(x79752,x79751)),x79754),x79753))+~P1(f335(f335(f243(f934(x79752,x79751)),x79753),x79754)) % 186.01/186.03 [8018]~P1(f335(x80184,x80182))+~P1(f335(f335(f337(x80181),x80182),x80183))+P1(f335(f335(f337(x80181),x80182),f335(f335(f108(f934(x80181,a922)),x80183),f335(f270(x80181),x80184)))) % 186.01/186.03 [8160]~P1(f335(f335(f337(x81601),x81603),x81604))+~P1(f335(f335(f244(f934(x81601,a922)),x81602),x81604))+P1(f335(f335(f244(f934(x81601,a922)),x81602),f335(f335(f317(x81601),x81603),x81604))) % 186.01/186.03 [8162]E(f335(f335(f108(f934(x81621,a922)),x81622),x81623),f195(f934(x81621,a922)))+~E(f335(f335(f108(f934(x81621,a922)),f43(f934(x81621,a922),x81624)),x81623),f195(f934(x81621,a922)))+~P1(f335(f335(f337(f934(x81621,a922)),x81622),x81624)) % 186.01/186.03 [8236]P1(f335(f335(f337(x82361),x82362),x82363))+~P1(f335(f335(f243(f934(x82361,a922)),x82363),f335(f335(f317(x82361),x82362),x82364)))+P1(f335(f335(f243(f934(x82361,a922)),x82363),x82364)) % 186.01/186.03 [8253]P1(f335(f335(f337(x82532),f683(x82531,x82533,x82532)),f335(f179(x82532),x82533)))+P1(f335(x82531,f335(f335(f171(x82532),x82533),x82534)))+~P1(f335(f335(f244(a927),x82534),f335(f196(f928(x82532)),x82533))) % 186.01/186.03 [8261]~P1(f335(f335(f243(f934(x82611,a922)),x82612),x82614))+P1(f335(f335(f243(f934(x82611,a922)),x82612),x82613))+~P1(f335(f335(f243(f934(x82611,a922)),x82614),x82613)) % 186.01/186.03 [8262]~P1(f335(f335(f244(f934(x82621,a922)),x82622),x82624))+~P1(f335(f335(f243(f934(x82621,a922)),x82624),x82623))+P1(f335(f335(f244(f934(x82621,a922)),x82622),x82623)) % 186.01/186.03 [8263]~P1(f335(f335(f243(f934(x82631,a922)),x82632),x82634))+~P1(f335(f335(f244(f934(x82631,a922)),x82634),x82633))+P1(f335(f335(f244(f934(x82631,a922)),x82632),x82633)) % 186.01/186.03 [8264]~P1(f335(f335(f244(f934(x82641,a922)),x82642),x82644))+P1(f335(f335(f244(f934(x82641,a922)),x82642),x82643))+~P1(f335(f335(f244(f934(x82641,a922)),x82644),x82643)) % 186.01/186.03 [8308]~P1(f335(f335(f337(x83081),x83084),x83083))+~P1(f335(f335(f244(f934(x83081,a922)),x83082),f335(f335(f317(x83081),x83084),x83083)))+P1(f335(f335(f244(f934(x83081,a922)),x83082),x83083)) % 186.01/186.03 [8319]~P85(x83191)+P1(f335(f335(f243(x83191),x83192),x83193))+~P1(f335(f335(f243(x83191),f335(f335(f86(x83191),x83194),x83192)),f335(f335(f86(x83191),x83194),x83193))) % 186.01/186.03 [8321]~P85(x83211)+P1(f335(f335(f243(x83211),x83212),x83213))+~P1(f335(f335(f243(x83211),f335(f335(f86(x83211),x83212),x83214)),f335(f335(f86(x83211),x83213),x83214))) % 186.01/186.03 [8323]~P85(x83231)+P1(f335(f335(f244(x83231),x83232),x83233))+~P1(f335(f335(f244(x83231),f335(f335(f86(x83231),x83234),x83232)),f335(f335(f86(x83231),x83234),x83233))) % 186.01/186.03 [8325]~P85(x83251)+P1(f335(f335(f244(x83251),x83252),x83253))+~P1(f335(f335(f244(x83251),f335(f335(f86(x83251),x83252),x83254)),f335(f335(f86(x83251),x83253),x83254))) % 186.01/186.03 [8371]P1(f335(x83711,x83712))+~E(f335(f335(f145(x83713),f335(f196(f928(x83713)),f184(x83713,x83711,x83714))),x83714),f120(x83713))+~P1(f335(f335(f337(x83713),x83712),f335(f179(x83713),x83714))) % 186.01/186.03 [8490]P1(f335(x84901,x84902))+~P1(f335(f335(f337(x84903),x84902),f335(f179(x84903),x84904)))+P1(f335(f335(f244(a927),f335(f196(f928(x84903)),f335(f143(x84903,x84901),x84904))),f335(f196(f928(x84903)),x84904))) % 186.01/186.03 [8979]~P1(f335(x89791,f775(x89791,x89793,x89792,x89794)))+P1(f335(x89791,f335(f335(f171(x89792),x89793),x89794)))+~P1(f335(f335(f244(a927),x89794),f335(f196(f928(x89792)),x89793))) % 186.01/186.03 [9003]~P26(x90034,x90033,x90031,f250(f934(x90034,a922)))+E(f335(x90031,f462(x90032,x90031,x90033,x90034)),x90032)+~P1(f335(f335(f337(x90033),x90032),f335(f318(x90034,x90033,x90031),f250(f934(x90034,a922))))) % 186.01/186.03 [9071]E(f184(x90711,x90712,x90713),f335(f335(f182(x90711),x90714),x90713))+P1(f335(f335(f244(a927),f746(x90712,x90713,x90711,x90714)),x90714))+P1(f335(f335(f244(a927),x90714),f335(f196(f928(x90711)),x90713))) % 186.01/186.03 [9074]E(f184(x90741,x90742,x90743),f335(f335(f182(x90741),x90744),x90743))+P1(f335(f335(f244(a927),f746(x90742,x90743,x90741,x90744)),x90744))+P1(f335(x90742,f335(f335(f171(x90741),x90743),x90744))) % 186.01/186.03 [9109]P1(f335(x91091,x91092))+~P1(f335(f335(f337(x91094),x91092),f335(f179(x91094),x91093)))+P1(f335(f335(f244(a927),f722(x91092,x91091,x91093,x91094)),f335(f196(f928(x91094)),x91093))) % 186.01/186.03 [9111]E(f184(x91111,x91112,x91113),f335(f335(f182(x91111),x91114),x91113))+P1(f335(f335(f244(a927),x91114),f335(f196(f928(x91111)),x91113)))+P1(f335(f335(f244(a927),f746(x91112,x91113,x91111,x91114)),f335(f196(f928(x91111)),x91113))) % 186.01/186.03 [9118]E(f184(x91181,x91182,x91183),f335(f335(f182(x91181),x91184),x91183))+P1(f335(x91182,f335(f335(f171(x91181),x91183),x91184)))+P1(f335(f335(f244(a927),f746(x91182,x91183,x91181,x91184)),f335(f196(f928(x91181)),x91183))) % 186.01/186.03 [9145]~P125(x91454)+P1(f335(f335(f337(x91451),f666(x91452,x91453,x91451,x91454)),x91453))+P1(f335(f335(f244(x91454),f2(x91454)),f335(f335(f9(x91451,x91454),x91452),x91453))) % 186.01/186.03 [9146]~P125(x91464)+P1(f335(f335(f337(x91461),f670(x91462,x91463,x91461,x91464)),x91463))+P1(f335(f335(f243(x91464),f2(x91464)),f335(f335(f9(x91461,x91464),x91462),x91463))) % 186.01/186.03 [9173]~P1(f335(f67(x91731),x91734))+P1(f335(f335(f337(x91731),f427(x91732,x91733,x91734,x91731)),x91734))+P1(f335(f67(f933(x91731,x91733)),f335(f335(f262(x91731,x91733),x91734),x91732))) % 186.01/186.03 [9205]P1(f335(f335(f337(x92052),f775(x92051,x92053,x92052,x92054)),f335(f179(x92052),x92053)))+P1(f335(x92051,f335(f335(f171(x92052),x92053),x92054)))+~P1(f335(f335(f244(a927),x92054),f335(f196(f928(x92052)),x92053))) % 186.01/186.03 [9335]P1(f335(f335(f243(a927),x93354),f335(f196(f928(x93352)),f184(x93352,x93353,x93351))))+P1(f335(f335(f244(a927),f747(x93351,x93352,x93353,x93354)),x93354))+~P1(f335(f335(f243(a927),x93354),f335(f196(f928(x93352)),x93351))) % 186.01/186.03 [9483]E(f184(x94831,x94832,x94833),f335(f335(f182(x94831),x94834),x94833))+~P1(f335(x94832,f335(f335(f171(x94831),x94833),f746(x94832,x94833,x94831,x94834))))+P1(f335(f335(f244(a927),x94834),f335(f196(f928(x94831)),x94833))) % 186.01/186.03 [9490]E(f184(x94901,x94902,x94903),f335(f335(f182(x94901),x94904),x94903))+~P1(f335(x94902,f335(f335(f171(x94901),x94903),f746(x94902,x94903,x94901,x94904))))+P1(f335(x94902,f335(f335(f171(x94901),x94903),x94904))) % 186.01/186.03 [9494]~P1(f335(f67(x94941),x94943))+~P1(f335(f67(x94942),f335(x94944,f427(x94944,x94942,x94943,x94941))))+P1(f335(f67(f933(x94941,x94942)),f335(f335(f262(x94941,x94942),x94943),x94944))) % 186.01/186.03 [9502]~P125(x95021)+~P1(f335(f335(f243(x95021),f2(x95021)),f335(x95023,f670(x95023,x95024,x95022,x95021))))+P1(f335(f335(f243(x95021),f2(x95021)),f335(f335(f9(x95022,x95021),x95023),x95024))) % 186.01/186.03 [9503]~P125(x95031)+~P1(f335(f335(f244(x95031),f2(x95031)),f335(x95033,f666(x95033,x95034,x95032,x95031))))+P1(f335(f335(f244(x95031),f2(x95031)),f335(f335(f9(x95032,x95031),x95033),x95034))) % 186.01/186.03 [9511]~E(f335(f196(f928(x95114)),x95112),f335(f196(f928(x95114)),x95113))+P1(f335(f335(f337(f933(f928(x95114),f928(x95114))),f335(f335(f260(f928(x95114),f928(x95114)),x95113),x95112)),f165(x95114,x95111)))+P1(f335(f335(f244(a927),f671(x95111,x95112,x95113,x95114)),f335(f196(f928(x95114)),x95113))) % 186.01/186.03 [9563]~P1(f335(x95633,f335(f335(f171(x95632),x95634),f747(x95634,x95632,x95633,x95631))))+P1(f335(f335(f243(a927),x95631),f335(f196(f928(x95632)),f184(x95632,x95633,x95634))))+~P1(f335(f335(f243(a927),x95631),f335(f196(f928(x95632)),x95634))) % 186.01/186.03 [9642]E(f335(f335(f182(x96421),f684(x96422,x96423,x96424,x96421)),x96423),f335(f335(f182(x96421),f684(x96422,x96423,x96424,x96421)),x96424))+~P1(f335(f335(f337(f933(f928(x96421),f928(x96421))),f335(f335(f260(f928(x96421),f928(x96421)),x96424),x96423)),f154(x96421,x96422)))+P1(f335(f335(f244(a927),f335(f196(f928(x96421)),x96424)),f335(f196(f928(x96421)),x96423))) % 186.01/186.03 [9698]~P1(f335(f335(f244(a927),f2(a927)),x96983))+~P1(f335(f335(f244(a927),x96984),x96981))+P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),x96981),f51(a927,x96982,x96983))),x96984)),f335(f335(f87(a927),x96981),x96983))) % 186.01/186.03 [9890]~P108(x98902)+~P1(f335(f335(f243(x98902),f335(x98903,f428(x98904,x98903,x98901,x98902))),f335(x98904,f428(x98904,x98903,x98901,x98902))))+P1(f335(f335(f243(f934(x98901,x98902)),x98903),x98904)) % 186.01/186.03 [9994]~P5(x99941)+E(f335(f335(f6(a927,x99941),f335(f335(f18(a927,x99941,x99941),f335(f335(f8(x99941,f934(x99941,x99941),a927),f23(x99941)),x99942)),f335(f335(f8(a927,x99941,a927),x99942),f335(f335(f7(a927,a927,a927),f86(a927)),f84(a927))))),f311(a927,x99943,x99944)),f335(f335(f23(x99941),f335(x99942,x99943)),f335(x99942,f335(f335(f86(a927),x99944),f84(a927)))))+~P1(f335(f335(f243(a927),x99943),x99944)) % 186.01/186.03 [10070]~P38(x100703,f335(f335(f297(x100703,x100703,x100703),x100702),f315(x100703,x100702)))+~P1(f335(f335(f337(f933(x100703,x100703)),f335(f335(f260(x100703,x100703),f335(x100701,f335(a119,f853(x100702,x100701,x100703)))),f335(x100701,f853(x100702,x100701,x100703)))),f315(x100703,x100702)))+E(f335(x100701,f335(f335(f86(a927),f855(x100702,x100701,x100703)),x100704)),f335(x100701,f855(x100702,x100701,x100703))) % 186.01/186.03 [7060]E(f335(f335(f141(x70601),x70602),x70603),x70604)+~E(x70603,f335(f335(f145(x70601),f335(f196(f928(x70601)),x70602)),x70604))+~E(f335(f335(f182(x70601),f335(f196(f928(x70601)),x70602)),x70604),x70602) % 186.01/186.03 [7113]~P67(x71132)+E(x71131,f2(x71132))+E(f335(f335(f299(x71132),f335(f335(f252(x71132),x71133),x71134)),f335(f335(f252(x71132),x71131),x71134)),f335(f335(f252(x71132),f335(f335(f299(x71132),x71133),x71131)),x71134)) % 186.01/186.03 [7262]~P97(x72621)+~P1(f335(f335(f243(x72621),x72623),x72624))+P1(f335(f335(f243(x72621),f335(f335(f108(x72621),x72622),x72623)),x72624)) % 186.01/186.03 [7263]~P97(x72631)+~P1(f335(f335(f243(x72631),x72632),x72634))+P1(f335(f335(f243(x72631),f335(f335(f108(x72631),x72632),x72633)),x72634)) % 186.01/186.03 [7265]~P109(x72651)+~P1(f335(f335(f243(x72651),x72653),x72654))+P1(f335(f335(f243(x72651),f335(f335(f241(x72651),x72652),x72653)),x72654)) % 186.01/186.03 [7267]~P109(x72671)+~P1(f335(f335(f243(x72671),x72672),x72674))+P1(f335(f335(f243(x72671),f335(f335(f241(x72671),x72672),x72673)),x72674)) % 186.01/186.03 [7268]~P97(x72681)+~P1(f335(f335(f244(x72681),x72683),x72684))+P1(f335(f335(f244(x72681),f335(f335(f108(x72681),x72682),x72683)),x72684)) % 186.01/186.03 [7269]~P97(x72691)+~P1(f335(f335(f244(x72691),x72692),x72694))+P1(f335(f335(f244(x72691),f335(f335(f108(x72691),x72692),x72693)),x72694)) % 186.01/186.03 [7271]~P109(x72711)+~P1(f335(f335(f244(x72711),x72713),x72714))+P1(f335(f335(f244(x72711),f335(f335(f241(x72711),x72712),x72713)),x72714)) % 186.01/186.03 [7273]~P109(x72731)+~P1(f335(f335(f244(x72731),x72732),x72734))+P1(f335(f335(f244(x72731),f335(f335(f241(x72731),x72732),x72733)),x72734)) % 186.01/186.03 [7296]~P1(f335(x72963,x72964))+~P1(f335(x72962,x72964))+P1(f335(f335(f335(f108(f934(x72961,a922)),x72962),x72963),x72964)) % 186.01/186.03 [7420]P25(x74201,x74202,x74203)+~P25(x74201,x74202,x74204)+~P1(f335(f335(f243(f934(f926(x74201),a922)),x74203),x74204)) % 186.01/186.03 [7559]~P63(x75591)+E(f335(f335(f42(x75591),f335(f335(f252(x75591),x75592),x75593)),f335(f335(f252(x75591),x75594),x75593)),f335(f335(f252(x75591),f335(f335(f42(x75591),x75592),x75594)),x75593))+~P1(f335(f335(f295(x75591),x75594),x75592)) % 186.01/186.03 [7786]~P76(x77861)+E(f335(f335(f86(x77861),f335(x77862,x77863)),f335(f335(f6(a927,x77861),x77862),f335(f310(a927,f335(a119,x77863)),x77864))),f335(f335(f6(a927,x77861),x77862),f335(f310(a927,x77863),x77864)))+~P1(f335(f335(f244(a927),x77863),x77864)) % 186.01/186.03 [7804]E(x78041,x78042)+P1(f335(f335(f179(x78043),x78044),x78042))+~P1(f335(f335(f179(x78043),f335(f335(f158(x78043),x78041),x78044)),x78042)) % 186.01/186.03 [7816]~P109(x78161)+P1(f335(f335(f243(x78161),x78162),x78163))+~P1(f335(f335(f243(x78161),f335(f335(f242(x78161),x78164),x78162)),x78163)) % 186.01/186.03 [7818]~P109(x78181)+P1(f335(f335(f243(x78181),x78182),x78183))+~P1(f335(f335(f243(x78181),f335(f335(f242(x78181),x78182),x78184)),x78183)) % 186.01/186.03 [7820]~P103(x78201)+P1(f335(f335(f243(x78201),x78202),x78203))+~P1(f335(f335(f243(x78201),f335(f335(f117(x78201),x78204),x78202)),x78203)) % 186.01/186.03 [7822]~P103(x78221)+P1(f335(f335(f243(x78221),x78222),x78223))+~P1(f335(f335(f243(x78221),f335(f335(f117(x78221),x78222),x78224)),x78223)) % 186.01/186.03 [7823]~P109(x78231)+P1(f335(f335(f244(x78231),x78232),x78233))+~P1(f335(f335(f244(x78231),f335(f335(f242(x78231),x78234),x78232)),x78233)) % 186.01/186.03 [7824]~P109(x78241)+P1(f335(f335(f244(x78241),x78242),x78243))+~P1(f335(f335(f244(x78241),f335(f335(f242(x78241),x78242),x78244)),x78243)) % 186.01/186.03 [7899]~P1(f335(f335(f337(x78991),x78992),x78994))+P1(f335(f335(f337(x78991),x78992),x78993))+P1(f335(f335(f337(x78991),x78992),f335(f335(f23(f934(x78991,a922)),x78994),x78993))) % 186.01/186.03 [7982]P1(f335(x79821,x79822))+P1(f335(x79823,x79822))+~P1(f335(f335(f335(f117(f934(x79824,a922)),x79823),x79821),x79822)) % 186.01/186.03 [7993]~P1(f335(f335(f337(x79931),x79932),x79934))+~P1(f335(f335(f337(x79931),x79932),x79933))+P1(f335(f335(f337(x79931),x79932),f335(f335(f108(f934(x79931,a922)),x79933),x79934))) % 186.01/186.03 [8040]~P97(x80401)+~P1(f335(f67(x80401),x80404))+E(f335(f335(f70(x80401,x80401,f108(x80401)),x80402),f335(f335(f317(x80401),x80403),x80404)),f335(f335(f108(x80401),x80403),f335(f335(f70(x80401,x80401,f108(x80401)),x80402),x80404))) % 186.01/186.03 [8041]~P103(x80411)+~P1(f335(f67(x80411),x80414))+E(f335(f335(f70(x80411,x80411,f117(x80411)),x80412),f335(f335(f317(x80411),x80413),x80414)),f335(f335(f117(x80411),x80413),f335(f335(f70(x80411,x80411,f117(x80411)),x80412),x80414))) % 186.01/186.03 [8042]~P109(x80421)+~P1(f335(f67(x80421),x80424))+E(f335(f335(f70(x80421,x80421,f241(x80421)),x80422),f335(f335(f317(x80421),x80423),x80424)),f335(f335(f241(x80421),x80423),f335(f335(f70(x80421,x80421,f241(x80421)),x80422),x80424))) % 186.01/186.03 [8043]~P109(x80431)+~P1(f335(f67(x80431),x80434))+E(f335(f335(f70(x80431,x80431,f242(x80431)),x80432),f335(f335(f317(x80431),x80433),x80434)),f335(f335(f242(x80431),x80433),f335(f335(f70(x80431,x80431,f242(x80431)),x80432),x80434))) % 186.01/186.03 [8044]~P112(x80441)+~P95(x80441)+E(f335(f335(f23(x80441),f335(f335(f87(x80441),f335(f110(x80441),x80442)),x80443)),f335(f335(f87(x80441),f335(f110(x80441),x80442)),x80444)),f335(f335(f87(x80441),f335(f110(x80441),x80442)),f335(f335(f23(x80441),x80443),x80444))) % 186.01/186.03 [8045]~P141(x80451)+~P95(x80451)+E(f335(f335(f86(x80451),f335(f335(f87(x80451),f335(f110(x80451),x80452)),x80453)),f335(f335(f87(x80451),f335(f110(x80451),x80452)),x80454)),f335(f335(f87(x80451),f335(f110(x80451),x80452)),f335(f335(f86(x80451),x80453),x80454))) % 186.01/186.03 [8158]E(x81581,x81582)+P1(f335(f335(f337(x81583),x81581),f335(f179(x81583),x81584)))+~P1(f335(f335(f337(x81583),x81581),f335(f179(x81583),f335(f335(f158(x81583),x81582),x81584)))) % 186.01/186.03 [8330]P56(x83301,x83302,x83303)+~P56(x83301,x83302,x83304)+~P1(f335(f335(f243(f934(f933(x83301,x83302),a922)),x83303),x83304)) % 186.01/186.03 [8373]P1(f335(f335(f337(x83731),x83732),x83733))+P1(f335(f335(f337(x83731),x83732),x83734))+~P1(f335(f335(f337(x83731),x83732),f335(f335(f117(f934(x83731,a922)),x83734),x83733))) % 186.01/186.03 [8383]~P54(x83831,x83834,x83833)+~P1(f335(f335(f337(x83831),x83832),x83834))+P1(f335(f335(f337(f933(x83831,x83831)),f335(f335(f260(x83831,x83831),x83832),x83832)),x83833)) % 186.01/186.03 [8395]~P1(f335(f67(x83952),x83954))+~P1(f335(f67(x83951),x83953))+P1(f335(f67(f933(x83951,x83952)),f335(f335(f262(x83951,x83952),x83953),f335(f16(f934(x83952,a922),x83951),x83954)))) % 186.01/186.03 [8396]~P1(f335(f335(f337(x83961),x83962),x83964))+~P1(f335(f335(f243(f934(x83961,a922)),x83963),x83964))+P1(f335(f335(f243(f934(x83961,a922)),f335(f335(f317(x83961),x83962),x83963)),x83964)) % 186.01/186.03 [8403]~P72(x84032)+~P146(x84032)+E(f335(f335(f9(x84031,x84032),f335(f335(f8(a927,x84032,x84031),f107(x84032)),x84033)),x84034),f335(f107(x84032),f335(f335(f9(x84031,a927),x84033),x84034))) % 186.01/186.03 [8404]~P72(x84042)+~P140(x84042)+E(f335(f335(f9(x84041,x84042),f335(f335(f8(a1,x84042,x84041),f109(x84042)),x84043)),x84044),f335(f109(x84042),f335(f335(f9(x84041,a1),x84043),x84044))) % 186.01/186.03 [8428]E(f335(f335(f23(f934(x84281,a922)),x84282),f335(f335(f23(f934(x84281,a922)),x84283),x84284)),x84284)+~P1(f335(f335(f243(f934(x84281,a922)),x84282),x84283))+~P1(f335(f335(f243(f934(x84281,a922)),x84284),x84282)) % 186.01/186.03 [8526]~P1(f335(f67(x85261),x85264))+E(f335(f335(f23(a927),f335(f335(f6(x85261,a927),x85262),x85263)),f335(f335(f6(x85261,a927),x85262),x85264)),f335(f335(f6(x85261,a927),x85262),f335(f335(f23(f934(x85261,a922)),x85263),x85264)))+~P1(f335(f335(f243(f934(x85261,a922)),x85264),x85263)) % 186.01/186.03 [8677]~P9(x86771,x86774,x86773)+~P1(f335(f335(f337(x86771),x86772),x86774))+P1(f335(f335(f337(x86771),x86772),f335(f293(x86771,x86771,x86773),f335(f335(f317(x86771),x86772),f195(f934(x86771,a922)))))) % 186.01/186.03 [8738]~P1(f335(f335(f243(f934(x87381,a922)),x87382),x87383))+~P1(f335(f335(f243(f934(x87381,a922)),x87382),x87384))+P1(f335(f335(f243(f934(x87381,a922)),x87382),f335(f335(f108(f934(x87381,a922)),x87383),x87384))) % 186.01/186.03 [8840]E(x88401,f195(f934(x88402,a922)))+P1(f335(f67(x88403),x88404))+~P1(f335(f67(f933(x88403,x88402)),f335(f335(f262(x88403,x88402),x88404),f335(f16(f934(x88402,a922),x88403),x88401)))) % 186.01/186.03 [8841]E(x88411,f195(f934(x88412,a922)))+P1(f335(f67(x88413),x88414))+~P1(f335(f67(f933(x88412,x88413)),f335(f335(f262(x88412,x88413),x88411),f335(f16(f934(x88413,a922),x88412),x88414)))) % 186.01/186.03 [8914]P1(f335(f335(f337(x89141),x89142),f324(x89141,x89143)))+~P1(f335(f335(f337(x89141),x89144),f324(x89141,x89143)))+~P1(f335(f335(f337(f933(x89141,x89141)),f335(f335(f260(x89141,x89141),x89142),x89144)),x89143)) % 186.01/186.03 [8971]~P38(x89711,x89714)+P1(f335(f335(f337(f933(x89711,x89711)),f335(f335(f260(x89711,x89711),x89713),x89712)),f315(x89711,x89714)))+P38(x89711,f335(f335(f317(f933(x89711,x89711)),f335(f335(f260(x89711,x89711),x89712),x89713)),x89714)) % 186.01/186.03 [8972]~P59(x89721,x89724)+P1(f335(f335(f337(f933(x89721,x89721)),f335(f335(f260(x89721,x89721),x89723),x89722)),f315(x89721,x89724)))+P59(x89721,f335(f335(f317(f933(x89721,x89721)),f335(f335(f260(x89721,x89721),x89722),x89723)),x89724)) % 186.01/186.03 [9054]~E(x90542,x90543)+~P1(f335(f335(f337(x90541),x90542),f335(f179(x90541),x90544)))+P1(f335(f335(f337(f933(x90541,x90541)),f335(f335(f260(x90541,x90541),x90542),x90543)),f335(f179(f933(x90541,x90541)),f335(f335(f188(x90541,x90541),x90544),x90544)))) % 186.01/186.03 [9144]~E(x91443,x91444)+P1(f335(f335(f265(x91441,x91441,a922),a332),x91442))+~P1(f335(f335(f337(f933(x91441,x91441)),x91442),f335(f179(f933(x91441,x91441)),f335(f335(f188(x91441,x91441),x91443),x91444)))) % 186.01/186.03 [9190]P1(f335(f335(f337(f933(f928(x91901),f928(x91901))),f335(f335(f260(f928(x91901),f928(x91901)),x91902),x91903)),f154(x91901,x91904)))+~E(f335(f335(f182(x91901),f335(f196(f928(x91901)),x91902)),x91903),x91902)+~P1(f335(f335(f244(a927),f335(f196(f928(x91901)),x91902)),f335(f196(f928(x91901)),x91903))) % 186.01/186.03 [9193]~P53(x91931,x91934)+~P1(f335(f335(f337(f933(x91931,x91931)),f335(f335(f260(x91931,x91931),x91933),x91932)),x91934))+P1(f335(f335(f337(f933(x91931,x91931)),f335(f335(f260(x91931,x91931),x91932),x91933)),x91934)) % 186.01/186.03 [9284]~P1(f335(f67(x92841),x92844))+P1(f335(f335(f337(x92841),f345(x92842,x92843,x92844,x92841)),x92844))+P1(f335(f67(x92843),f335(f335(f45(x92841,f934(x92843,a922)),x92844),x92842))) % 186.01/186.03 [9285]~P1(f335(f67(x92851),x92854))+P1(f335(f335(f337(x92851),f592(x92852,x92853,x92854,x92851)),x92854))+P1(f335(f67(x92853),f335(f335(f45(x92851,f934(x92853,a922)),x92854),x92852))) % 186.01/186.03 [9371]P1(f335(f335(f337(f933(x93711,x93711)),x93712),f335(f335(f297(x93711,x93711,x93711),x93713),f315(x93711,x93713))))+~P1(f335(f335(f244(a927),f2(a927)),x93714))+~P1(f335(f335(f337(f933(x93711,x93711)),x93712),f335(f335(f190(f933(x93711,x93711),a922),x93714),x93713))) % 186.01/186.03 [9379]~P38(x93791,x93792)+~P1(f335(f335(f337(f933(x93791,x93791)),f335(f335(f260(x93791,x93791),x93794),x93793)),x93792))+~P1(f335(f335(f337(f933(x93791,x93791)),f335(f335(f260(x93791,x93791),x93793),x93794)),x93792)) % 186.01/186.03 [9501]~P1(f335(f67(x95011),x95014))+E(f335(f335(f6(x95011,a927),f335(f335(f8(f934(x95012,a922),a927,x95011),f41(x95012)),x95013)),x95014),f335(f41(f933(x95011,x95012)),f335(f335(f262(x95011,x95012),x95014),x95013)))+P1(f335(f335(f337(x95011),f410(x95013,x95012,x95014,x95011)),x95014)) % 186.01/186.03 [9505]~P1(f335(f144(x95051),x95052))+P1(f335(f144(x95051),f335(f335(f166(x95051,x95052),x95053),x95054)))+P1(f335(f335(f337(x95051),x95054),f335(f335(f23(f934(x95051,a922)),f335(f179(x95051),x95052)),f335(f335(f317(x95051),f335(f335(f171(x95051),x95052),x95053)),f195(f934(x95051,a922)))))) % 186.01/186.03 [9522]~P1(f335(f67(x95222),x95223))+~P1(f335(f67(x95221),f335(x95224,f345(x95224,x95221,x95223,x95222))))+P1(f335(f67(x95221),f335(f335(f45(x95222,f934(x95221,a922)),x95223),x95224))) % 186.01/186.03 [9523]~P1(f335(f67(x95232),x95233))+~P1(f335(f67(x95231),f335(x95234,f592(x95234,x95231,x95233,x95232))))+P1(f335(f67(x95231),f335(f335(f45(x95232,f934(x95231,a922)),x95233),x95234))) % 186.01/186.03 [9601]~P1(f335(f335(f337(f933(x96011,x96011)),x96012),f335(f335(f297(x96011,x96011,x96011),x96014),f315(x96011,x96014))))+P1(f335(f335(f337(f933(x96011,x96011)),x96012),f335(f335(f297(x96011,x96011,x96011),x96013),f315(x96011,x96013))))+~P1(f335(f335(f243(f934(f933(x96011,x96011),a922)),x96014),x96013)) % 186.01/186.03 [9609]E(f335(f335(f182(x96091),f684(x96094,x96093,x96092,x96091)),x96093),f335(f335(f182(x96091),f684(x96094,x96093,x96092,x96091)),x96092))+~P1(f335(f335(f337(f933(f928(x96091),f928(x96091))),f335(f335(f260(f928(x96091),f928(x96091)),x96092),x96093)),f154(x96091,x96094)))+E(f335(f335(f182(x96091),f335(f196(f928(x96091)),x96092)),x96093),x96092) % 186.01/186.03 [9625]~P1(f335(f67(x96251),x96254))+E(f335(f335(f6(x96251,a927),f335(f335(f8(f934(x96252,a922),a927,x96251),f41(x96252)),x96253)),x96254),f335(f41(f933(x96251,x96252)),f335(f335(f262(x96251,x96252),x96254),x96253)))+~P1(f335(f67(x96252),f335(x96253,f410(x96253,x96252,x96254,x96251)))) % 186.01/186.03 [9629]~E(f335(f196(f928(x96291)),x96293),f335(f196(f928(x96291)),x96292))+P1(f335(f335(f337(f933(f928(x96291),f928(x96291))),f335(f335(f260(f928(x96291),f928(x96291)),x96292),x96293)),f165(x96291,x96294)))+P1(f335(f335(f337(f933(x96291,x96291)),f688(x96294,x96293,x96292,x96291)),f335(f179(f933(x96291,x96291)),f335(f335(f188(x96291,x96291),x96292),x96293)))) % 186.01/186.03 [9709]~P1(f335(f335(f337(f933(f928(x97091),f928(x97091))),f335(f335(f260(f928(x97091),f928(x97091)),x97092),x97093)),f154(x97091,x97094)))+E(f335(f335(f182(x97091),f335(f196(f928(x97091)),x97092)),x97093),x97092)+P1(f335(f335(f244(a927),f684(x97094,x97093,x97092,x97091)),f335(f335(f241(a927),f335(f196(f928(x97091)),x97092)),f335(f196(f928(x97091)),x97093)))) % 186.01/186.03 [9733]~P1(f335(f335(f337(f933(f928(x97331),f928(x97331))),f335(f335(f260(f928(x97331),f928(x97331)),x97332),x97333)),f154(x97331,x97334)))+P1(f335(f335(f244(a927),f335(f196(f928(x97331)),x97332)),f335(f196(f928(x97331)),x97333)))+P1(f335(f335(f244(a927),f684(x97334,x97333,x97332,x97331)),f335(f335(f241(a927),f335(f196(f928(x97331)),x97332)),f335(f196(f928(x97331)),x97333)))) % 186.01/186.03 [10138]~P1(f335(f335(f337(f933(f928(x101381),f928(x101381))),f335(f335(f260(f928(x101381),f928(x101381)),x101382),x101383)),f154(x101381,x101384)))+E(f335(f335(f182(x101381),f335(f196(f928(x101381)),x101382)),x101383),x101382)+P1(f335(f335(f337(f933(x101381,x101381)),f335(f335(f260(x101381,x101381),f335(f335(f171(x101381),x101382),f684(x101384,x101383,x101382,x101381))),f335(f335(f171(x101381),x101383),f684(x101384,x101383,x101382,x101381)))),x101384)) % 186.01/186.03 [10139]~P1(f335(f335(f337(f933(f928(x101391),f928(x101391))),f335(f335(f260(f928(x101391),f928(x101391)),x101392),x101393)),f154(x101391,x101394)))+P1(f335(f335(f244(a927),f335(f196(f928(x101391)),x101392)),f335(f196(f928(x101391)),x101393)))+P1(f335(f335(f337(f933(x101391,x101391)),f335(f335(f260(x101391,x101391),f335(f335(f171(x101391),x101392),f684(x101394,x101393,x101392,x101391))),f335(f335(f171(x101391),x101393),f684(x101394,x101393,x101392,x101391)))),x101394)) % 186.01/186.03 [10209]~E(f335(f196(f928(x102091)),x102092),f335(f196(f928(x102091)),x102093))+P1(f335(f335(f337(f933(f928(x102091),f928(x102091))),f335(f335(f260(f928(x102091),f928(x102091)),x102092),x102093)),f165(x102091,x102094)))+~P1(f335(f335(f337(f933(x102091,x102091)),f335(f335(f260(x102091,x102091),f335(f335(f171(x102091),x102092),f671(x102094,x102093,x102092,x102091))),f335(f335(f171(x102091),x102093),f671(x102094,x102093,x102092,x102091)))),x102094)) % 186.01/186.03 [10358]~P76(x103581)+~P1(f335(f67(x103582),x103584))+E(f335(f172(x103581),f335(f335(f161(x103582,x103581),x103583),f96(f928(x103582),f335(f335(f18(f928(x103582),a922,a922),f335(f335(f8(a922,f934(a922,a922),f928(x103582)),a333),f335(f335(f7(f928(x103582),f934(x103582,a922),a922),f335(f335(f8(f934(x103582,a922),f934(f934(x103582,a922),a922),f928(x103582)),a332),f179(x103582))),x103584))),f144(x103582))))),f240(x103582,x103581,x103583,x103584)) % 186.01/186.03 [7638]~P66(x76382)+E(x76381,f2(x76382))+E(f335(f335(f299(x76382),f335(f335(f86(x76382),x76383),f335(f335(f87(x76382),x76384),x76381))),x76381),f335(f335(f86(x76382),x76384),f335(f335(f299(x76382),x76383),x76381))) % 186.01/186.03 [7639]~P63(x76392)+E(x76391,f2(x76392))+E(f335(f335(f42(x76392),f335(f335(f86(x76392),x76393),f335(f335(f87(x76392),x76394),x76391))),x76391),f335(f335(f86(x76392),x76394),f335(f335(f42(x76392),x76393),x76391))) % 186.01/186.03 [7640]~P63(x76402)+E(x76401,f2(x76402))+E(f335(f335(f42(x76402),f335(f335(f86(x76402),x76403),f335(f335(f87(x76402),x76401),x76404))),x76401),f335(f335(f86(x76402),x76404),f335(f335(f42(x76402),x76403),x76401))) % 186.01/186.03 [7863]~P67(x78632)+E(x78631,f2(x78632))+E(f335(f335(f299(x78632),f335(f335(f23(x78632),x78633),f335(f335(f87(x78632),x78631),x78634))),x78631),f335(f335(f23(x78632),f335(f335(f299(x78632),x78633),x78631)),x78634)) % 186.01/186.03 [7864]~P66(x78642)+E(x78641,f2(x78642))+E(f335(f335(f299(x78642),f335(f335(f86(x78642),x78643),f335(f335(f87(x78642),x78644),x78641))),x78641),f335(f335(f86(x78642),f335(f335(f299(x78642),x78643),x78641)),x78644)) % 186.01/186.03 [7865]~P67(x78652)+E(x78651,f2(x78652))+E(f335(f335(f299(x78652),f335(f335(f86(x78652),x78653),f335(f335(f87(x78652),x78651),x78654))),x78651),f335(f335(f86(x78652),f335(f335(f299(x78652),x78653),x78651)),x78654)) % 186.01/186.03 [8557]~P1(f335(f167(x85571,x85573),x85574))+~P1(f335(f167(x85571,x85572),x85574))+P1(f335(f167(x85571,f335(f335(f108(f934(x85571,a922)),x85572),x85573)),x85574)) % 186.01/186.03 [8929]~E(f335(f335(f297(x89291,x89291,x89291),x89292),x89294),f195(f934(f933(x89291,x89291),a922)))+~E(f335(f335(f297(x89291,x89291,x89291),x89292),x89293),f195(f934(f933(x89291,x89291),a922)))+E(f335(f335(f297(x89291,x89291,x89291),x89292),f335(f335(f117(f934(f933(x89291,x89291),a922)),x89293),x89294)),f195(f934(f933(x89291,x89291),a922))) % 186.01/186.03 [9055]~P1(f335(f335(f243(f934(x90551,a922)),x90553),x90554))+~P1(f335(f335(f243(f934(x90551,a922)),x90552),x90554))+P1(f335(f335(f243(f934(x90551,a922)),f335(f335(f117(f934(x90551,a922)),x90552),x90553)),x90554)) % 186.01/186.03 [9431]~P1(f335(f67(x94311),x94314))+~P1(f335(f67(x94311),x94313))+E(f335(f335(f23(a927),f335(f335(f86(a927),f335(f335(f6(x94311,a927),x94312),x94313)),f335(f335(f6(x94311,a927),x94312),x94314))),f335(f335(f6(x94311,a927),x94312),f335(f335(f108(f934(x94311,a922)),x94313),x94314))),f335(f335(f6(x94311,a927),x94312),f335(f335(f117(f934(x94311,a922)),x94313),x94314))) % 186.01/186.03 [9519]~P1(f335(f335(f337(x95191),x95193),x95192))+~P1(f335(f335(f243(f934(x95191,a922)),x95192),f335(f335(f317(x95191),x95193),x95194)))+P1(f335(f335(f243(f934(x95191,a922)),f335(f335(f23(f934(x95191,a922)),x95192),f335(f335(f317(x95191),x95193),f195(f934(x95191,a922))))),x95194)) % 186.01/186.03 [9685]~P1(f335(f335(f337(x96851),x96853),x96852))+P1(f335(f335(f243(f934(x96851,a922)),x96852),f335(f335(f317(x96851),x96853),x96854)))+~P1(f335(f335(f243(f934(x96851,a922)),f335(f335(f23(f934(x96851,a922)),x96852),f335(f335(f317(x96851),x96853),f195(f934(x96851,a922))))),x96854)) % 186.01/186.03 [9773]~P1(f335(f335(f243(a927),x97731),x97733))+~P1(f335(f335(f244(a927),x97732),x97734))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x97731),x97732)),f335(f335(f260(a927,a927),x97733),x97734))),a38)) % 186.01/186.03 [9774]~P1(f335(f335(f243(a927),x97742),x97744))+~P1(f335(f335(f243(a927),x97741),x97743))+P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),f335(f335(f260(a927,a927),x97741),x97742)),f335(f335(f260(a927,a927),x97743),x97744))),a76)) % 186.01/186.03 [10068]~P1(f335(f335(f337(f928(x100681)),x100684),f168(x100681,x100683)))+~P1(f335(f335(f337(f928(x100681)),x100684),f168(x100681,x100682)))+P1(f335(f167(x100681,f335(f335(f108(f934(x100681,a922)),f335(f335(f7(x100681,f934(x100681,a922),a922),f337(x100681)),x100682)),f335(f335(f7(x100681,f934(x100681,a922),a922),f337(x100681)),x100683))),x100684)) % 186.01/186.03 [10175]~P26(x101751,f934(f934(x101751,a922),a922),f335(f335(f7(x101751,f934(f933(x101751,x101751),a922),f934(f934(x101751,a922),a922)),f335(f335(f8(f934(x101751,a922),f934(f934(f933(x101751,x101751),a922),f934(f934(x101751,a922),a922)),x101751),f66(x101751)),f335(f335(f7(x101751,f934(x101751,a922),f934(x101751,a922)),f317(x101751)),f195(f934(x101751,a922))))),x101753),x101752)+~P1(f335(f335(f337(x101751),x101754),x101752))+E(f335(f335(f23(f934(f934(x101751,a922),a922)),f335(f335(f66(x101751),x101752),x101753)),f335(f335(f66(x101751),f335(f335(f317(x101751),x101754),f195(f934(x101751,a922)))),x101753)),f335(f335(f66(x101751),f335(f335(f23(f934(x101751,a922)),x101752),f335(f335(f317(x101751),x101754),f195(f934(x101751,a922))))),x101753)) % 186.01/186.03 [10312]~P54(x103121,x103122,x103124)+~P1(f335(f335(f337(f933(x103121,x103121)),x103123),x103124))+P1(f335(f335(f265(x103121,x103121,a922),f335(f335(f7(x103121,f934(x103121,a922),f934(x103121,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x103121,a922),f934(x103121,a922)),x103121),f8(a922,a922,x103121)),f335(f335(f8(a922,f934(a922,a922),x103121),a333),f335(f335(f7(x103121,f934(x103121,a922),a922),f337(x103121)),x103122)))),f335(f335(f7(x103121,f934(x103121,a922),a922),f337(x103121)),x103122))),x103123)) % 186.01/186.03 [10326]P1(f335(f67(x103261),x103262))+~P1(f335(f67(x103263),f335(f318(x103261,x103263,x103264),x103262)))+~P1(f335(f67(x103261),f335(f270(x103261),f335(f335(f18(x103261,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103261),a333),f335(f335(f7(x103261,f934(x103261,a922),a922),f337(x103261)),x103262))),f335(f335(f7(x103261,x103263,a922),f335(f335(f8(x103263,f934(x103263,a922),x103261),a332),x103264)),f335(x103264,f570(x103264,x103263,x103262,x103261))))))) % 186.01/186.03 [8314]~P67(x83142)+E(x83141,f2(x83142))+E(f335(f335(f299(x83142),f335(f335(f23(x83142),f335(f335(f87(x83142),x83141),x83143)),x83144)),x83141),f335(f335(f23(x83142),x83143),f335(f335(f299(x83142),x83144),x83141))) % 186.01/186.03 [8315]~P67(x83152)+E(x83151,f2(x83152))+E(f335(f335(f299(x83152),f335(f335(f86(x83152),f335(f335(f87(x83152),x83151),x83153)),x83154)),x83151),f335(f335(f86(x83152),x83153),f335(f335(f299(x83152),x83154),x83151))) % 186.01/186.03 [9219]~E(f335(f335(f297(x92191,x92191,x92191),x92193),x92194),f195(f934(f933(x92191,x92191),a922)))+~E(f335(f335(f297(x92191,x92191,x92191),x92192),x92194),f195(f934(f933(x92191,x92191),a922)))+E(f335(f335(f297(x92191,x92191,x92191),f335(f335(f117(f934(f933(x92191,x92191),a922)),x92192),x92193)),x92194),f195(f934(f933(x92191,x92191),a922))) % 186.01/186.03 [9984]~P1(f335(f167(x99841,x99843),x99844))+~P1(f335(f167(x99841,x99842),x99844))+P1(f335(f167(x99841,f335(f335(f18(x99841,a922,a922),f335(f335(f8(a922,f934(a922,a922),x99841),a333),x99842)),x99843)),x99844)) % 186.01/186.03 [10248]P1(f335(x102481,f347(x102482,x102483,x102481,x102484)))+~P1(f335(f67(x102484),f335(f270(x102484),x102481)))+P1(f335(f67(x102483),f335(f270(x102483),f335(f335(f8(f934(x102484,a922),a922,x102483),f93(x102484)),f335(f335(f8(f934(x102484,a922),f934(x102484,a922),x102483),f335(f18(x102484,a922,a922),f335(f335(f8(a922,f934(a922,a922),x102484),a333),x102481))),x102482))))) % 186.01/186.03 [10266]~P1(f335(f67(x102662),f335(f270(x102662),x102663)))+~P1(f335(f67(x102661),f335(f270(x102661),f335(f335(f7(x102661,x102662,a922),x102664),f347(x102664,x102661,x102663,x102662)))))+P1(f335(f67(x102661),f335(f270(x102661),f335(f335(f8(f934(x102662,a922),a922,x102661),f93(x102662)),f335(f335(f8(f934(x102662,a922),f934(x102662,a922),x102661),f335(f18(x102662,a922,a922),f335(f335(f8(a922,f934(a922,a922),x102662),a333),x102663))),x102664))))) % 186.01/186.03 [10337]~P1(f335(f67(x103371),x103374))+P1(f335(f335(f337(x103371),f820(x103372,x103373,x103374,x103371)),x103374))+P1(f335(f67(x103373),f335(f270(x103373),f335(f335(f8(f934(x103371,a922),a922,x103373),f93(x103371)),f335(f335(f8(f934(x103371,a922),f934(x103371,a922),x103373),f335(f18(x103371,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103371),a333),f335(f335(f7(x103371,f934(x103371,a922),a922),f337(x103371)),x103374)))),x103372))))) % 186.01/186.03 [10343]~P1(f335(f67(x103432),x103433))+~P1(f335(f67(x103431),f335(f270(x103431),f335(f335(f7(x103431,x103432,a922),x103434),f820(x103434,x103431,x103433,x103432)))))+P1(f335(f67(x103431),f335(f270(x103431),f335(f335(f8(f934(x103432,a922),a922,x103431),f93(x103432)),f335(f335(f8(f934(x103432,a922),f934(x103432,a922),x103431),f335(f18(x103432,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103432),a333),f335(f335(f7(x103432,f934(x103432,a922),a922),f337(x103432)),x103433)))),x103434))))) % 186.01/186.03 [5275]~E(x52752,x52754)+E(f176(x52751,x52752,x52753),f176(x52751,x52754,x52755))+~E(x52752,f2(a927)) % 186.01/186.03 [5528]E(x55281,x55282)+~E(f176(x55284,x55283,x55281),f176(x55284,x55285,x55282))+E(x55283,f2(a927)) % 186.01/186.03 [6779]E(x67791,x67792)+~E(f335(x67793,x67791),f335(x67793,x67792))+~P26(x67794,x67795,x67793,f250(f934(x67794,a922))) % 186.01/186.03 [7670]E(x76701,x76702)+~P26(x76703,x76704,x76705,f250(f934(x76703,a922)))+~E(f335(f318(x76703,x76704,x76705),x76701),f335(f318(x76703,x76704,x76705),x76702)) % 186.01/186.03 [7916]P26(x79162,x79163,f500(x79164,x79163,x79162,x79161),x79161)+~E(f335(f318(x79163,x79162,x79165),x79164),x79161)+E(x79161,f195(f934(x79162,a922))) % 186.01/186.03 [8439]~P1(f335(f335(x84393,x84392),x84395))+~P1(f335(f335(x84393,x84394),x84392))+P1(f335(f335(f337(x84391),x84392),f307(x84391,x84393,x84394,x84395))) % 186.01/186.03 [8440]~P1(f335(f335(x84403,x84402),x84405))+~P1(f335(f335(x84403,x84404),x84402))+P1(f335(f335(f337(x84401),x84402),f298(x84401,x84403,x84404,x84405))) % 186.01/186.03 [8746]~P26(x87461,x87462,x87463,x87464)+P27(x87461,x87462,x87463,x87464,x87465)+~E(f335(f318(x87461,x87462,x87463),x87464),x87465) % 186.01/186.03 [8879]~P27(x88791,x88793,x88794,x88792,x88795)+~P1(f335(f67(x88793),x88795))+P1(f335(f67(x88791),x88792)) % 186.01/186.03 [8880]~P27(x88803,x88801,x88804,x88805,x88802)+~P1(f335(f67(x88803),x88805))+P1(f335(f67(x88801),x88802)) % 186.01/186.03 [9012]~P26(x90121,x90123,x90125,f250(f934(x90121,a922)))+~P26(x90123,x90122,x90124,f250(f934(x90123,a922)))+P26(x90121,x90122,f335(f78(x90123,x90122,x90121,x90124),x90125),f250(f934(x90121,a922))) % 186.01/186.03 [9578]P1(f335(f335(f337(f933(x95781,x95781)),f335(f335(f260(x95781,x95781),x95782),x95783)),f315(x95781,x95784)))+~P1(f335(f335(f337(f933(x95781,x95781)),f335(f335(f260(x95781,x95781),x95782),x95785)),f315(x95781,x95784)))+~P1(f335(f335(f337(f933(x95781,x95781)),f335(f335(f260(x95781,x95781),x95785),x95783)),f315(x95781,x95784))) % 186.01/186.03 [9616]~P109(x96162)+~P1(f335(f144(x96161),x96165))+P1(f335(f144(x96161),f156(x96161,x96162,x96163,x96164,x96165))) % 186.01/186.03 [5602]~E(x56022,f120(x56021))+E(f335(f335(f141(x56021),x56022),x56023),f335(f335(f158(x56021),x56024),x56025))+~E(x56023,f335(f335(f158(x56021),x56024),x56025)) % 186.01/186.03 [5603]~E(x56032,f120(x56031))+E(f335(f335(f141(x56031),x56032),x56033),f335(f335(f158(x56031),x56034),x56035))+~E(f335(f335(f158(x56031),x56034),x56035),x56033) % 186.01/186.03 [6735]~E(f335(f196(f928(x67351)),x67355),f335(f196(f928(x67352)),x67354))+E(f335(f335(f161(f933(x67351,x67352),x67352),f264(x67351,x67352)),x67353),x67354)+~E(f335(f335(f188(x67351,x67352),x67355),x67354),x67353) % 186.01/186.03 [6736]~E(f335(f196(f928(x67361)),x67364),f335(f196(f928(x67362)),x67365))+E(f335(f335(f161(f933(x67361,x67362),x67361),f259(x67361,x67362)),x67363),x67364)+~E(f335(f335(f188(x67361,x67362),x67364),x67365),x67363) % 186.01/186.03 [7208]~P109(x72081)+~P14(x72081,f335(f335(f161(x72082,x72081),x72083),x72085))+P14(x72081,f335(f335(f161(x72082,x72081),x72083),f335(f143(x72082,x72084),x72085))) % 186.01/186.03 [7250]~P1(f335(x72503,x72505))+~P1(f335(f335(x72502,x72504),x72505))+P1(f335(f335(f99(x72501,x72502,x72503),x72504),x72505)) % 186.01/186.03 [7349]~P109(x73491)+P14(x73491,f335(f335(f161(x73492,x73491),x73493),f177(x73492,x73494,x73495)))+~P14(x73491,f335(f335(f161(x73492,x73491),x73493),x73495)) % 186.01/186.03 [7372]~P56(x73723,x73722,x73725)+~P56(x73721,x73723,x73724)+P56(x73721,x73722,f335(f335(f297(x73721,x73723,x73722),x73724),x73725)) % 186.01/186.03 [7466]E(x74661,x74662)+~P26(x74663,x74664,x74665,f250(f934(x74663,a922)))+~E(f335(f335(f161(x74663,x74664),x74665),x74661),f335(f335(f161(x74663,x74664),x74665),x74662)) % 186.01/186.03 [7624]~P1(f335(f335(f243(a927),x76241),f335(x76243,x76245)))+P1(f335(f335(f243(a927),x76241),f162(x76242,x76243,x76244)))+~P1(f335(f335(f337(x76242),x76245),f335(f179(x76242),x76244))) % 186.01/186.03 [7625]~P1(f335(f335(f244(a927),x76251),f335(x76253,x76255)))+P1(f335(f335(f244(a927),x76251),f162(x76252,x76253,x76254)))+~P1(f335(f335(f337(x76252),x76255),f335(f179(x76252),x76254))) % 186.01/186.03 [8012]P1(f335(x80121,x80122))+~P1(f335(x80121,x80123))+~P1(f335(f335(f337(x80124),x80122),f335(f179(x80124),f176(x80124,x80125,x80123)))) % 186.01/186.03 [8013]P1(f335(x80131,x80132))+~P1(f335(x80131,x80133))+~P1(f335(f335(f337(x80134),x80133),f335(f179(x80134),f176(x80134,x80135,x80132)))) % 186.01/186.03 [8017]~P110(x80171)+P1(f335(f335(f243(f934(x80171,a922)),f311(x80171,x80172,x80173)),f311(x80171,x80174,x80175)))+P1(f335(f335(f243(x80171),x80172),x80173)) % 186.01/186.03 [8038]~P6(x80381)+P1(f335(f335(f243(x80381),f335(f335(f46(x80382,x80381),x80383),x80384)),f335(x80384,x80385)))+~P1(f335(f335(f337(x80382),x80385),x80383)) % 186.01/186.03 [8105]~P26(x81051,x81052,x81054,x81053)+E(f335(f83(x81051,x81052,x81053,x81054),f335(x81054,x81055)),x81055)+~P1(f335(f335(f337(x81051),x81055),x81053)) % 186.01/186.03 [8106]~P26(x81061,x81062,x81064,x81063)+E(f335(f97(x81061,x81062,x81063,x81064),f335(x81064,x81065)),x81065)+~P1(f335(f335(f337(x81061),x81065),x81063)) % 186.01/186.03 [8303]~P1(f335(x83031,x83035))+P1(f335(x83031,f882(x83031,x83032,x83033,x83034)))+~P1(f335(f335(f337(x83034),x83035),x83033)) % 186.01/186.03 [8304]~P1(f335(x83041,x83045))+P1(f335(x83041,f882(x83041,x83042,x83043,x83044)))+~P1(f335(f335(f337(x83044),x83045),x83042)) % 186.01/186.03 [8393]P1(f335(f67(x83931),x83932))+~P1(f335(f67(x83933),x83934))+~P1(f335(f335(f243(f934(x83931,a922)),x83932),f335(f318(x83933,x83931,x83935),x83934))) % 186.01/186.03 [8561]E(x85611,x85612)+~P26(x85613,x85614,x85615,f335(f335(f117(f934(x85613,a922)),f335(f179(x85613),x85611)),f335(f179(x85613),x85612)))+~E(f335(f335(f161(x85613,x85614),x85615),x85611),f335(f335(f161(x85613,x85614),x85615),x85612)) % 186.01/186.03 [8614]~P110(x86141)+~P1(f335(f335(f244(f934(x86141,a922)),f311(x86141,x86144,x86145)),f311(x86141,x86142,x86143)))+P1(f335(f335(f243(x86141),x86142),x86143)) % 186.01/186.03 [8676]~P26(x86761,x86764,x86765,f250(f934(x86761,a922)))+~P1(f335(f335(f337(x86764),f335(x86765,x86762)),f335(f318(x86761,x86764,x86765),x86763)))+P1(f335(f335(f337(x86761),x86762),x86763)) % 186.01/186.03 [8752]P1(f335(x87521,x87522))+~P1(f335(x87521,f883(x87521,x87523,x87524,x87525)))+~P1(f335(f335(f337(x87525),x87522),x87524)) % 186.01/186.03 [8753]P1(f335(x87531,x87532))+~P1(f335(x87531,f883(x87531,x87533,x87534,x87535)))+~P1(f335(f335(f337(x87535),x87532),x87533)) % 186.01/186.03 [9052]~P26(x90522,x90523,x90521,x90524)+E(f335(x90521,f335(f83(x90522,x90523,x90524,x90521),x90525)),x90525)+~P1(f335(f335(f337(x90523),x90525),f335(f318(x90522,x90523,x90521),x90524))) % 186.01/186.03 [9159]E(x91591,f120(x91592))+E(f335(f335(f158(x91592),x91593),f704(x91594,x91593,x91595,x91591,x91592)),x91591)+~E(f335(f335(f141(x91592),x91591),x91595),f335(f335(f158(x91592),x91593),x91594)) % 186.01/186.03 [9160]E(x91601,f120(x91602))+E(f335(f335(f158(x91602),x91603),f705(x91604,x91601,x91605,x91603,x91602)),x91601)+~E(f335(f335(f141(x91602),x91601),x91604),f335(f335(f158(x91602),x91603),x91605)) % 186.01/186.03 [9178]E(f335(f335(f158(x91782),x91783),f704(x91784,x91783,x91781,x91785,x91782)),x91785)+~E(f335(f335(f141(x91782),x91785),x91781),f335(f335(f158(x91782),x91783),x91784))+E(x91781,f335(f335(f158(x91782),x91783),x91784)) % 186.01/186.03 [9179]E(f335(f335(f158(x91791),x91792),f705(x91794,x91795,x91793,x91792,x91791)),x91795)+~E(f335(f335(f141(x91791),x91795),x91794),f335(f335(f158(x91791),x91792),x91793))+E(f335(f335(f158(x91791),x91792),x91793),x91794) % 186.01/186.03 [9255]~E(f335(f318(x92553,x92552,x92554),f250(f934(x92553,a922))),f250(f934(x92552,a922)))+~E(f335(f318(x92551,x92553,x92555),f250(f934(x92551,a922))),f250(f934(x92553,a922)))+E(f335(f318(x92551,x92552,f335(f78(x92553,x92552,x92551,x92554),x92555)),f250(f934(x92551,a922))),f250(f934(x92552,a922))) % 186.01/186.03 [9622]E(x96221,f120(x96222))+~E(f335(f335(f141(x96222),x96221),x96223),f335(f335(f158(x96222),x96225),x96224))+E(f335(f335(f141(x96222),f705(x96223,x96221,x96224,x96225,x96222)),x96223),x96224) % 186.01/186.03 [9623]E(x96231,f120(x96232))+~E(f335(f335(f141(x96232),x96231),x96235),f335(f335(f158(x96232),x96234),x96233))+E(f335(f335(f141(x96232),f704(x96233,x96234,x96235,x96231,x96232)),x96235),x96233) % 186.01/186.03 [9630]E(f335(f335(f141(x96302),f704(x96304,x96303,x96301,x96305,x96302)),x96301),x96304)+~E(f335(f335(f141(x96302),x96305),x96301),f335(f335(f158(x96302),x96303),x96304))+E(x96301,f335(f335(f158(x96302),x96303),x96304)) % 186.01/186.03 [9631]~E(f335(f335(f141(x96311),x96315),x96314),f335(f335(f158(x96311),x96312),x96313))+E(f335(f335(f141(x96311),f705(x96314,x96315,x96313,x96312,x96311)),x96314),x96313)+E(f335(f335(f158(x96311),x96312),x96313),x96314) % 186.01/186.03 [9632]E(f335(f335(f141(x96321),x96325),f707(x96323,x96322,x96324,x96325,x96321)),x96322)+E(f335(f335(f141(x96321),x96322),f706(x96323,x96322,x96324,x96325,x96321)),x96325)+~E(f335(f335(f141(x96321),x96325),x96324),f335(f335(f141(x96321),x96322),x96323)) % 186.01/186.03 [9668]~P109(x96681)+P14(x96681,f335(f335(f161(x96682,x96681),x96683),f156(x96682,x96681,x96683,x96684,x96685)))+~P14(x96681,f335(f335(f161(x96682,x96681),x96683),x96685)) % 186.01/186.03 [9682]~P60(x96825,x96821,x96824,x96823)+P1(f335(f335(x96821,x96822),f360(x96823,x96824,x96821,x96825,x96822)))+~P1(f335(f335(f337(x96825),x96822),x96824)) % 186.01/186.03 [9683]~P60(x96835,x96831,x96834,x96833)+P1(f335(f335(x96831,x96832),f824(x96833,x96834,x96831,x96835,x96832)))+~P1(f335(f335(f337(x96835),x96832),x96834)) % 186.01/186.03 [9785]~P1(f335(f335(f337(f933(x97851,x97851)),f335(f335(f260(x97851,x97851),x97855),x97853)),f315(x97851,x97854)))+P1(f335(f335(f337(f933(x97851,x97851)),f335(f335(f260(x97851,x97851),x97852),x97853)),f335(f335(f297(x97851,x97851,x97851),x97854),f315(x97851,x97854))))+~P1(f335(f335(f337(f933(x97851,x97851)),f335(f335(f260(x97851,x97851),x97852),x97855)),f335(f335(f297(x97851,x97851,x97851),x97854),f315(x97851,x97854)))) % 186.01/186.03 [9786]~P1(f335(f335(f337(f933(x97861,x97861)),f335(f335(f260(x97861,x97861),x97862),x97865)),f315(x97861,x97864)))+P1(f335(f335(f337(f933(x97861,x97861)),f335(f335(f260(x97861,x97861),x97862),x97863)),f335(f335(f297(x97861,x97861,x97861),x97864),f315(x97861,x97864))))+~P1(f335(f335(f337(f933(x97861,x97861)),f335(f335(f260(x97861,x97861),x97865),x97863)),f335(f335(f297(x97861,x97861,x97861),x97864),f315(x97861,x97864)))) % 186.01/186.03 [9788]P1(f335(f335(f337(f933(f928(x97881),f928(x97881))),f335(f335(f260(f928(x97881),f928(x97881)),x97882),x97883)),f165(x97881,f315(x97881,x97884))))+~P1(f335(f335(f337(f933(f928(x97881),f928(x97881))),f335(f335(f260(f928(x97881),f928(x97881)),x97882),x97885)),f165(x97881,f315(x97881,x97884))))+~P1(f335(f335(f337(f933(f928(x97881),f928(x97881))),f335(f335(f260(f928(x97881),f928(x97881)),x97885),x97883)),f165(x97881,f315(x97881,x97884)))) % 186.01/186.03 [9792]E(f335(f335(f141(x97921),x97922),f706(x97923,x97922,x97924,x97925,x97921)),x97925)+E(f335(f335(f141(x97921),f707(x97923,x97922,x97924,x97925,x97921)),x97923),x97924)+~E(f335(f335(f141(x97921),x97922),x97923),f335(f335(f141(x97921),x97925),x97924)) % 186.01/186.03 [9793]E(f335(f335(f141(x97931),x97932),f707(x97933,x97934,x97935,x97932,x97931)),x97934)+E(f335(f335(f141(x97931),f706(x97933,x97934,x97935,x97932,x97931)),x97935),x97933)+~E(f335(f335(f141(x97931),x97932),x97935),f335(f335(f141(x97931),x97934),x97933)) % 186.01/186.03 [9847]P1(f335(f335(f337(f933(x98471,x98471)),f335(f335(f260(x98471,x98471),x98472),x98473)),f335(f335(f297(x98471,x98471,x98471),x98474),f315(x98471,x98474))))+~P1(f335(f335(f337(f933(x98471,x98471)),f335(f335(f260(x98471,x98471),x98472),x98475)),f335(f335(f297(x98471,x98471,x98471),x98474),f315(x98471,x98474))))+~P1(f335(f335(f337(f933(x98471,x98471)),f335(f335(f260(x98471,x98471),x98475),x98473)),f335(f335(f297(x98471,x98471,x98471),x98474),f315(x98471,x98474)))) % 186.01/186.03 [9874]P35(x98741,x98742,x98743,x98744,x98745)+~E(f335(f196(f928(x98741)),x98744),f335(f196(f928(x98742)),x98745))+~P1(f335(f335(f265(x98741,x98742,a922),x98743),f723(x98745,x98744,x98743,x98742,x98741))) % 186.01/186.03 [9875]P35(x98751,x98752,x98753,x98754,x98755)+~E(f335(f196(f928(x98751)),x98754),f335(f196(f928(x98752)),x98755))+~P1(f335(f335(f265(x98751,x98752,a922),x98753),f724(x98753,x98755,x98754,x98752,x98751))) % 186.01/186.03 [9881]E(f335(f335(f141(x98811),f706(x98812,x98813,x98814,x98815,x98811)),x98814),x98812)+~E(f335(f335(f141(x98811),x98813),x98812),f335(f335(f141(x98811),x98815),x98814))+E(f335(f335(f141(x98811),f707(x98812,x98813,x98814,x98815,x98811)),x98812),x98814) % 186.01/186.03 [9896]~P109(x98962)+E(f335(f335(f155(x98961,x98962,x98963),x98964),x98965),f335(f335(f158(x98961),x98964),x98965))+P1(f335(f335(f337(x98961),f767(x98964,x98963,x98965,x98961,x98962)),f335(f179(x98961),x98965))) % 186.01/186.03 [9900]~P60(x99001,x99004,x99003,x99002)+~P1(f335(f335(f337(x99001),x99005),x99003))+P1(f335(f335(f337(x99001),f360(x99002,x99003,x99004,x99001,x99005)),x99002)) % 186.01/186.03 [9901]~P60(x99011,x99014,x99013,x99012)+~P1(f335(f335(f337(x99011),x99015),x99013))+P1(f335(f335(f337(x99011),f824(x99012,x99013,x99014,x99011,x99015)),x99012)) % 186.01/186.03 [10017]~P1(f335(f335(f337(f933(f934(x100171,a922),f934(x100171,a922))),f335(f335(f260(f934(x100171,a922),f934(x100171,a922)),x100174),x100173)),f327(x100171,x100172)))+~P1(f335(f335(f337(x100171),x100175),x100174))+P1(f335(f335(f337(x100171),f611(x100172,x100173,x100174,x100171,x100175)),x100173)) % 186.01/186.03 [10027]~P109(x100272)+E(f335(f335(f155(x100271,x100272,x100273),x100274),x100275),f335(f335(f158(x100271),x100274),x100275))+~P1(f335(f335(f243(x100272),f335(x100273,x100274)),f335(x100273,f767(x100274,x100273,x100275,x100271,x100272)))) % 186.01/186.03 [10077]~P26(x100773,x100774,x100775,f250(f934(x100773,a922)))+P1(f335(x100771,x100772))+~P1(f335(x100771,f335(f97(x100773,x100774,f250(f934(x100773,a922)),x100775),f608(x100772,x100771,x100775,x100774,x100773)))) % 186.01/186.03 [10226]P35(x102261,x102262,x102263,x102264,x102265)+~E(f335(f196(f928(x102261)),x102264),f335(f196(f928(x102262)),x102265))+~P1(f335(f335(x102263,f335(f335(f171(x102261),x102264),f725(x102265,x102264,x102263,x102262,x102261))),f335(f335(f171(x102262),x102265),f725(x102265,x102264,x102263,x102262,x102261)))) % 186.01/186.03 [10227]P35(x102271,x102272,x102273,x102274,x102275)+~E(f335(f196(f928(x102271)),x102274),f335(f196(f928(x102272)),x102275))+~P1(f335(f335(x102273,f335(f335(f171(x102271),x102274),f759(x102273,x102275,x102272,x102274,x102271))),f335(f335(f171(x102272),x102275),f759(x102273,x102275,x102272,x102274,x102271)))) % 186.01/186.03 [6809]~P18(x68092,x68095,x68091)+~P1(f335(f67(x68092),x68094))+E(f335(x68091,f335(f335(f317(x68092),x68093),x68094)),f335(f335(f70(x68092,x68092,x68095),x68093),x68094)) % 186.01/186.03 [6810]~E(x68103,x68104)+~E(x68102,x68105)+E(f335(f335(f317(x68101),x68102),f335(f335(f317(x68101),x68103),f195(f934(x68101,a922)))),f335(f335(f317(x68101),x68104),f335(f335(f317(x68101),x68105),f195(f934(x68101,a922))))) % 186.01/186.03 [6820]P1(f335(x68202,x68205))+E(f184(x68201,x68202,f335(f335(f141(x68201),x68203),x68204)),f184(x68201,x68202,x68203))+~P1(f335(f335(f337(x68201),x68205),f335(f179(x68201),x68203))) % 186.01/186.03 [6858]E(f335(x68581,x68582),f195(f934(x68583,a922)))+~E(f335(f335(f45(x68584,f934(x68583,a922)),x68585),x68581),f195(f934(x68583,a922)))+~P1(f335(f335(f337(x68584),x68582),x68585)) % 186.01/186.03 [6859]E(f335(x68591,x68592),f250(f934(x68593,a922)))+~E(f335(f335(f46(x68594,f934(x68593,a922)),x68595),x68591),f250(f934(x68593,a922)))+~P1(f335(f335(f337(x68594),x68592),x68595)) % 186.01/186.03 [7359]~E(x73592,x73594)+~P143(x73591)+E(f335(f335(f86(x73591),f335(f335(f87(x73591),x73592),x73593)),f335(f335(f87(x73591),x73594),x73595)),f335(f335(f86(x73591),f335(f335(f87(x73591),x73592),x73595)),f335(f335(f87(x73591),x73594),x73593))) % 186.01/186.03 [7419]~P6(x74191)+~P1(f335(f335(f337(x74194),x74193),x74195))+P1(f335(f335(f243(x74191),f335(x74192,x74193)),f335(f335(f45(x74194,x74191),x74195),x74192))) % 186.01/186.03 [7471]~P108(x74711)+P1(f335(f335(f243(x74711),f335(x74712,x74713)),f335(x74714,x74713)))+~P1(f335(f335(f243(f934(x74715,x74711)),x74712),x74714)) % 186.01/186.03 [7595]E(x75951,x75952)+E(x75953,x75951)+~E(f335(f335(f317(x75954),x75951),f335(f335(f317(x75954),x75955),f195(f934(x75954,a922)))),f335(f335(f317(x75954),x75952),f335(f335(f317(x75954),x75953),f195(f934(x75954,a922))))) % 186.01/186.03 [7596]E(x75961,x75962)+E(x75963,x75961)+~E(f335(f335(f317(x75964),x75963),f335(f335(f317(x75964),x75962),f195(f934(x75964,a922)))),f335(f335(f317(x75964),x75965),f335(f335(f317(x75964),x75961),f195(f934(x75964,a922))))) % 186.01/186.03 [7597]E(x75971,x75972)+E(x75971,x75973)+~E(f335(f335(f317(x75974),x75973),f335(f335(f317(x75974),x75972),f195(f934(x75974,a922)))),f335(f335(f317(x75974),x75975),f335(f335(f317(x75974),x75971),f195(f934(x75974,a922))))) % 186.01/186.03 [7598]E(x75981,x75982)+E(x75981,x75983)+~E(f335(f335(f317(x75984),x75981),f335(f335(f317(x75984),x75985),f195(f934(x75984,a922)))),f335(f335(f317(x75984),x75982),f335(f335(f317(x75984),x75983),f195(f934(x75984,a922))))) % 186.01/186.03 [8115]P26(x81151,x81152,x81153,x81154)+~P26(x81151,x81152,x81153,x81155)+~P1(f335(f335(f243(f934(x81151,a922)),x81154),x81155)) % 186.01/186.03 [8144]~E(f335(x81443,x81445),x81444)+~P26(x81441,x81442,x81443,f250(f934(x81441,a922)))+E(f335(f97(x81441,x81442,f250(f934(x81441,a922)),x81443),x81444),x81445) % 186.01/186.03 [8291]E(x82911,x82912)+~E(f335(f318(x82913,x82914,x82915),x82911),f335(f318(x82913,x82914,x82915),x82912))+~P26(x82913,x82914,x82915,f335(f335(f117(f934(x82913,a922)),x82911),x82912)) % 186.01/186.03 [8363]P1(f335(x83632,x83634))+E(f335(f335(f145(x83631),f335(f196(f928(x83631)),f184(x83631,x83632,x83633))),x83633),f335(f335(f158(x83631),x83634),x83635))+~E(f335(f335(f141(x83631),f184(x83631,x83632,x83633)),f335(f335(f158(x83631),x83634),x83635)),x83633) % 186.01/186.03 [8391]~P26(x83911,x83912,x83913,x83915)+~P26(x83911,x83912,x83913,x83914)+P26(x83911,x83912,x83913,f335(f335(f108(f934(x83911,a922)),x83914),x83915)) % 186.01/186.03 [8500]~P76(x85001)+E(f335(f335(f86(x85001),f335(x85002,x85003)),f335(f172(x85001),f335(f335(f161(x85004,x85001),x85002),f177(x85004,x85003,x85005)))),f335(f172(x85001),f335(f335(f161(x85004,x85001),x85002),x85005)))+~P1(f335(f335(f337(x85004),x85003),f335(f179(x85004),x85005))) % 186.01/186.03 [8587]~P109(x85871)+~P14(x85871,f335(f335(f161(x85872,x85871),x85873),x85875))+P14(x85871,f335(f335(f161(x85872,x85871),x85873),f335(f335(f155(x85872,x85871,x85873),x85874),x85875))) % 186.01/186.03 [8672]~P6(x86721)+P1(f335(f335(f243(x86721),f335(f335(f45(x86722,x86721),x86723),x86724)),f335(f335(f45(x86722,x86721),x86725),x86724)))+~P1(f335(f335(f243(f934(x86722,a922)),x86723),x86725)) % 186.01/186.03 [8673]~P6(x86731)+P1(f335(f335(f243(x86731),f335(f335(f46(x86732,x86731),x86733),x86734)),f335(f335(f46(x86732,x86731),x86735),x86734)))+~P1(f335(f335(f243(f934(x86732,a922)),x86735),x86733)) % 186.01/186.03 [8706]~P109(x87063)+P1(f335(f144(x87061),x87062))+~P1(f335(f144(x87061),f335(f335(f155(x87061,x87063,x87064),x87065),x87062))) % 186.01/186.03 [8851]~P109(x88511)+~P1(f335(f335(f337(x88512),x88513),f335(f179(x88512),x88514)))+~P1(f335(f144(x88512),f335(f335(f155(x88512,x88511,x88515),x88513),x88514))) % 186.01/186.03 [8941]~P109(x89411)+P14(x89411,f335(f335(f161(x89412,x89411),x89413),x89414))+~P14(x89411,f335(f335(f161(x89412,x89411),x89413),f335(f335(f155(x89412,x89411,x89413),x89415),x89414))) % 186.01/186.03 [8987]~P26(x89872,x89871,x89874,x89873)+E(f335(f318(x89871,x89872,f97(x89872,x89871,x89873,x89874)),f335(f318(x89872,x89871,x89874),x89875)),x89875)+~P1(f335(f335(f243(f934(x89872,a922)),x89875),x89873)) % 186.01/186.03 [9040]~P109(x90402)+E(f335(f335(f155(x90401,x90402,x90403),x90404),x90405),f156(x90401,x90402,x90403,x90404,x90405))+P1(f335(f335(f337(x90402),f335(x90403,x90404)),f335(f318(x90401,x90402,x90403),f335(f179(x90401),x90405)))) % 186.01/186.03 [9121]~P109(x91212)+E(f156(x91211,x91212,x91213,x91214,x91215),x91215)+~P1(f335(f335(f337(x91212),f335(x91213,x91214)),f335(f318(x91211,x91212,x91213),f335(f179(x91211),x91215)))) % 186.01/186.03 [9137]~P26(x91372,x91371,x91373,x91375)+P1(f335(f335(f244(f934(x91371,a922)),f335(f318(x91372,x91371,x91373),x91374)),f335(f318(x91372,x91371,x91373),x91375)))+~P1(f335(f335(f244(f934(x91372,a922)),x91374),x91375)) % 186.01/186.03 [9296]~P26(x92961,x92962,x92963,f250(f934(x92961,a922)))+~P1(f335(f335(f243(f934(x92962,a922)),x92964),f335(f318(x92961,x92962,x92963),x92965)))+P1(f335(f335(f243(f934(x92961,a922)),f335(f319(x92961,x92962,x92963),x92964)),x92965)) % 186.01/186.03 [9320]~E(f335(f318(x93203,x93201,x93204),f250(f934(x93203,a922))),f250(f934(x93201,a922)))+P1(f335(f335(f243(f934(x93201,a922)),x93202),f335(f318(x93203,x93201,x93204),x93205)))+~P1(f335(f335(f243(f934(x93203,a922)),f335(f319(x93203,x93201,x93204),x93202)),x93205)) % 186.01/186.03 [9424]~P26(x94241,x94244,x94245,f250(f934(x94241,a922)))+~P1(f335(f335(f243(f934(x94244,a922)),f335(f318(x94241,x94244,x94245),x94242)),f335(f318(x94241,x94244,x94245),x94243)))+P1(f335(f335(f243(f934(x94241,a922)),x94242),x94243)) % 186.01/186.03 [9546]~P82(x95461)+~E(f335(x95463,f743(x95463,x95464,x95465,x95462,x95461)),f2(x95461))+E(f335(f172(x95461),f335(f335(f161(x95462,x95461),x95463),f335(f143(x95462,x95464),x95465))),f335(f172(x95461),f335(f335(f161(x95462,x95461),x95463),x95465))) % 186.01/186.03 [9573]~P27(x95731,x95732,x95733,f250(f934(x95731,a922)),f250(f934(x95732,a922)))+~P1(f335(f335(f243(f934(x95732,a922)),x95734),f335(f318(x95731,x95732,x95733),x95735)))+P1(f335(f335(f243(f934(x95731,a922)),f335(f319(x95731,x95732,x95733),x95734)),x95735)) % 186.01/186.03 [9602]~P27(x96023,x96021,x96024,f250(f934(x96023,a922)),f250(f934(x96021,a922)))+P1(f335(f335(f243(f934(x96021,a922)),x96022),f335(f318(x96023,x96021,x96024),x96025)))+~P1(f335(f335(f243(f934(x96023,a922)),f335(f319(x96023,x96021,x96024),x96022)),x96025)) % 186.01/186.03 [9726]~P17(x97261,x97262,x97263)+~P1(f335(f67(x97261),x97265))+P1(f335(f72(x97261,x97262,x97263,x97264,x97265),f335(f335(f70(x97261,x97262,x97263),x97264),x97265))) % 186.01/186.03 [9805]~P27(x98052,x98051,x98054,f250(f934(x98052,a922)),f250(f934(x98051,a922)))+~P27(x98051,x98053,x98055,f250(f934(x98051,a922)),f250(f934(x98053,a922)))+E(f335(f78(x98051,x98052,x98053,f97(x98052,x98051,f250(f934(x98052,a922)),x98054)),f97(x98051,x98053,f250(f934(x98051,a922)),x98055)),f97(x98052,x98053,f250(f934(x98052,a922)),f335(f78(x98051,x98053,x98052,x98055),x98054))) % 186.01/186.03 [9806]P1(f335(x98061,f878(x98062,x98061,x98063,x98064,x98065)))+~P1(f335(f335(f243(f934(x98065,a922)),x98064),x98063))+P1(f335(f335(f243(f934(x98065,a922)),f335(f335(f108(f934(x98065,a922)),x98064),f335(f270(x98065),x98061))),f335(f335(f108(f934(x98065,a922)),x98063),f335(f270(x98065),x98062)))) % 186.01/186.03 [9820]~P82(x98201)+~P1(f335(x98204,f743(x98203,x98204,x98205,x98202,x98201)))+E(f335(f172(x98201),f335(f335(f161(x98202,x98201),x98203),f335(f143(x98202,x98204),x98205))),f335(f172(x98201),f335(f335(f161(x98202,x98201),x98203),x98205))) % 186.01/186.03 [9898]~P6(x98985)+P1(f335(f335(f337(x98981),f652(x98982,x98983,x98981,x98984,x98985)),x98983))+P1(f335(f335(f243(x98985),x98984),f335(f335(f46(x98981,x98985),x98983),x98982))) % 186.01/186.03 [9902]~P82(x99021)+E(f335(f172(x99021),f335(f335(f161(x99022,x99021),x99023),f335(f143(x99022,x99024),x99025))),f335(f172(x99021),f335(f335(f161(x99022,x99021),x99023),x99025)))+P1(f335(f335(f337(x99022),f743(x99023,x99024,x99025,x99022,x99021)),f335(f179(x99022),x99025))) % 186.01/186.03 [9912]~P1(f335(x99125,f878(x99125,x99123,x99124,x99122,x99121)))+~P1(f335(f335(f243(f934(x99121,a922)),x99122),x99124))+P1(f335(f335(f243(f934(x99121,a922)),f335(f335(f108(f934(x99121,a922)),x99122),f335(f270(x99121),x99123))),f335(f335(f108(f934(x99121,a922)),x99124),f335(f270(x99121),x99125)))) % 186.01/186.03 [9928]~P26(x99285,x99283,x99284,f250(f934(x99285,a922)))+P1(f335(x99281,x99282))+P1(f335(f335(f337(x99283),f608(x99282,x99281,x99284,x99283,x99285)),f335(f318(x99285,x99283,x99284),f250(f934(x99285,a922))))) % 186.01/186.03 [9952]P35(x99521,x99522,x99523,x99524,x99525)+~E(f335(f196(f928(x99522)),x99525),f335(f196(f928(x99521)),x99524))+P1(f335(f335(f244(a927),f725(x99525,x99524,x99523,x99522,x99521)),f335(f196(f928(x99521)),x99524))) % 186.01/186.03 [9953]P35(x99531,x99532,x99533,x99534,x99535)+~E(f335(f196(f928(x99532)),x99535),f335(f196(f928(x99531)),x99534))+P1(f335(f335(f244(a927),f759(x99533,x99535,x99532,x99534,x99531)),f335(f196(f928(x99531)),x99534))) % 186.01/186.03 [9985]P1(f335(f335(f337(x99851),f878(x99852,x99853,x99854,x99855,x99851)),x99855))+~P1(f335(f335(f243(f934(x99851,a922)),x99855),x99854))+P1(f335(f335(f243(f934(x99851,a922)),f335(f335(f108(f934(x99851,a922)),x99855),f335(f270(x99851),x99853))),f335(f335(f108(f934(x99851,a922)),x99854),f335(f270(x99851),x99852)))) % 186.01/186.03 [10028]~P6(x100281)+~P1(f335(f335(f243(x100281),x100282),f335(x100285,f652(x100285,x100284,x100283,x100282,x100281))))+P1(f335(f335(f243(x100281),x100282),f335(f335(f46(x100283,x100281),x100284),x100285))) % 186.01/186.03 [10066]~P72(x100661)+~P1(f335(f67(x100662),x100665))+E(f335(f335(f335(f71(x100661,x100662,f87(x100661)),f335(f335(f18(x100662,x100661,x100661),f335(f335(f8(x100661,f934(x100661,x100661),x100662),f87(x100661)),x100663)),x100664)),f84(x100661)),x100665),f335(f335(f87(x100661),f335(f335(f335(f71(x100661,x100662,f87(x100661)),x100663),f84(x100661)),x100665)),f335(f335(f335(f71(x100661,x100662,f87(x100661)),x100664),f84(x100661)),x100665))) % 186.01/186.03 [10122]~P1(f335(f335(f337(f933(f934(x101221,a922),f934(x101221,a922))),f335(f335(f260(f934(x101221,a922),f934(x101221,a922)),x101225),x101224)),f327(x101221,x101223)))+~P1(f335(f335(f337(x101221),x101222),x101225))+P1(f335(f335(f337(f933(x101221,x101221)),f335(f335(f260(x101221,x101221),x101222),f611(x101223,x101224,x101225,x101221,x101222))),x101223)) % 186.01/186.03 [10263]~P1(f335(f335(f337(f933(f928(x102631),f928(x102631))),f335(f335(f260(f928(x102631),f928(x102631)),f335(f335(f141(x102631),x102635),x102632)),f335(f335(f141(x102631),x102635),x102633))),f154(x102631,x102634)))+P1(f335(f335(f337(f933(f928(x102631),f928(x102631))),f335(f335(f260(f928(x102631),f928(x102631)),x102632),x102633)),f154(x102631,x102634)))+P1(f335(f335(f337(f933(x102631,x102631)),f335(f335(f260(x102631,x102631),f712(x102634,x102633,x102632,x102635,x102631)),f712(x102634,x102633,x102632,x102635,x102631))),x102634)) % 186.01/186.03 [7474]~E(x74743,x74745)+E(f335(f335(f171(x74741),f335(f335(f166(x74741,x74742),x74743),x74744)),x74745),x74744)+~P1(f335(f335(f244(a927),x74743),f335(f196(f928(x74741)),x74742))) % 186.01/186.03 [7592]~E(f335(f335(f141(x75921),x75922),x75924),f335(f335(f141(x75921),x75923),x75925))+E(f335(f335(f182(x75921),f335(f196(f928(x75921)),x75922)),x75923),x75922)+P1(f335(f335(f243(a927),f335(f196(f928(x75921)),x75923)),f335(f196(f928(x75921)),x75922))) % 186.01/186.03 [8076]~E(f335(f335(f141(x80761),x80762),x80764),f335(f335(f141(x80761),x80763),x80765))+E(f335(f335(f182(x80761),f335(f196(f928(x80761)),x80762)),x80763),x80762)+~P1(f335(f335(f243(a927),f335(f196(f928(x80761)),x80762)),f335(f196(f928(x80761)),x80763))) % 186.01/186.03 [8100]~P1(f335(f67(x81001),f335(x81004,x81005)))+~P1(f335(f335(f337(x81002),x81005),x81003))+P1(f335(f67(x81001),f335(f335(f46(x81002,f934(x81001,a922)),x81003),x81004))) % 186.01/186.03 [8275]~P54(x82751,x82753,x82755)+~P54(x82751,x82752,x82754)+P54(x82751,f335(f335(f108(f934(x82751,a922)),x82752),x82753),f335(f335(f108(f934(f933(x82751,x82751),a922)),x82754),x82755)) % 186.01/186.03 [8276]~P54(x82761,x82763,x82765)+~P54(x82761,x82762,x82764)+P54(x82761,f335(f335(f117(f934(x82761,a922)),x82762),x82763),f335(f335(f117(f934(f933(x82761,x82761),a922)),x82764),x82765)) % 186.01/186.03 [8627]E(f335(f335(f260(x86271,x86272),f335(f335(f171(x86271),x86273),x86274)),f335(f335(f171(x86272),x86275),x86274)),f335(f335(f171(f933(x86271,x86272)),f335(f335(f188(x86271,x86272),x86273),x86275)),x86274))+~P1(f335(f335(f244(a927),x86274),f335(f196(f928(x86271)),x86273)))+~P1(f335(f335(f244(a927),x86274),f335(f196(f928(x86272)),x86275))) % 186.01/186.03 [8780]~P54(x87801,x87803,x87804)+P1(f335(f335(f337(x87801),x87802),x87803))+~P1(f335(f335(f337(f933(x87801,x87801)),f335(f335(f260(x87801,x87801),x87805),x87802)),x87804)) % 186.01/186.03 [8781]~P54(x87811,x87813,x87814)+P1(f335(f335(f337(x87811),x87812),x87813))+~P1(f335(f335(f337(f933(x87811,x87811)),f335(f335(f260(x87811,x87811),x87812),x87815)),x87814)) % 186.01/186.03 [8782]~P9(x87821,x87823,x87824)+P1(f335(f335(f337(x87821),x87822),x87823))+~P1(f335(f335(f337(f933(x87821,x87821)),f335(f335(f260(x87821,x87821),x87825),x87822)),x87824)) % 186.01/186.03 [8783]~P9(x87831,x87833,x87834)+P1(f335(f335(f337(x87831),x87832),x87833))+~P1(f335(f335(f337(f933(x87831,x87831)),f335(f335(f260(x87831,x87831),x87832),x87835)),x87834)) % 186.01/186.03 [9064]~P9(x90641,x90645,x90642)+E(f335(f293(x90641,x90641,x90642),f335(f335(f317(x90641),x90643),f195(f934(x90641,a922)))),f335(f293(x90641,x90641,x90642),f335(f335(f317(x90641),x90644),f195(f934(x90641,a922)))))+~P1(f335(f335(f337(f933(x90641,x90641)),f335(f335(f260(x90641,x90641),x90643),x90644)),x90642)) % 186.01/186.03 [9252]P1(f335(x92521,x92522))+~P1(f335(f335(f337(x92523),x92522),x92525))+P1(f335(f335(f337(x92523),f883(x92521,x92524,x92525,x92523)),f335(f335(f117(f934(x92523,a922)),x92525),x92524))) % 186.01/186.03 [9253]P1(f335(x92531,x92532))+~P1(f335(f335(f337(x92533),x92532),x92534))+P1(f335(f335(f337(x92533),f883(x92531,x92534,x92535,x92533)),f335(f335(f117(f934(x92533,a922)),x92535),x92534))) % 186.01/186.03 [9261]~P1(f335(x92612,x92615))+~P1(f335(f335(f337(x92611),x92615),x92614))+P1(f335(f335(f337(x92611),f882(x92612,x92613,x92614,x92611)),f335(f335(f117(f934(x92611,a922)),x92614),x92613))) % 186.01/186.03 [9262]~P1(f335(x92622,x92625))+~P1(f335(f335(f337(x92621),x92625),x92623))+P1(f335(f335(f337(x92621),f882(x92622,x92623,x92624,x92621)),f335(f335(f117(f934(x92621,a922)),x92624),x92623))) % 186.01/186.03 [9277]~P1(f335(f335(f243(f934(x92771,a922)),x92775),x92773))+~P1(f335(f335(f243(f934(x92771,a922)),x92772),x92774))+P1(f335(f335(f243(f934(x92771,a922)),f335(f335(f23(f934(x92771,a922)),x92772),x92773)),f335(f335(f23(f934(x92771,a922)),x92774),x92775))) % 186.01/186.03 [9278]~P1(f335(f335(f243(f934(x92781,a922)),x92783),x92785))+~P1(f335(f335(f243(f934(x92781,a922)),x92782),x92784))+P1(f335(f335(f243(f934(x92781,a922)),f335(f335(f108(f934(x92781,a922)),x92782),x92783)),f335(f335(f108(f934(x92781,a922)),x92784),x92785))) % 186.01/186.03 [9279]~P1(f335(f335(f243(f934(x92791,a922)),x92793),x92795))+~P1(f335(f335(f243(f934(x92791,a922)),x92792),x92794))+P1(f335(f335(f243(f934(x92791,a922)),f335(f335(f117(f934(x92791,a922)),x92792),x92793)),f335(f335(f117(f934(x92791,a922)),x92794),x92795))) % 186.01/186.03 [9374]P1(f335(f335(f337(f933(x93741,x93741)),f335(f335(f260(x93741,x93741),x93742),x93743)),f329(x93741,x93744,x93745)))+~P1(f335(f335(f243(a927),f335(x93744,x93742)),f335(x93744,x93743)))+~P1(f335(f335(f337(f933(x93741,x93741)),f335(f335(f260(x93741,x93741),x93742),x93743)),x93745)) % 186.01/186.03 [9556]P1(f335(f335(f337(f933(x95561,x95561)),f335(f335(f260(x95561,x95561),x95562),x95563)),f315(x95561,x95564)))+~P1(f335(f335(f337(f933(x95561,x95561)),f335(f335(f260(x95561,x95561),x95562),x95565)),f315(x95561,x95564)))+~P1(f335(f335(f337(f933(x95561,x95561)),f335(f335(f260(x95561,x95561),x95565),x95563)),x95564)) % 186.01/186.03 [9557]P1(f335(f335(f337(f933(x95571,x95571)),f335(f335(f260(x95571,x95571),x95572),x95573)),f315(x95571,x95574)))+~P1(f335(f335(f337(f933(x95571,x95571)),f335(f335(f260(x95571,x95571),x95575),x95573)),f315(x95571,x95574)))+~P1(f335(f335(f337(f933(x95571,x95571)),f335(f335(f260(x95571,x95571),x95572),x95575)),x95574)) % 186.01/186.03 [9655]E(x96551,x96552)+E(f335(a119,f621(x96553,x96554,x96551,x96552,x96555)),x96554)+~P1(f335(f335(f337(f933(x96555,x96555)),f335(f335(f260(x96555,x96555),x96552),x96551)),f335(f335(f190(f933(x96555,x96555),a922),x96554),x96553))) % 186.01/186.03 [9656]E(x96561,x96562)+E(f335(a119,f623(x96563,x96564,x96561,x96562,x96565)),x96564)+~P1(f335(f335(f337(f933(x96565,x96565)),f335(f335(f260(x96565,x96565),x96562),x96561)),f335(f335(f190(f933(x96565,x96565),a922),x96564),x96563))) % 186.01/186.03 [9657]E(x96571,f2(a927))+E(f335(a119,f621(x96572,x96571,x96573,x96574,x96575)),x96571)+~P1(f335(f335(f337(f933(x96575,x96575)),f335(f335(f260(x96575,x96575),x96574),x96573)),f335(f335(f190(f933(x96575,x96575),a922),x96571),x96572))) % 186.01/186.03 [9658]E(x96581,f2(a927))+E(f335(a119,f623(x96582,x96581,x96583,x96584,x96585)),x96581)+~P1(f335(f335(f337(f933(x96585,x96585)),f335(f335(f260(x96585,x96585),x96584),x96583)),f335(f335(f190(f933(x96585,x96585),a922),x96581),x96582))) % 186.01/186.03 [9679]P1(f335(f335(f337(f933(x96791,x96791)),f335(f335(f260(x96791,x96791),x96792),x96793)),f335(f335(f297(x96791,x96791,x96791),x96794),f315(x96791,x96794))))+~P1(f335(f335(f337(f933(x96791,x96791)),f335(f335(f260(x96791,x96791),x96792),x96795)),x96794))+~P1(f335(f335(f337(f933(x96791,x96791)),f335(f335(f260(x96791,x96791),x96795),x96793)),x96794)) % 186.01/186.03 [9686]~P1(f335(f335(f337(f933(x96861,x96861)),f335(f335(f260(x96861,x96861),x96862),x96865)),f315(x96861,x96864)))+P1(f335(f335(f337(f933(x96861,x96861)),f335(f335(f260(x96861,x96861),x96862),x96863)),f335(f335(f297(x96861,x96861,x96861),x96864),f315(x96861,x96864))))+~P1(f335(f335(f337(f933(x96861,x96861)),f335(f335(f260(x96861,x96861),x96865),x96863)),x96864)) % 186.01/186.03 [9720]~P9(x97201,x97205,x97202)+~P1(f335(f335(f337(f933(x97201,x97201)),f335(f335(f260(x97201,x97201),x97203),x97204)),x97202))+P1(f335(f335(f243(f934(x97201,a922)),f335(f293(x97201,x97201,x97202),f335(f335(f317(x97201),x97203),f195(f934(x97201,a922))))),f335(f293(x97201,x97201,x97202),f335(f335(f317(x97201),x97204),f195(f934(x97201,a922)))))) % 186.01/186.03 [9778]P1(f335(f335(f337(f933(x97781,x97781)),f335(f335(f260(x97781,x97781),x97782),x97783)),f335(f335(f297(x97781,x97781,x97781),x97784),f315(x97781,x97784))))+~P1(f335(f335(f337(f933(x97781,x97781)),f335(f335(f260(x97781,x97781),x97782),x97785)),f335(f335(f297(x97781,x97781,x97781),x97784),f315(x97781,x97784))))+~P1(f335(f335(f337(f933(x97781,x97781)),f335(f335(f260(x97781,x97781),x97785),x97783)),x97784)) % 186.01/186.03 [9779]P1(f335(f335(f337(f933(x97791,x97791)),f335(f335(f260(x97791,x97791),x97792),x97793)),f335(f335(f297(x97791,x97791,x97791),x97794),f315(x97791,x97794))))+~P1(f335(f335(f337(f933(x97791,x97791)),f335(f335(f260(x97791,x97791),x97795),x97793)),f335(f335(f297(x97791,x97791,x97791),x97794),f315(x97791,x97794))))+~P1(f335(f335(f337(f933(x97791,x97791)),f335(f335(f260(x97791,x97791),x97792),x97795)),x97794)) % 186.01/186.03 [9829]~P1(f335(f72(x98291,x98291,x98294,x98292,x98293),x98295))+P1(f335(f335(f337(x98291),x98292),x98293))+P1(f335(f68(x98291,x98294,f335(f335(f317(x98291),x98292),x98293)),x98295)) % 186.01/186.03 [9867]~E(f335(f318(x98673,x98672,x98675),x98674),x98671)+E(x98671,f195(f934(x98672,a922)))+P1(f335(f335(f243(f934(x98673,a922)),f335(f318(x98672,x98673,f500(x98674,x98673,x98672,x98671)),x98671)),x98674)) % 186.01/186.03 [9915]~P6(x99155)+P1(f335(f335(f337(x99151),f663(x99152,x99153,x99154,x99151,x99155)),x99154))+P1(f335(f335(f243(x99155),f335(f335(f45(x99151,x99155),x99154),x99153)),x99152)) % 186.01/186.03 [9972]P35(x99721,x99722,x99723,x99724,x99725)+~E(f335(f196(f928(x99721)),x99724),f335(f196(f928(x99722)),x99725))+P1(f335(f335(f337(f933(x99721,x99722)),f723(x99725,x99724,x99723,x99722,x99721)),f335(f179(f933(x99721,x99722)),f335(f335(f188(x99721,x99722),x99724),x99725)))) % 186.01/186.03 [9973]P35(x99731,x99732,x99733,x99734,x99735)+~E(f335(f196(f928(x99731)),x99734),f335(f196(f928(x99732)),x99735))+P1(f335(f335(f337(f933(x99731,x99732)),f724(x99733,x99735,x99734,x99732,x99731)),f335(f179(f933(x99731,x99732)),f335(f335(f188(x99731,x99732),x99734),x99735)))) % 186.01/186.03 [10100]E(x101001,x101002)+P1(f335(f335(f337(f933(x101003,x101003)),f335(f335(f260(x101003,x101003),x101001),f622(x101004,x101005,x101002,x101001,x101003))),x101004))+~P1(f335(f335(f337(f933(x101003,x101003)),f335(f335(f260(x101003,x101003),x101001),x101002)),f335(f335(f190(f933(x101003,x101003),a922),x101005),x101004))) % 186.01/186.03 [10101]E(x101011,f2(a927))+P1(f335(f335(f337(f933(x101012,x101012)),f335(f335(f260(x101012,x101012),x101013),f622(x101014,x101011,x101015,x101013,x101012))),x101014))+~P1(f335(f335(f337(f933(x101012,x101012)),f335(f335(f260(x101012,x101012),x101013),x101015)),f335(f335(f190(f933(x101012,x101012),a922),x101011),x101014))) % 186.01/186.03 [10141]~P6(x101411)+~P1(f335(f335(f243(x101411),f335(x101414,f663(x101415,x101414,x101413,x101412,x101411))),x101415))+P1(f335(f335(f243(x101411),f335(f335(f45(x101412,x101411),x101413),x101414)),x101415)) % 186.01/186.03 [10196]E(x101961,x101962)+P1(f335(f335(f337(f933(x101963,x101963)),f335(f335(f260(x101963,x101963),f624(x101964,x101965,x101961,x101962,x101963)),x101961)),x101964))+~P1(f335(f335(f337(f933(x101963,x101963)),f335(f335(f260(x101963,x101963),x101962),x101961)),f335(f335(f190(f933(x101963,x101963),a922),x101965),x101964))) % 186.01/186.03 [10197]E(x101971,f2(a927))+P1(f335(f335(f337(f933(x101972,x101972)),f335(f335(f260(x101972,x101972),f624(x101973,x101971,x101974,x101975,x101972)),x101974)),x101973))+~P1(f335(f335(f337(f933(x101972,x101972)),f335(f335(f260(x101972,x101972),x101975),x101974)),f335(f335(f190(f933(x101972,x101972),a922),x101971),x101973))) % 186.01/186.03 [10201]E(x102011,x102012)+P1(f335(f335(f337(f933(x102013,x102013)),f335(f335(f260(x102013,x102013),x102011),f624(x102014,x102015,x102012,x102011,x102013))),f335(f335(f190(f933(x102013,x102013),a922),f623(x102014,x102015,x102012,x102011,x102013)),x102014)))+~P1(f335(f335(f337(f933(x102013,x102013)),f335(f335(f260(x102013,x102013),x102011),x102012)),f335(f335(f190(f933(x102013,x102013),a922),x102015),x102014))) % 186.01/186.03 [10202]E(x102021,f2(a927))+P1(f335(f335(f337(f933(x102022,x102022)),f335(f335(f260(x102022,x102022),x102023),f624(x102024,x102021,x102025,x102023,x102022))),f335(f335(f190(f933(x102022,x102022),a922),f623(x102024,x102021,x102025,x102023,x102022)),x102024)))+~P1(f335(f335(f337(f933(x102022,x102022)),f335(f335(f260(x102022,x102022),x102023),x102025)),f335(f335(f190(f933(x102022,x102022),a922),x102021),x102024))) % 186.01/186.03 [10254]E(x102541,x102542)+P1(f335(f335(f337(f933(x102543,x102543)),f335(f335(f260(x102543,x102543),f622(x102544,x102545,x102541,x102542,x102543)),x102541)),f335(f335(f190(f933(x102543,x102543),a922),f621(x102544,x102545,x102541,x102542,x102543)),x102544)))+~P1(f335(f335(f337(f933(x102543,x102543)),f335(f335(f260(x102543,x102543),x102542),x102541)),f335(f335(f190(f933(x102543,x102543),a922),x102545),x102544))) % 186.01/186.03 [10255]E(x102551,f2(a927))+P1(f335(f335(f337(f933(x102552,x102552)),f335(f335(f260(x102552,x102552),f622(x102553,x102551,x102554,x102555,x102552)),x102554)),f335(f335(f190(f933(x102552,x102552),a922),f621(x102553,x102551,x102554,x102555,x102552)),x102553)))+~P1(f335(f335(f337(f933(x102552,x102552)),f335(f335(f260(x102552,x102552),x102555),x102554)),f335(f335(f190(f933(x102552,x102552),a922),x102551),x102553))) % 186.01/186.03 [10290]~P76(x102902)+~P1(f335(f67(x102901),x102905))+E(f335(f335(f6(x102901,x102902),f335(f335(f7(x102901,x102902,x102902),f335(f335(f18(x102901,x102902,f934(x102902,x102902)),f335(f335(f8(a922,f934(x102902,f934(x102902,x102902)),x102901),f103(x102902)),f335(f335(f7(x102901,f934(x102901,a922),a922),f337(x102901)),x102903))),x102904)),f2(x102902))),x102905),f335(f335(f6(x102901,x102902),x102904),f335(f335(f108(f934(x102901,a922)),x102905),x102903))) % 186.01/186.03 [8848]~P76(x88481)+~P1(f335(f67(x88484),x88485))+E(f335(f335(f86(x88481),f335(x88482,x88483)),f335(f335(f6(x88484,x88481),x88482),f335(f335(f23(f934(x88484,a922)),x88485),f335(f335(f317(x88484),x88483),f195(f934(x88484,a922)))))),f335(f335(f6(x88484,x88481),x88482),f335(f335(f317(x88484),x88483),x88485))) % 186.01/186.03 [8849]~P72(x88491)+~P1(f335(f67(x88494),x88495))+E(f335(f335(f87(x88491),f335(x88492,x88493)),f335(f335(f9(x88494,x88491),x88492),f335(f335(f23(f934(x88494,a922)),x88495),f335(f335(f317(x88494),x88493),f195(f934(x88494,a922)))))),f335(f335(f9(x88494,x88491),x88492),f335(f335(f317(x88494),x88493),x88495))) % 186.01/186.03 [9185]~P109(x91852)+~P14(x91852,f335(f175(x91852),f335(f335(f161(x91851,x91852),x91854),x91855)))+E(f335(f143(x91851,f335(f335(f8(x91852,a922,x91851),f335(f244(x91852),x91853)),x91854)),x91855),f184(x91851,f335(f335(f8(x91852,a922,x91851),f335(f244(x91852),x91853)),x91854),x91855)) % 186.01/186.03 [9209]~P76(x92091)+E(f335(f335(f86(x92091),f335(f335(f6(a927,x92091),x92092),f311(a927,x92093,x92094))),f335(f335(f6(a927,x92091),x92092),f311(a927,f335(f335(f86(a927),x92094),f84(a927)),f335(f335(f86(a927),x92094),x92095)))),f335(f335(f6(a927,x92091),x92092),f311(a927,x92093,f335(f335(f86(a927),x92094),x92095))))+~P1(f335(f335(f243(a927),x92093),f335(f335(f86(a927),x92094),f84(a927)))) % 186.01/186.03 [9210]~P1(f335(f335(f337(x92101),x92104),x92105))+~P1(f335(f335(f243(f934(x92101,a922)),f335(f179(x92101),x92102)),x92105))+P1(f335(f335(f243(f934(x92101,a922)),f335(f179(x92101),f335(f335(f166(x92101,x92102),x92103),x92104))),x92105)) % 186.01/186.03 [9432]~P6(x94322)+~P1(f335(f67(x94321),x94325))+E(f335(f335(f70(x94321,x94322,f335(f335(f8(x94322,f934(x94322,x94322),x94321),f108(x94322)),x94323)),x94324),x94325),f335(f335(f108(x94322),x94324),f335(f335(f46(x94321,x94322),x94325),x94323))) % 186.01/186.03 [9433]~P6(x94332)+~P1(f335(f67(x94331),x94335))+E(f335(f335(f70(x94331,x94332,f335(f335(f8(x94332,f934(x94332,x94332),x94331),f117(x94332)),x94333)),x94334),x94335),f335(f335(f117(x94332),x94334),f335(f335(f45(x94331,x94332),x94335),x94333))) % 186.01/186.03 [9481]E(f335(x94811,x94812),f335(x94811,x94813))+P1(f335(f335(f244(a927),f335(x94811,x94812)),f335(x94811,x94813)))+~P1(f335(f335(f337(f933(x94814,x94814)),f335(f335(f260(x94814,x94814),x94812),x94813)),f160(x94814,f335(f335(f158(f934(x94814,a927)),x94811),x94815)))) % 186.01/186.03 [9514]~E(f335(x95144,x95142),f335(x95144,x95143))+~P1(f335(f335(f337(f933(x95141,x95141)),f335(f335(f260(x95141,x95141),x95142),x95143)),f160(x95141,x95145)))+P1(f335(f335(f337(f933(x95141,x95141)),f335(f335(f260(x95141,x95141),x95142),x95143)),f160(x95141,f335(f335(f158(f934(x95141,a927)),x95144),x95145)))) % 186.01/186.03 [9534]~P26(x95341,x95342,x95343,x95345)+P26(x95341,x95342,x95343,f335(f335(f317(x95341),x95344),x95345))+P1(f335(f335(f337(x95342),f335(x95343,x95344)),f335(f318(x95341,x95342,x95343),f335(f335(f23(f934(x95341,a922)),x95345),f335(f335(f317(x95341),x95344),f195(f934(x95341,a922))))))) % 186.01/186.03 [9537]P1(f335(x95372,x95375))+~P1(f335(f335(f337(x95371),x95375),f335(f179(x95371),x95373)))+E(f335(f335(f145(x95371),f335(f196(f928(x95371)),f184(x95371,x95372,f335(f335(f141(x95371),x95373),x95374)))),f335(f335(f141(x95371),x95373),x95374)),f335(f335(f141(x95371),f335(f335(f145(x95371),f335(f196(f928(x95371)),f184(x95371,x95372,x95373))),x95373)),x95374)) % 186.01/186.03 [9542]~P1(f335(f335(f337(f933(x95421,x95421)),f335(f335(f260(x95421,x95421),x95422),x95423)),f160(x95421,x95425)))+~P1(f335(f335(f243(a927),f335(x95424,x95422)),f335(x95424,x95423)))+P1(f335(f335(f337(f933(x95421,x95421)),f335(f335(f260(x95421,x95421),x95422),x95423)),f160(x95421,f335(f335(f158(f934(x95421,a927)),x95424),x95425)))) % 186.01/186.03 [9607]P1(f335(f335(f337(f933(x96074,x96074)),f335(f335(f260(x96074,x96074),x96072),x96073)),f160(x96074,x96075)))+P1(f335(f335(f244(a927),f335(x96071,x96072)),f335(x96071,x96073)))+~P1(f335(f335(f337(f933(x96074,x96074)),f335(f335(f260(x96074,x96074),x96072),x96073)),f160(x96074,f335(f335(f158(f934(x96074,a927)),x96071),x96075)))) % 186.01/186.03 [9750]~P1(f335(f335(f337(f933(f928(x97501),f928(x97501))),f335(f335(f260(f928(x97501),f928(x97501)),x97502),x97504)),f165(x97501,x97505)))+~P1(f335(f335(f244(a927),x97503),f335(f196(f928(x97501)),x97502)))+P1(f335(f335(f337(f933(x97501,x97501)),f335(f335(f260(x97501,x97501),f335(f335(f171(x97501),x97502),x97503)),f335(f335(f171(x97501),x97504),x97503))),x97505)) % 186.01/186.03 [9995]E(x99951,f2(a1))+~P1(f335(f55(x99953,x99951),f335(f335(f260(a1,a1),x99954),x99955)))+P1(f335(f55(f335(f335(f87(a1),x99952),x99953),x99951),f335(f335(f260(a1,a1),f335(f335(f86(a1),f335(f335(f87(a1),x99952),x99954)),f335(f335(f42(a1),f335(f335(f87(a1),x99952),x99955)),x99951))),f51(a1,f335(f335(f87(a1),x99952),x99955),x99951)))) % 186.01/186.03 [9996]~P1(f335(f335(f244(a927),f2(a927)),x99963))+~P1(f335(f54(x99962,x99963),f335(f335(f260(a927,a927),x99964),x99965)))+P1(f335(f54(f335(f335(f87(a927),x99961),x99962),x99963),f335(f335(f260(a927,a927),f335(f335(f86(a927),f335(f335(f87(a927),x99961),x99964)),f335(f335(f42(a927),f335(f335(f87(a927),x99961),x99965)),x99963))),f51(a927,f335(f335(f87(a927),x99961),x99965),x99963)))) % 186.01/186.03 [10313]~P76(x103132)+~P1(f335(f67(x103131),x103134))+E(f335(f335(f6(x103131,x103132),x103133),f335(f270(x103131),f335(f335(f18(x103131,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103131),a333),f335(f335(f7(x103131,f934(x103131,a922),a922),f337(x103131)),x103134))),f335(f335(f7(x103131,f934(x103131,a922),a922),f337(x103131)),x103135)))),f335(f335(f6(x103131,x103132),f335(f335(f7(x103131,x103132,x103132),f335(f335(f18(x103131,x103132,f934(x103132,x103132)),f335(f335(f8(a922,f934(x103132,f934(x103132,x103132)),x103131),f103(x103132)),f335(f335(f7(x103131,f934(x103131,a922),a922),f337(x103131)),x103135))),x103133)),f2(x103132))),x103134)) % 186.01/186.03 [8478]~E(f335(f335(f141(x84781),x84782),x84785),f335(f335(f141(x84781),x84783),x84784))+E(f335(f335(f141(x84781),f335(f335(f145(x84781),f335(f196(f928(x84781)),x84782)),x84783)),x84784),x84785)+P1(f335(f335(f243(a927),f335(f196(f928(x84781)),x84783)),f335(f196(f928(x84781)),x84782))) % 186.01/186.03 [8675]~E(f335(f335(f141(x86752),x86753),x86751),f335(f335(f141(x86752),x86754),x86755))+E(x86751,f335(f335(f141(x86752),f335(f335(f145(x86752),f335(f196(f928(x86752)),x86753)),x86754)),x86755))+~P1(f335(f335(f243(a927),f335(f196(f928(x86752)),x86753)),f335(f196(f928(x86752)),x86754))) % 186.01/186.03 [8763]~E(f335(f335(f86(a927),f335(f335(f87(a927),x87633),x87634)),x87631),f335(f335(f86(a927),f335(f335(f87(a927),x87632),x87634)),x87635))+~P1(f335(f335(f243(a927),x87633),x87632))+E(x87631,f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x87632),x87633)),x87634)),x87635)) % 186.01/186.03 [8764]~E(f335(f335(f86(a927),f335(f335(f87(a927),x87641),x87643)),x87644),f335(f335(f86(a927),f335(f335(f87(a927),x87642),x87643)),x87645))+~P1(f335(f335(f243(a927),x87642),x87641))+E(f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x87641),x87642)),x87643)),x87644),x87645) % 186.01/186.03 [8932]E(f335(f335(f86(a927),f335(f335(f87(a927),x89321),x89322)),x89323),f335(f335(f86(a927),f335(f335(f87(a927),x89324),x89322)),x89325))+~P1(f335(f335(f243(a927),x89324),x89321))+~E(x89325,f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x89321),x89324)),x89322)),x89323)) % 186.01/186.03 [8933]E(f335(f335(f86(a927),f335(f335(f87(a927),x89331),x89332)),x89333),f335(f335(f86(a927),f335(f335(f87(a927),x89334),x89332)),x89335))+~P1(f335(f335(f243(a927),x89334),x89331))+~E(f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x89331),x89334)),x89332)),x89333),x89335) % 186.01/186.03 [9804]~P66(x98042)+~P1(f335(f67(x98041),x98045))+E(f335(f335(f9(x98041,x98042),f335(f335(f18(x98041,x98042,x98042),f335(f335(f8(x98042,f934(x98042,x98042),x98041),f299(x98042)),x98043)),x98044)),x98045),f335(f335(f299(x98042),f335(f335(f9(x98041,x98042),x98043),x98045)),f335(f335(f9(x98041,x98042),x98044),x98045))) % 186.01/186.03 [9935]~E(f626(x99355,x99354,x99353,x99352,x99351),f627(x99355,x99354,x99353,x99352,x99351))+P1(f335(f335(f337(f933(x99351,x99351)),f335(f335(f260(x99351,x99351),x99352),x99353)),f315(x99351,x99354)))+~P1(f335(f335(f337(f933(x99351,x99351)),f335(f335(f260(x99351,x99351),x99352),x99353)),f315(x99351,f335(f335(f117(f934(f933(x99351,x99351),a922)),x99354),x99355)))) % 186.01/186.03 [9936]~E(f637(x99365,x99364,x99363,x99362,x99361),f638(x99365,x99364,x99363,x99362,x99361))+P1(f335(f335(f337(f933(x99361,x99361)),f335(f335(f260(x99361,x99361),x99362),x99363)),f315(x99361,x99364)))+~P1(f335(f335(f337(f933(x99361,x99361)),f335(f335(f260(x99361,x99361),x99362),x99363)),f315(x99361,f335(f335(f117(f934(f933(x99361,x99361),a922)),x99364),x99365)))) % 186.01/186.03 [10131]P1(f335(f335(f337(f933(x101311,x101311)),f335(f335(f260(x101311,x101311),x101312),f627(x101315,x101314,x101313,x101312,x101311))),f315(x101311,x101314)))+P1(f335(f335(f337(f933(x101311,x101311)),f335(f335(f260(x101311,x101311),x101312),x101313)),f315(x101311,x101314)))+~P1(f335(f335(f337(f933(x101311,x101311)),f335(f335(f260(x101311,x101311),x101312),x101313)),f315(x101311,f335(f335(f117(f934(f933(x101311,x101311),a922)),x101314),x101315)))) % 186.01/186.03 [10223]P1(f335(f335(f337(f933(x102231,x102231)),f335(f335(f260(x102231,x102231),f638(x102235,x102234,x102233,x102232,x102231)),x102233)),f315(x102231,x102234)))+P1(f335(f335(f337(f933(x102231,x102231)),f335(f335(f260(x102231,x102231),x102232),x102233)),f315(x102231,x102234)))+~P1(f335(f335(f337(f933(x102231,x102231)),f335(f335(f260(x102231,x102231),x102232),x102233)),f315(x102231,f335(f335(f117(f934(f933(x102231,x102231),a922)),x102234),x102235)))) % 186.01/186.03 [10261]P1(f335(f335(f337(f933(x102611,x102611)),f335(f335(f260(x102611,x102611),x102612),x102613)),f315(x102611,x102614)))+P1(f335(f335(f337(f933(x102611,x102611)),f335(f335(f260(x102611,x102611),f627(x102615,x102614,x102613,x102612,x102611)),f626(x102615,x102614,x102613,x102612,x102611))),x102615))+~P1(f335(f335(f337(f933(x102611,x102611)),f335(f335(f260(x102611,x102611),x102612),x102613)),f315(x102611,f335(f335(f117(f934(f933(x102611,x102611),a922)),x102614),x102615)))) % 186.01/186.03 [10262]P1(f335(f335(f337(f933(x102621,x102621)),f335(f335(f260(x102621,x102621),x102622),x102623)),f315(x102621,x102624)))+P1(f335(f335(f337(f933(x102621,x102621)),f335(f335(f260(x102621,x102621),f637(x102625,x102624,x102623,x102622,x102621)),f638(x102625,x102624,x102623,x102622,x102621))),x102625))+~P1(f335(f335(f337(f933(x102621,x102621)),f335(f335(f260(x102621,x102621),x102622),x102623)),f315(x102621,f335(f335(f117(f934(f933(x102621,x102621),a922)),x102624),x102625)))) % 186.01/186.03 [10410]~P1(f335(f335(f337(f933(f928(x104101),f928(x104101))),f335(f335(f260(f928(x104101),f928(x104101)),x104104),x104105)),f165(x104101,x104102)))+~P1(f335(f335(f337(f933(x104101,x104101)),x104103),f335(f179(f933(x104101,x104101)),f335(f335(f188(x104101,x104101),x104104),x104105))))+P1(f335(f335(f265(x104101,x104101,a922),f335(f335(f7(x104101,f934(f933(x104101,x104101),a922),f934(x104101,a922)),f335(f335(f8(f934(x104101,f934(f934(f933(x104101,x104101),a922),a922)),f934(f934(f933(x104101,x104101),a922),f934(x104101,a922)),x104101),f7(x104101,f934(f933(x104101,x104101),a922),a922)),f335(f335(f8(f934(x104101,f933(x104101,x104101)),f934(x104101,f934(f934(f933(x104101,x104101),a922),a922)),x104101),f335(f8(f933(x104101,x104101),f934(f934(f933(x104101,x104101),a922),a922),x104101),f337(f933(x104101,x104101)))),f260(x104101,x104101)))),x104102)),x104103)) % 186.01/186.03 [9833]~P1(f335(f335(f243(a927),x98333),x98332))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),x98333),x98334)),x98331)),f335(f335(f86(a927),f335(f335(f87(a927),x98332),x98334)),x98335)))+P1(f335(f335(f243(a927),x98331),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x98332),x98333)),x98334)),x98335))) % 186.01/186.03 [9834]~P1(f335(f335(f243(a927),x98343),x98342))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),x98343),x98344)),x98341)),f335(f335(f86(a927),f335(f335(f87(a927),x98342),x98344)),x98345)))+P1(f335(f335(f244(a927),x98341),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x98342),x98343)),x98344)),x98345))) % 186.01/186.03 [9851]~P1(f335(f335(f243(a927),x98511),x98514))+P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),x98511),x98512)),x98513)),f335(f335(f86(a927),f335(f335(f87(a927),x98514),x98512)),x98515)))+~P1(f335(f335(f243(a927),x98513),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x98514),x98511)),x98512)),x98515))) % 186.01/186.03 [9852]~P1(f335(f335(f243(a927),x98521),x98524))+P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),x98521),x98522)),x98523)),f335(f335(f86(a927),f335(f335(f87(a927),x98524),x98522)),x98525)))+~P1(f335(f335(f244(a927),x98523),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x98524),x98521)),x98522)),x98525))) % 186.01/186.03 [9970]~P1(f335(f335(f243(a927),x99702),x99701))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),x99701),x99703)),x99704)),f335(f335(f86(a927),f335(f335(f87(a927),x99702),x99703)),x99705)))+P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x99701),x99702)),x99703)),x99704)),x99705)) % 186.01/186.03 [9971]~P1(f335(f335(f243(a927),x99712),x99711))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),x99711),x99713)),x99714)),f335(f335(f86(a927),f335(f335(f87(a927),x99712),x99713)),x99715)))+P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x99711),x99712)),x99713)),x99714)),x99715)) % 186.01/186.03 [10014]~P1(f335(f335(f243(a927),x100144),x100141))+P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),x100141),x100142)),x100143)),f335(f335(f86(a927),f335(f335(f87(a927),x100144),x100142)),x100145)))+~P1(f335(f335(f243(a927),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x100141),x100144)),x100142)),x100143)),x100145)) % 186.01/186.03 [10015]~P1(f335(f335(f243(a927),x100154),x100151))+P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),x100151),x100152)),x100153)),f335(f335(f86(a927),f335(f335(f87(a927),x100154),x100152)),x100155)))+~P1(f335(f335(f244(a927),f335(f335(f86(a927),f335(f335(f87(a927),f335(f335(f23(a927),x100151),x100154)),x100152)),x100153)),x100155)) % 186.01/186.03 [10249]~P12(x102491,x102492,x102495,x102493)+~P1(f335(f335(f337(f933(x102491,x102491)),x102494),x102495))+P1(f335(f335(f265(x102491,x102491,a922),f335(f335(f7(x102491,f934(x102491,x102492),f934(x102491,a922)),f335(f335(f8(f934(x102492,a922),f934(f934(x102491,x102492),f934(x102491,a922)),x102491),f8(x102492,a922,x102491)),f335(f335(f8(x102492,f934(x102492,a922),x102491),a332),x102493))),x102493)),x102494)) % 186.01/186.03 [8639]~P20(x86396,x86391,x86392,x86394)+E(f335(f78(x86391,x86391,x86391,f335(x86392,x86393)),f335(x86394,x86395)),f335(f78(x86391,x86391,x86391,f335(x86394,x86395)),f335(x86392,x86393)))+~P1(f335(f67(x86396),x86395)) % 186.01/186.03 [9076]~P26(x90761,x90763,x90765,x90766)+~P26(x90763,x90762,x90764,f335(f318(x90761,x90763,x90765),x90766))+P26(x90761,x90762,f335(f78(x90763,x90762,x90761,x90764),x90765),x90766) % 186.01/186.03 [9639]~P1(f335(f335(x96393,x96392),x96396))+~P1(f335(f335(x96394,x96395),x96392))+P1(f335(f335(f337(x96391),x96392),f308(x96391,x96393,x96394,x96395,x96396))) % 186.01/186.03 [9640]~P1(f335(f335(x96404,x96402),x96406))+~P1(f335(f335(x96403,x96405),x96402))+P1(f335(f335(f337(x96401),x96402),f305(x96401,x96403,x96404,x96405,x96406))) % 186.01/186.03 [9751]E(x97511,x97512)+E(x97513,x97514)+~P1(f335(f335(f337(f933(f928(x97515),f928(x97515))),f335(f335(f260(f928(x97515),f928(x97515)),f335(f335(f158(x97515),x97513),x97511)),f335(f335(f158(x97515),x97514),x97512))),f164(x97515,x97516))) % 186.01/186.03 [9760]~E(x97602,x97604)+P1(f335(f335(f337(f933(f928(x97601),f928(x97601))),f335(f335(f260(f928(x97601),f928(x97601)),f335(f335(f158(x97601),x97602),x97603)),f335(f335(f158(x97601),x97604),x97605))),f152(x97601,x97606)))+~P1(f335(f335(f337(f933(f928(x97601),f928(x97601))),f335(f335(f260(f928(x97601),f928(x97601)),x97603),x97605)),f152(x97601,x97606))) % 186.01/186.03 [9761]~E(x97612,x97614)+P1(f335(f335(f337(f933(f928(x97611),f928(x97611))),f335(f335(f260(f928(x97611),f928(x97611)),f335(f335(f158(x97611),x97612),x97613)),f335(f335(f158(x97611),x97614),x97615))),f154(x97611,x97616)))+~P1(f335(f335(f337(f933(f928(x97611),f928(x97611))),f335(f335(f260(f928(x97611),f928(x97611)),x97613),x97615)),f154(x97611,x97616))) % 186.01/186.03 [9762]~E(x97622,x97624)+P1(f335(f335(f337(f933(f928(x97621),f928(x97621))),f335(f335(f260(f928(x97621),f928(x97621)),f335(f335(f158(x97621),x97622),x97623)),f335(f335(f158(x97621),x97624),x97625))),f164(x97621,x97626)))+~P1(f335(f335(f337(f933(f928(x97621),f928(x97621))),f335(f335(f260(f928(x97621),f928(x97621)),x97623),x97625)),f164(x97621,x97626))) % 186.01/186.03 [9763]~E(x97632,x97634)+P1(f335(f335(f337(f933(f928(x97631),f928(x97631))),f335(f335(f260(f928(x97631),f928(x97631)),f335(f335(f141(x97631),x97632),x97633)),f335(f335(f141(x97631),x97634),x97635))),f164(x97631,x97636)))+~P1(f335(f335(f337(f933(f928(x97631),f928(x97631))),f335(f335(f260(f928(x97631),f928(x97631)),x97633),x97635)),f164(x97631,x97636))) % 186.01/186.03 [9764]~E(x97643,x97645)+P1(f335(f335(f337(f933(f928(x97641),f928(x97641))),f335(f335(f260(f928(x97641),f928(x97641)),f335(f335(f141(x97641),x97642),x97643)),f335(f335(f141(x97641),x97644),x97645))),f164(x97641,x97646)))+~P1(f335(f335(f337(f933(f928(x97641),f928(x97641))),f335(f335(f260(f928(x97641),f928(x97641)),x97642),x97644)),f164(x97641,x97646))) % 186.01/186.03 [9821]E(x98211,x98212)+P1(f335(f335(f337(f933(f928(x98213),f928(x98213))),f335(f335(f260(f928(x98213),f928(x98213)),x98211),x98212)),f164(x98213,x98214)))+~P1(f335(f335(f337(f933(f928(x98213),f928(x98213))),f335(f335(f260(f928(x98213),f928(x98213)),f335(f335(f158(x98213),x98215),x98211)),f335(f335(f158(x98213),x98216),x98212))),f164(x98213,x98214))) % 186.01/186.03 [9974]~E(x99743,x99745)+P1(f335(f335(f337(f933(f928(x99741),f928(x99741))),f335(f335(f260(f928(x99741),f928(x99741)),f335(f335(f141(x99741),x99742),f335(f335(f158(x99741),x99743),f120(x99741)))),f335(f335(f141(x99741),x99744),f335(f335(f158(x99741),x99745),f120(x99741))))),f164(x99741,x99746)))+~P1(f335(f335(f337(f933(f928(x99741),f928(x99741))),f335(f335(f260(f928(x99741),f928(x99741)),x99742),x99744)),f164(x99741,x99746))) % 186.01/186.03 [10018]E(x100181,x100182)+E(x100183,x100184)+~P1(f335(f335(f337(f933(f928(x100185),f928(x100185))),f335(f335(f260(f928(x100185),f928(x100185)),f335(f335(f141(x100185),x100183),f335(f335(f158(x100185),x100181),f120(x100185)))),f335(f335(f141(x100185),x100184),f335(f335(f158(x100185),x100182),f120(x100185))))),f164(x100185,x100186))) % 186.01/186.03 [10044]E(x100441,x100442)+~P1(f335(f335(f337(f933(f928(x100443),f928(x100443))),f335(f335(f260(f928(x100443),f928(x100443)),f335(f335(f141(x100443),x100441),f335(f335(f158(x100443),x100445),f120(x100443)))),f335(f335(f141(x100443),x100442),f335(f335(f158(x100443),x100446),f120(x100443))))),f164(x100443,x100444)))+P1(f335(f335(f337(f933(f928(x100443),f928(x100443))),f335(f335(f260(f928(x100443),f928(x100443)),x100441),x100442)),f164(x100443,x100444))) % 186.01/186.03 [10083]~P1(f335(f335(f337(f933(f934(x100831,a922),f934(x100831,a922))),f335(f335(f260(f934(x100831,a922),f934(x100831,a922)),x100832),x100834)),f327(x100831,x100836)))+~P1(f335(f335(f337(f933(f934(x100831,a922),f934(x100831,a922))),f335(f335(f260(f934(x100831,a922),f934(x100831,a922)),x100833),x100835)),f327(x100831,x100836)))+P1(f335(f335(f337(f933(f934(x100831,a922),f934(x100831,a922))),f335(f335(f260(f934(x100831,a922),f934(x100831,a922)),f335(f335(f117(f934(x100831,a922)),x100832),x100833)),f335(f335(f117(f934(x100831,a922)),x100834),x100835))),f327(x100831,x100836))) % 186.01/186.03 [5905]~E(f335(f335(f141(x59051),x59056),x59053),x59055)+E(f335(f335(f141(x59051),x59052),x59053),f335(f335(f158(x59051),x59054),x59055))+~E(x59052,f335(f335(f158(x59051),x59054),x59056)) % 186.01/186.03 [5906]~E(f335(f335(f141(x59061),x59066),x59063),x59065)+E(f335(f335(f141(x59061),x59062),x59063),f335(f335(f141(x59061),x59064),x59065))+~E(x59062,f335(f335(f141(x59061),x59064),x59066)) % 186.01/186.03 [5908]E(f335(f335(f141(x59081),x59082),x59083),f335(f335(f158(x59081),x59084),x59085))+~E(f335(f335(f158(x59081),x59084),x59086),x59082)+~E(x59085,f335(f335(f141(x59081),x59086),x59083)) % 186.01/186.03 [5910]~E(f335(f335(f141(x59101),x59102),x59106),x59104)+E(f335(f335(f141(x59101),x59102),x59103),f335(f335(f141(x59101),x59104),x59105))+~E(x59103,f335(f335(f141(x59101),x59106),x59105)) % 186.01/186.03 [7042]E(f335(x70421,x70422),f335(x70423,x70422))+~E(f335(f335(f161(x70424,x70425),x70421),x70426),f335(f335(f161(x70424,x70425),x70423),x70426))+~P1(f335(f335(f337(x70424),x70422),f335(f179(x70424),x70426))) % 186.01/186.03 [7421]~P20(x74214,x74215,x74216,x74211)+E(f335(f335(x74211,x74212),x74213),f335(f335(f70(x74214,x74215,x74216),x74213),x74212))+~P1(f335(f67(x74214),x74212)) % 186.01/186.03 [7492]~E(x74922,f335(x74924,x74926))+~P1(f335(f335(f337(x74923),x74926),x74925))+P1(f335(f335(f337(x74921),x74922),f335(f318(x74923,x74921,x74924),x74925))) % 186.01/186.03 [7493]~E(f335(x74934,x74932),x74936)+~P1(f335(f335(f337(x74933),x74936),x74935))+P1(f335(f335(f337(x74931),x74932),f335(f319(x74931,x74933,x74934),x74935))) % 186.01/186.03 [7937]~P33(x79371,x79372,x79374,x79376)+P33(x79371,x79372,f335(f335(f158(x79371),x79373),x79374),f335(f335(f158(x79371),x79375),x79376))+~P1(f335(f335(x79372,x79373),x79375)) % 186.01/186.03 [8942]~P58(x89424,x89425,x89421,x89422,x89426)+E(f335(x89421,f335(x89422,x89423)),x89423)+~P1(f335(f335(f337(x89425),x89423),x89426)) % 186.01/186.03 [9441]~P27(x94412,x94411,x94415,x94414,x94413)+E(f335(f97(x94411,x94412,x94413,f97(x94412,x94411,x94414,x94415)),x94416),f335(x94415,x94416))+~P1(f335(f335(f337(x94412),x94416),x94414)) % 186.01/186.03 [9452]~P26(x94521,x94522,x94523,x94526)+P26(x94521,x94522,f80(x94521,x94522,x94523,x94524,x94525),x94526)+P1(f335(f335(f337(x94522),x94525),f335(f318(x94521,x94522,x94523),x94526))) % 186.01/186.03 [9753]E(x97531,x97532)+E(f335(f196(f928(x97533)),x97534),f335(f196(f928(x97533)),x97535))+~P1(f335(f335(f337(f933(f928(x97533),f928(x97533))),f335(f335(f260(f928(x97533),f928(x97533)),f335(f335(f158(x97533),x97531),x97534)),f335(f335(f158(x97533),x97532),x97535))),f152(x97533,x97536))) % 186.01/186.03 [9816]~P17(x98161,x98162,x98163)+E(f335(f335(f70(x98161,x98162,x98163),x98164),x98165),x98166)+~P1(f335(f72(x98161,x98162,x98163,x98164,x98165),x98166)) % 186.01/186.03 [9824]E(f335(f196(f928(x98241)),x98242),f335(f196(f928(x98241)),x98243))+P1(f335(f335(f337(f933(f928(x98241),f928(x98241))),f335(f335(f260(f928(x98241),f928(x98241)),x98242),x98243)),f152(x98241,x98244)))+~P1(f335(f335(f337(f933(f928(x98241),f928(x98241))),f335(f335(f260(f928(x98241),f928(x98241)),f335(f335(f158(x98241),x98245),x98242)),f335(f335(f158(x98241),x98246),x98243))),f152(x98241,x98244))) % 186.01/186.03 [9845]~P1(f335(f335(f337(f933(x98451,x98451)),f335(f335(f260(x98451,x98451),x98452),x98454)),f315(x98451,x98456)))+P1(f335(f335(f337(f933(f928(x98451),f928(x98451))),f335(f335(f260(f928(x98451),f928(x98451)),f335(f335(f158(x98451),x98452),x98453)),f335(f335(f158(x98451),x98454),x98455))),f315(f928(x98451),f164(x98451,x98456))))+~P1(f335(f335(f337(f933(f928(x98451),f928(x98451))),f335(f335(f260(f928(x98451),f928(x98451)),x98453),x98455)),f315(f928(x98451),f164(x98451,x98456)))) % 186.01/186.03 [10024]~P1(f335(x100242,x100246))+~E(f335(f143(x100241,x100242),x100243),f335(f335(f158(x100241),x100244),x100245))+~P1(f335(f335(f337(x100241),x100246),f335(f179(x100241),f769(x100245,x100244,x100243,x100242,x100241)))) % 186.01/186.03 [10025]~P1(f335(x100254,x100256))+~E(f335(f335(f158(x100251),x100252),x100253),f335(f143(x100251,x100254),x100255))+~P1(f335(f335(f337(x100251),x100256),f335(f179(x100251),f766(x100255,x100254,x100253,x100252,x100251)))) % 186.01/186.03 [10348]~P76(x103482)+E(f335(f335(f6(x103481,x103482),f335(f335(f8(f934(x103483,a922),x103482,x103481),f335(f6(x103483,x103482),x103484)),f335(f335(f8(f934(x103483,a922),f934(x103483,a922),x103481),f270(x103483)),f335(f335(f8(f934(x103483,a922),f934(x103483,a922),x103481),f335(f18(x103483,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103483),a333),f335(f335(f7(x103483,f934(x103483,a922),a922),f337(x103483)),x103485)))),f335(f7(x103483,x103481,a922),f335(f335(f8(x103481,f934(x103481,a922),x103483),a332),x103486)))))),f335(f318(x103483,x103481,x103486),x103485)),f335(f335(f6(x103483,x103482),x103484),x103485))+~P1(f335(f67(x103483),x103485)) % 186.01/186.03 [7098]~P109(x70983)+P1(f335(x70982,x70985))+E(f335(f143(x70981,x70982),f335(f335(f155(x70981,x70983,x70984),x70985),x70986)),f335(f143(x70981,x70982),x70986)) % 186.01/186.03 [7100]P1(f335(x71001,x71002))+~E(f173(x71003,x71001,x71004),f335(f335(f260(f928(x71003),f928(x71003)),x71005),x71006))+~P1(f335(f335(f337(x71003),x71002),f335(f179(x71003),x71005))) % 186.01/186.03 [7142]~P1(f335(x71422,x71426))+~E(f173(x71421,x71422,x71423),f335(f335(f260(f928(x71421),f928(x71421)),x71424),x71425))+~P1(f335(f335(f337(x71421),x71426),f335(f179(x71421),x71425))) % 186.01/186.03 [7803]~P15(x78031,x78032,x78033)+~P1(f335(f67(x78031),x78036))+E(f335(f335(f70(x78031,x78032,x78033),x78034),f335(f335(f317(x78031),x78035),x78036)),f335(f335(f70(x78031,x78032,x78033),f335(f335(x78033,x78035),x78034)),x78036)) % 186.01/186.03 [7854]~P109(x78542)+~P1(f335(f335(f243(x78542),f335(x78543,x78544)),f335(x78543,x78545)))+E(f335(f335(f155(x78541,x78542,x78543),x78544),f335(f335(f158(x78541),x78545),x78546)),f335(f335(f158(x78541),x78544),f335(f335(f158(x78541),x78545),x78546))) % 186.01/186.03 [7965]E(x79651,x79652)+~E(f335(f335(f262(x79653,x79654),x79651),f335(f16(f934(x79654,a922),x79653),x79655)),f335(f335(f262(x79653,x79654),x79652),f335(f16(f934(x79654,a922),x79653),x79655)))+~P1(f335(f335(f337(x79654),x79656),x79655)) % 186.01/186.03 [8030]~P15(x80301,x80302,x80303)+~P1(f335(f67(x80301),x80306))+E(f335(f335(f70(x80301,x80302,x80303),x80304),f335(f335(f317(x80301),x80305),x80306)),f335(f335(x80303,x80305),f335(f335(f70(x80301,x80302,x80303),x80304),x80306))) % 186.01/186.03 [8145]~P17(x81451,x81452,x81453)+~P1(f335(f67(x81451),x81456))+E(f335(f335(f70(x81451,x81452,x81453),f335(f335(x81453,x81454),x81455)),x81456),f335(f335(x81453,x81454),f335(f335(f70(x81451,x81452,x81453),x81455),x81456))) % 186.01/186.03 [8214]~P21(x82142,x82145,x82146,x82141)+~P1(f335(f67(x82142),x82144))+E(f335(x82141,f335(f335(f317(x82142),x82143),x82144)),f335(f78(x82145,x82145,x82145,f335(x82141,x82144)),f335(x82146,x82143))) % 186.01/186.03 [8246]~P109(x82462)+P1(f335(f335(f243(x82462),f335(x82463,x82464)),f335(x82463,x82465)))+E(f335(f335(f155(x82461,x82462,x82463),x82464),f335(f335(f158(x82461),x82465),x82466)),f335(f335(f158(x82461),x82465),f335(f335(f155(x82461,x82462,x82463),x82464),x82466))) % 186.01/186.03 [8384]~E(f335(f196(f928(x83841)),x83845),f335(f196(f928(x83842)),x83846))+~E(f335(f196(f928(x83841)),x83843),f335(f196(f928(x83842)),x83844))+E(f335(f335(f141(f933(x83841,x83842)),f335(f335(f188(x83841,x83842),x83843),x83844)),f335(f335(f188(x83841,x83842),x83845),x83846)),f335(f335(f188(x83841,x83842),f335(f335(f141(x83841),x83843),x83845)),f335(f335(f141(x83842),x83844),x83846))) % 186.01/186.03 [8496]~E(x84962,f335(f318(x84963,x84961,x84964),x84966))+P1(f335(f335(f243(f934(x84961,a922)),x84962),f335(f318(x84963,x84961,x84964),x84965)))+~P1(f335(f335(f243(f934(x84963,a922)),x84966),x84965)) % 186.01/186.03 [8598]~P109(x85985)+E(f335(x85981,x85982),f335(x85981,x85983))+E(f335(f335(f155(x85984,x85985,x85981),x85982),f335(f335(f155(x85984,x85985,x85981),x85983),x85986)),f335(f335(f155(x85984,x85985,x85981),x85983),f335(f335(f155(x85984,x85985,x85981),x85982),x85986))) % 186.01/186.03 [8772]~P1(f335(f335(f337(x87722),x87724),f335(x87726,x87723)))+~P1(f335(f335(f337(x87721),x87723),x87725))+P1(f335(f335(f337(f933(x87721,x87722)),f335(f335(f260(x87721,x87722),x87723),x87724)),f335(f335(f262(x87721,x87722),x87725),x87726))) % 186.01/186.03 [9250]~P76(x92502)+~P26(x92504,x92501,x92505,x92506)+E(f335(f335(f6(x92501,x92502),x92503),f335(f318(x92504,x92501,x92505),x92506)),f335(f335(f6(x92504,x92502),f335(f78(x92501,x92502,x92504,x92503),x92505)),x92506)) % 186.01/186.03 [9251]~P72(x92512)+~P26(x92514,x92511,x92515,x92516)+E(f335(f335(f9(x92511,x92512),x92513),f335(f318(x92514,x92511,x92515),x92516)),f335(f335(f9(x92514,x92512),f335(f78(x92511,x92512,x92514,x92513),x92515)),x92516)) % 186.01/186.03 [9298]~P35(x92982,x92985,x92981,x92983,x92986)+P1(f335(f335(x92981,f335(f335(f171(x92982),x92983),x92984)),f335(f335(f171(x92985),x92986),x92984)))+~P1(f335(f335(f244(a927),x92984),f335(f196(f928(x92985)),x92986))) % 186.01/186.03 [9299]~P35(x92992,x92995,x92991,x92993,x92996)+P1(f335(f335(x92991,f335(f335(f171(x92992),x92993),x92994)),f335(f335(f171(x92995),x92996),x92994)))+~P1(f335(f335(f244(a927),x92994),f335(f196(f928(x92992)),x92993))) % 186.01/186.03 [9310]~E(f335(f318(x93101,x93102,x93103),x93104),x93106)+E(f335(f318(x93101,x93102,x93103),f335(f318(x93102,x93101,f97(x93101,x93102,x93104,x93103)),x93105)),x93105)+~P1(f335(f335(f243(f934(x93102,a922)),x93105),x93106)) % 186.01/186.03 [9509]~P20(x95093,x95091,x95096,x95092)+~P1(f335(f67(x95093),x95094))+E(f335(f78(x95091,x95091,x95091,f335(x95092,f335(f335(f23(f934(x95093,a922)),x95094),f335(f335(f317(x95093),x95095),f195(f934(x95093,a922)))))),f335(x95096,x95095)),f335(x95092,f335(f335(f317(x95093),x95095),x95094))) % 186.01/186.03 [10113]~E(f335(f318(x101132,x101134,x101136),f250(f934(x101132,a922))),f250(f934(x101134,a922)))+~E(f335(f318(x101131,x101133,x101135),f250(f934(x101131,a922))),f250(f934(x101133,a922)))+E(f335(f318(f933(x101131,x101132),f933(x101133,x101134),f266(x101131,x101133,x101132,x101134,x101135,x101136)),f250(f934(f933(x101131,x101132),a922))),f250(f934(f933(x101133,x101134),a922))) % 186.01/186.03 [10173]~P26(x101733,x101734,x101735,f335(x101736,f659(x101736,x101735,x101734,x101733,x101732,x101731)))+P26(x101733,x101734,x101735,f335(f335(f46(x101732,f934(x101733,a922)),x101731),x101736))+E(x101731,f195(f934(x101732,a922))) % 186.01/186.03 [10230]P26(x102306,x102305,x102304,f335(f335(f46(x102302,f934(x102306,a922)),x102301),x102303))+E(x102301,f195(f934(x102302,a922)))+P1(f335(f335(f337(x102302),f659(x102303,x102304,x102305,x102306,x102302,x102301)),x102301)) % 186.01/186.03 [10235]P1(f335(f335(f337(x102351),f605(x102352,x102353,x102354,x102355,x102356,x102351)),x102356))+P1(f335(f335(f243(f934(f933(x102351,x102354),a922)),f335(f335(f262(x102351,x102354),x102356),x102353)),f335(f335(f262(x102351,x102354),x102355),x102352)))+~P1(f335(f335(f243(f934(x102351,a922)),x102356),x102355)) % 186.01/186.03 [10278]P25(x102786,x102785,f335(f335(f317(f926(x102786)),f98(x102786,x102784,x102783,x102782)),f195(f934(f926(x102786),a922))))+~P25(x102786,x102785,f335(f335(f317(f926(x102786)),f98(x102786,x102784,x102783,x102781)),f195(f934(f926(x102786),a922))))+P1(f335(f335(x102781,f789(x102782,x102781,x102783,x102784,x102785,x102786)),f881(x102782,x102781,x102783,x102784,x102785,x102786))) % 186.01/186.03 [10279]P25(x102796,x102795,f335(f335(f317(f926(x102796)),f98(x102796,x102791,x102793,x102792)),f195(f934(f926(x102796),a922))))+~P25(x102796,x102795,f335(f335(f317(f926(x102796)),f98(x102796,x102794,x102793,x102792)),f195(f934(f926(x102796),a922))))+P1(f335(f335(x102791,f889(x102791,x102792,x102793,x102794,x102795,x102796)),f902(x102791,x102792,x102793,x102794,x102795,x102796))) % 186.01/186.03 [10322]~P25(x103221,x103222,f335(f335(f317(f926(x103221)),f98(x103221,x103223,x103224,x103226)),f195(f934(f926(x103221),a922))))+P25(x103221,x103222,f335(f335(f317(f926(x103221)),f98(x103221,x103223,x103224,x103225)),f195(f934(f926(x103221),a922))))+~P1(f335(f335(x103225,f789(x103225,x103226,x103224,x103223,x103222,x103221)),f881(x103225,x103226,x103224,x103223,x103222,x103221))) % 186.01/186.03 [10323]~P25(x103231,x103232,f335(f335(f317(f926(x103231)),f98(x103231,x103236,x103234,x103235)),f195(f934(f926(x103231),a922))))+P25(x103231,x103232,f335(f335(f317(f926(x103231)),f98(x103231,x103233,x103234,x103235)),f195(f934(f926(x103231),a922))))+~P1(f335(f335(x103236,f889(x103233,x103235,x103234,x103236,x103232,x103231)),f902(x103233,x103235,x103234,x103236,x103232,x103231))) % 186.01/186.03 [10362]~P1(f335(f335(f243(f934(x103622,a922)),f335(x103624,f605(x103626,x103624,x103622,x103625,x103623,x103621))),f335(x103626,f605(x103626,x103624,x103622,x103625,x103623,x103621))))+~P1(f335(f335(f243(f934(x103621,a922)),x103623),x103625))+P1(f335(f335(f243(f934(f933(x103621,x103622),a922)),f335(f335(f262(x103621,x103622),x103623),x103624)),f335(f335(f262(x103621,x103622),x103625),x103626))) % 186.01/186.03 [7987]~P1(f335(x79871,x79875))+~P1(f335(x79876,x79874))+P1(f335(x79871,f335(f264(x79872,x79873),f335(f335(f260(x79872,x79873),x79874),x79875)))) % 186.01/186.03 [7988]~P1(f335(x79881,x79884))+~P1(f335(x79886,x79885))+P1(f335(x79881,f335(f259(x79882,x79883),f335(f335(f260(x79882,x79883),x79884),x79885)))) % 186.01/186.03 [8035]~P1(f335(f335(x80354,x80356),x80355))+~P1(f335(f335(f337(x80351),x80356),x80353))+P1(f335(f335(f335(f45(x80351,f934(x80352,a922)),x80353),x80354),x80355)) % 186.01/186.03 [8336]~P1(f335(f335(f337(x83361),x83362),f335(x83365,x83366)))+~P1(f335(f335(f337(x83363),x83366),x83364))+P1(f335(f335(f337(x83361),x83362),f335(f335(f45(x83363,f934(x83361,a922)),x83364),x83365))) % 186.01/186.03 [8378]P1(f335(f335(x83781,x83782),x83783))+~P1(f335(f335(x83784,x83782),x83783))+~P1(f335(f335(f243(f934(x83785,f934(x83786,a922))),x83784),x83781)) % 186.01/186.03 [8520]P1(f335(f335(x85201,x85202),x85203))+~P1(f335(f335(f337(x85204),x85202),x85205))+~P1(f335(f335(f335(f46(x85204,f934(x85206,a922)),x85205),x85201),x85203)) % 186.01/186.03 [8654]P1(f335(f335(f337(x86541),x86542),f335(x86543,x86544)))+~P1(f335(f335(f337(x86545),x86544),x86546))+~P1(f335(f335(f337(x86541),x86542),f335(f335(f46(x86545,f934(x86541,a922)),x86546),x86543))) % 186.01/186.03 [8921]~P12(x89214,x89215,x89216,x89211)+E(f335(x89211,x89212),f335(x89211,x89213))+~P1(f335(f335(f337(f933(x89214,x89214)),f335(f335(f260(x89214,x89214),x89212),x89213)),x89216)) % 186.01/186.03 [8956]P1(f335(f335(f243(f934(x89561,a922)),x89562),f335(x89563,x89564)))+~P1(f335(f335(f337(x89565),x89564),x89566))+~P1(f335(f335(f243(f934(x89561,a922)),x89562),f335(f335(f46(x89565,f934(x89561,a922)),x89566),x89563))) % 186.01/186.03 [8989]~P56(x89893,x89894,f335(f294(x89894,x89893),x89895))+E(x89891,f195(f934(x89892,a922)))+E(f335(f335(f46(x89892,f934(x89893,a922)),x89891),f335(f335(f8(f934(x89894,a922),f934(x89893,a922),x89892),f293(x89894,x89893,x89895)),x89896)),f335(f293(x89894,x89893,x89895),f335(f335(f46(x89892,f934(x89894,a922)),x89891),x89896))) % 186.01/186.03 [9067]P1(f335(f335(f337(x90671),x90672),f335(f293(x90673,x90671,x90674),x90675)))+~P1(f335(f335(f337(x90673),x90676),x90675))+~P1(f335(f335(f337(f933(x90673,x90671)),f335(f335(f260(x90673,x90671),x90676),x90672)),x90674)) % 186.01/186.03 [9376]P1(f335(f335(f243(f934(x93761,a922)),f335(f293(x93762,x93761,x93763),x93764)),f335(f293(x93762,x93761,x93765),x93766)))+~P1(f335(f335(f243(f934(x93762,a922)),x93764),x93766))+~P1(f335(f335(f243(f934(f933(x93762,x93761),a922)),x93763),x93765)) % 186.01/186.03 [9558]~P1(f335(f335(f337(x95582),x95586),x95584))+~P1(f335(f335(f243(f934(x95581,a922)),x95583),x95585))+P1(f335(f335(f243(f934(f933(x95581,x95582),a922)),f335(f335(f262(x95581,x95582),x95583),f335(f16(f934(x95582,a922),x95581),x95584))),f335(f335(f262(x95581,x95582),x95585),f335(f16(f934(x95582,a922),x95581),x95584)))) % 186.01/186.03 [9570]~P35(x95701,x95702,x95703,x95705,x95706)+P1(f335(f335(f265(x95701,x95702,a922),x95703),x95704))+~P1(f335(f335(f337(f933(x95701,x95702)),x95704),f335(f179(f933(x95701,x95702)),f335(f335(f188(x95701,x95702),x95705),x95706)))) % 186.01/186.03 [9707]~E(x97073,x97075)+P1(f335(f335(f337(f933(f928(x97071),f928(x97071))),f335(f335(f260(f928(x97071),f928(x97071)),f335(f335(f158(x97071),x97072),x97073)),f335(f335(f158(x97071),x97074),x97075))),f164(x97071,x97076)))+~P1(f335(f335(f337(f933(x97071,x97071)),f335(f335(f260(x97071,x97071),x97072),x97074)),x97076)) % 186.01/186.03 [9713]~E(f335(f196(f928(x97131)),x97133),f335(f196(f928(x97131)),x97135))+P1(f335(f335(f337(f933(f928(x97131),f928(x97131))),f335(f335(f260(f928(x97131),f928(x97131)),f335(f335(f158(x97131),x97132),x97133)),f335(f335(f158(x97131),x97134),x97135))),f152(x97131,x97136)))+~P1(f335(f335(f337(f933(x97131,x97131)),f335(f335(f260(x97131,x97131),x97132),x97134)),x97136)) % 186.01/186.03 [9745]P1(f335(f335(f337(f933(x97451,x97451)),f335(f335(f260(x97451,x97451),x97452),x97453)),f335(f335(f190(f933(x97451,x97451),a922),f335(a119,x97454)),x97455)))+~P1(f335(f335(f337(f933(x97451,x97451)),f335(f335(f260(x97451,x97451),x97456),x97453)),x97455))+~P1(f335(f335(f337(f933(x97451,x97451)),f335(f335(f260(x97451,x97451),x97452),x97456)),f335(f335(f190(f933(x97451,x97451),a922),x97454),x97455))) % 186.01/186.03 [9746]P1(f335(f335(f337(f933(x97461,x97461)),f335(f335(f260(x97461,x97461),x97462),x97463)),f335(f335(f190(f933(x97461,x97461),a922),f335(a119,x97464)),x97465)))+~P1(f335(f335(f337(f933(x97461,x97461)),f335(f335(f260(x97461,x97461),x97462),x97466)),x97465))+~P1(f335(f335(f337(f933(x97461,x97461)),f335(f335(f260(x97461,x97461),x97466),x97463)),f335(f335(f190(f933(x97461,x97461),a922),x97464),x97465))) % 186.01/186.03 [9749]~P1(f335(f335(f337(x97494),x97495),x97496))+P1(f335(f335(f243(f934(x97491,a922)),x97492),x97493))+~P1(f335(f335(f243(f934(f933(x97491,x97494),a922)),f335(f335(f262(x97491,x97494),x97492),f335(f16(f934(x97494,a922),x97491),x97496))),f335(f335(f262(x97491,x97494),x97493),f335(f16(f934(x97494,a922),x97491),x97496)))) % 186.01/186.03 [9794]E(x97941,x97942)+~P1(f335(f335(f337(f933(f928(x97943),f928(x97943))),f335(f335(f260(f928(x97943),f928(x97943)),f335(f335(f158(x97943),x97941),x97945)),f335(f335(f158(x97943),x97942),x97946))),f152(x97943,x97944)))+P1(f335(f335(f337(f933(x97943,x97943)),f335(f335(f260(x97943,x97943),x97941),x97942)),x97944)) % 186.01/186.03 [9795]E(x97951,x97952)+~P1(f335(f335(f337(f933(f928(x97953),f928(x97953))),f335(f335(f260(f928(x97953),f928(x97953)),f335(f335(f158(x97953),x97951),x97955)),f335(f335(f158(x97953),x97952),x97956))),f154(x97953,x97954)))+P1(f335(f335(f337(f933(x97953,x97953)),f335(f335(f260(x97953,x97953),x97951),x97952)),x97954)) % 186.01/186.03 [9796]E(x97961,x97962)+~P1(f335(f335(f337(f933(f928(x97963),f928(x97963))),f335(f335(f260(f928(x97963),f928(x97963)),f335(f335(f158(x97963),x97961),x97965)),f335(f335(f158(x97963),x97962),x97966))),f164(x97963,x97964)))+P1(f335(f335(f337(f933(x97963,x97963)),f335(f335(f260(x97963,x97963),x97961),x97962)),x97964)) % 186.01/186.03 [9832]P1(f335(f335(f337(f933(f928(x98321),f928(x98321))),f335(f335(f260(f928(x98321),f928(x98321)),f335(f335(f158(x98321),x98322),x98323)),f335(f335(f158(x98321),x98324),x98325))),f165(x98321,x98326)))+~P1(f335(f335(f337(f933(f928(x98321),f928(x98321))),f335(f335(f260(f928(x98321),f928(x98321)),x98323),x98325)),f165(x98321,x98326)))+~P1(f335(f335(f337(f933(x98321,x98321)),f335(f335(f260(x98321,x98321),x98322),x98324)),x98326)) % 186.01/186.03 [9849]P1(f335(x98491,x98492))+~P1(f335(x98491,f651(x98491,x98493,x98494,x98495,x98496)))+~P1(f335(f335(f337(x98496),x98492),f335(f335(f45(x98495,f934(x98496,a922)),x98494),x98493))) % 186.01/186.03 [9854]~P1(f335(f335(f337(f933(f928(x98541),f928(x98541))),f335(f335(f260(f928(x98541),f928(x98541)),f335(f335(f158(x98541),x98542),x98545)),f335(f335(f158(x98541),x98543),x98546))),f152(x98541,x98544)))+P1(f335(f335(f337(f933(f928(x98541),f928(x98541))),f335(f335(f260(f928(x98541),f928(x98541)),x98545),x98546)),f152(x98541,x98544)))+P1(f335(f335(f337(f933(x98541,x98541)),f335(f335(f260(x98541,x98541),x98542),x98543)),x98544)) % 186.01/186.03 [9855]~P1(f335(f335(f337(f933(f928(x98551),f928(x98551))),f335(f335(f260(f928(x98551),f928(x98551)),f335(f335(f158(x98551),x98552),x98555)),f335(f335(f158(x98551),x98553),x98556))),f154(x98551,x98554)))+P1(f335(f335(f337(f933(f928(x98551),f928(x98551))),f335(f335(f260(f928(x98551),f928(x98551)),x98555),x98556)),f154(x98551,x98554)))+P1(f335(f335(f337(f933(x98551,x98551)),f335(f335(f260(x98551,x98551),x98552),x98553)),x98554)) % 186.01/186.03 [9856]~P1(f335(f335(f337(f933(f928(x98561),f928(x98561))),f335(f335(f260(f928(x98561),f928(x98561)),f335(f335(f158(x98561),x98562),x98565)),f335(f335(f158(x98561),x98563),x98566))),f164(x98561,x98564)))+P1(f335(f335(f337(f933(f928(x98561),f928(x98561))),f335(f335(f260(f928(x98561),f928(x98561)),x98565),x98566)),f164(x98561,x98564)))+P1(f335(f335(f337(f933(x98561,x98561)),f335(f335(f260(x98561,x98561),x98562),x98563)),x98564)) % 186.01/186.03 [9946]P1(f335(x99461,x99462))+P1(f335(f335(f337(x99463),f643(x99461,x99464,x99465,x99463,x99466)),x99465))+~P1(f335(f335(f337(x99466),x99462),f335(f335(f45(x99463,f934(x99466,a922)),x99465),x99464))) % 186.01/186.03 [9957]~E(x99572,x99574)+P1(f335(f335(f337(f933(f928(x99571),f928(x99571))),f335(f335(f260(f928(x99571),f928(x99571)),f335(f335(f141(x99571),x99572),f335(f335(f158(x99571),x99573),f120(x99571)))),f335(f335(f141(x99571),x99574),f335(f335(f158(x99571),x99575),f120(x99571))))),f164(x99571,x99576)))+~P1(f335(f335(f337(f933(x99571,x99571)),f335(f335(f260(x99571,x99571),x99573),x99575)),x99576)) % 186.01/186.03 [10032]E(x100321,x100322)+~P1(f335(f335(f337(f933(f928(x100323),f928(x100323))),f335(f335(f260(f928(x100323),f928(x100323)),f335(f335(f141(x100323),x100325),f335(f335(f158(x100323),x100321),f120(x100323)))),f335(f335(f141(x100323),x100326),f335(f335(f158(x100323),x100322),f120(x100323))))),f164(x100323,x100324)))+P1(f335(f335(f337(f933(x100323,x100323)),f335(f335(f260(x100323,x100323),x100321),x100322)),x100324)) % 186.01/186.03 [10064]~P1(f335(f335(f337(f933(f928(x100641),f928(x100641))),f335(f335(f260(f928(x100641),f928(x100641)),f335(f335(f141(x100641),x100645),f335(f335(f158(x100641),x100642),f120(x100641)))),f335(f335(f141(x100641),x100646),f335(f335(f158(x100641),x100643),f120(x100641))))),f164(x100641,x100644)))+P1(f335(f335(f337(f933(f928(x100641),f928(x100641))),f335(f335(f260(f928(x100641),f928(x100641)),x100645),x100646)),f164(x100641,x100644)))+P1(f335(f335(f337(f933(x100641,x100641)),f335(f335(f260(x100641,x100641),x100642),x100643)),x100644)) % 186.01/186.03 [10084]P1(f335(x100841,x100842))+P1(f335(f335(f337(x100843),f651(x100841,x100844,x100845,x100846,x100843)),f335(x100844,f643(x100841,x100844,x100845,x100846,x100843))))+~P1(f335(f335(f337(x100843),x100842),f335(f335(f45(x100846,f934(x100843,a922)),x100845),x100844))) % 186.01/186.03 [10239]P1(f335(f335(f337(x102391),f856(x102392,x102393,x102394,x102395,x102396,x102391)),x102395))+~P1(f335(f335(f243(f934(x102391,a922)),x102396),x102395))+P1(f335(f335(f243(f934(x102394,a922)),f335(f335(f46(x102391,f934(x102394,a922)),x102395),x102393)),f335(f335(f46(x102391,f934(x102394,a922)),x102395),x102392))) % 186.01/186.03 [10363]~P1(f335(f335(f243(f934(x103631,a922)),f335(x103634,f856(x103635,x103634,x103631,x103633,x103636,x103632))),f335(x103635,f856(x103635,x103634,x103631,x103633,x103636,x103632))))+~P1(f335(f335(f243(f934(x103632,a922)),x103636),x103633))+P1(f335(f335(f243(f934(x103631,a922)),f335(f335(f46(x103632,f934(x103631,a922)),x103633),x103634)),f335(f335(f46(x103632,f934(x103631,a922)),x103633),x103635))) % 186.01/186.03 [9087]~P17(x90873,x90874,x90871)+~P1(f335(f67(x90873),x90876))+E(f335(f335(x90871,x90872),f335(f335(f70(x90873,x90874,x90871),x90875),f335(f335(f23(f934(x90873,a922)),x90876),f335(f335(f317(x90873),x90872),f195(f934(x90873,a922)))))),f335(f335(f70(x90873,x90874,x90871),x90875),f335(f335(f317(x90873),x90872),x90876))) % 186.01/186.03 [9385]~P1(f335(f335(f337(x93855),x93853),x93856))+P1(f335(f335(f243(f934(x93851,a922)),f335(x93852,x93853)),x93854))+~P1(f335(f335(f243(f934(x93851,a922)),f335(f335(f45(x93855,f934(x93851,a922)),x93856),x93852)),x93854)) % 186.01/186.03 [10007]~P9(x100071,x100075,x100074)+P1(f335(f335(f337(f933(x100071,x100071)),f335(f335(f260(x100071,x100071),x100072),x100073)),x100074))+~P1(f335(f335(f337(x100071),x100076),f335(f335(f108(f934(x100071,a922)),f335(f293(x100071,x100071,x100074),f335(f335(f317(x100071),x100072),f195(f934(x100071,a922))))),f335(f293(x100071,x100071,x100074),f335(f335(f317(x100071),x100073),f195(f934(x100071,a922))))))) % 186.01/186.03 [8809]~P112(x88092)+~E(f335(f335(f86(x88092),f335(f335(f87(x88092),x88094),x88095)),x88091),f335(f335(f86(x88092),f335(f335(f87(x88092),x88093),x88095)),x88096))+E(x88091,f335(f335(f86(x88092),f335(f335(f87(x88092),f335(f335(f23(x88092),x88093),x88094)),x88095)),x88096)) % 186.01/186.03 [8810]~P112(x88101)+~E(f335(f335(f86(x88101),f335(f335(f87(x88101),x88102),x88104)),x88105),f335(f335(f86(x88101),f335(f335(f87(x88101),x88103),x88104)),x88106))+E(f335(f335(f86(x88101),f335(f335(f87(x88101),f335(f335(f23(x88101),x88102),x88103)),x88104)),x88105),x88106) % 186.01/186.03 [8992]~P112(x89921)+E(f335(f335(f86(x89921),f335(f335(f87(x89921),x89922),x89923)),x89924),f335(f335(f86(x89921),f335(f335(f87(x89921),x89925),x89923)),x89926))+~E(x89926,f335(f335(f86(x89921),f335(f335(f87(x89921),f335(f335(f23(x89921),x89922),x89925)),x89923)),x89924)) % 186.01/186.03 [8993]~P112(x89931)+E(f335(f335(f86(x89931),f335(f335(f87(x89931),x89932),x89933)),x89934),f335(f335(f86(x89931),f335(f335(f87(x89931),x89935),x89933)),x89936))+~E(f335(f335(f86(x89931),f335(f335(f87(x89931),f335(f335(f23(x89931),x89932),x89935)),x89933)),x89934),x89936) % 186.01/186.03 [9322]~P1(f335(f335(x93224,x93225),x93226))+~P1(f335(f335(x93223,x93225),x93226))+P1(f335(f335(f335(f335(f108(f934(x93221,f934(x93222,a922))),x93223),x93224),x93225),x93226)) % 186.01/186.03 [9579]P1(f335(f335(x95791,x95792),x95793))+P1(f335(f335(x95794,x95792),x95793))+~P1(f335(f335(f335(f335(f117(f934(x95795,f934(x95796,a922))),x95794),x95791),x95792),x95793)) % 186.01/186.03 [9869]~P128(x98691)+~P1(f335(f335(f243(x98691),f335(f335(f86(x98691),f335(f335(f87(x98691),x98694),x98695)),x98692)),f335(f335(f86(x98691),f335(f335(f87(x98691),x98693),x98695)),x98696)))+P1(f335(f335(f243(x98691),x98692),f335(f335(f86(x98691),f335(f335(f87(x98691),f335(f335(f23(x98691),x98693),x98694)),x98695)),x98696))) % 186.01/186.03 [9870]~P128(x98701)+~P1(f335(f335(f244(x98701),f335(f335(f86(x98701),f335(f335(f87(x98701),x98704),x98705)),x98702)),f335(f335(f86(x98701),f335(f335(f87(x98701),x98703),x98705)),x98706)))+P1(f335(f335(f244(x98701),x98702),f335(f335(f86(x98701),f335(f335(f87(x98701),f335(f335(f23(x98701),x98703),x98704)),x98705)),x98706))) % 186.01/186.03 [9894]~P128(x98941)+P1(f335(f335(f243(x98941),f335(f335(f86(x98941),f335(f335(f87(x98941),x98942),x98943)),x98944)),f335(f335(f86(x98941),f335(f335(f87(x98941),x98945),x98943)),x98946)))+~P1(f335(f335(f243(x98941),x98944),f335(f335(f86(x98941),f335(f335(f87(x98941),f335(f335(f23(x98941),x98945),x98942)),x98943)),x98946))) % 186.01/186.03 [9895]~P128(x98951)+P1(f335(f335(f244(x98951),f335(f335(f86(x98951),f335(f335(f87(x98951),x98952),x98953)),x98954)),f335(f335(f86(x98951),f335(f335(f87(x98951),x98955),x98953)),x98956)))+~P1(f335(f335(f244(x98951),x98954),f335(f335(f86(x98951),f335(f335(f87(x98951),f335(f335(f23(x98951),x98955),x98952)),x98953)),x98956))) % 186.01/186.03 [9999]~P128(x99991)+~P1(f335(f335(f243(x99991),f335(f335(f86(x99991),f335(f335(f87(x99991),x99992),x99994)),x99995)),f335(f335(f86(x99991),f335(f335(f87(x99991),x99993),x99994)),x99996)))+P1(f335(f335(f243(x99991),f335(f335(f86(x99991),f335(f335(f87(x99991),f335(f335(f23(x99991),x99992),x99993)),x99994)),x99995)),x99996)) % 186.01/186.03 [10000]~P128(x100001)+~P1(f335(f335(f244(x100001),f335(f335(f86(x100001),f335(f335(f87(x100001),x100002),x100004)),x100005)),f335(f335(f86(x100001),f335(f335(f87(x100001),x100003),x100004)),x100006)))+P1(f335(f335(f244(x100001),f335(f335(f86(x100001),f335(f335(f87(x100001),f335(f335(f23(x100001),x100002),x100003)),x100004)),x100005)),x100006)) % 186.01/186.03 [10047]~P128(x100471)+P1(f335(f335(f243(x100471),f335(f335(f86(x100471),f335(f335(f87(x100471),x100472),x100473)),x100474)),f335(f335(f86(x100471),f335(f335(f87(x100471),x100475),x100473)),x100476)))+~P1(f335(f335(f243(x100471),f335(f335(f86(x100471),f335(f335(f87(x100471),f335(f335(f23(x100471),x100472),x100475)),x100473)),x100474)),x100476)) % 186.01/186.03 [10048]~P128(x100481)+P1(f335(f335(f244(x100481),f335(f335(f86(x100481),f335(f335(f87(x100481),x100482),x100483)),x100484)),f335(f335(f86(x100481),f335(f335(f87(x100481),x100485),x100483)),x100486)))+~P1(f335(f335(f244(x100481),f335(f335(f86(x100481),f335(f335(f87(x100481),f335(f335(f23(x100481),x100482),x100485)),x100483)),x100484)),x100486)) % 186.01/186.03 [10224]~P76(x102242)+~P1(f335(f67(x102241),x102246))+E(f335(f335(f6(x102241,x102242),f335(f335(f18(x102241,x102242,x102242),f335(f335(f18(x102241,x102242,f934(x102242,x102242)),f335(f335(f8(a922,f934(x102242,f934(x102242,x102242)),x102241),f103(x102242)),x102243)),x102244)),x102245)),x102246),f335(f335(f86(x102242),f335(f335(f6(x102241,x102242),x102244),f335(f335(f108(f934(x102241,a922)),x102246),f335(f270(x102241),x102243)))),f335(f335(f6(x102241,x102242),x102245),f335(f335(f108(f934(x102241,a922)),x102246),f335(f85(f934(x102241,a922)),f335(f270(x102241),x102243)))))) % 186.01/186.03 [10286]P1(f335(f335(f337(x102862),x102864),x102866))+P1(f335(f335(f337(x102862),x102865),x102866))+E(f335(f319(x102861,x102862,f335(f335(f7(x102861,x102862,x102862),f335(f335(f7(x102861,x102862,f934(x102862,x102862)),f335(f335(f8(a922,f934(x102862,f934(x102862,x102862)),x102861),f103(x102862)),f335(f335(f7(x102861,f934(x102861,a922),a922),f337(x102861)),x102863))),x102864)),x102865)),x102866),f195(f934(x102861,a922))) % 186.01/186.03 [10287]P1(f335(f335(f337(x102872),x102875),x102876))+~P1(f335(f335(f337(x102872),x102874),x102876))+E(f335(f319(x102871,x102872,f335(f335(f7(x102871,x102872,x102872),f335(f335(f7(x102871,x102872,f934(x102872,x102872)),f335(f335(f8(a922,f934(x102872,f934(x102872,x102872)),x102871),f103(x102872)),f335(f335(f7(x102871,f934(x102871,a922),a922),f337(x102871)),x102873))),x102874)),x102875)),x102876),x102873) % 186.01/186.03 [10288]P1(f335(f335(f337(x102882),x102884),x102886))+~P1(f335(f335(f337(x102882),x102885),x102886))+E(f335(f319(x102881,x102882,f335(f335(f7(x102881,x102882,x102882),f335(f335(f7(x102881,x102882,f934(x102882,x102882)),f335(f335(f8(a922,f934(x102882,f934(x102882,x102882)),x102881),f103(x102882)),f335(f335(f7(x102881,f934(x102881,a922),a922),f337(x102881)),x102883))),x102884)),x102885)),x102886),f335(f85(f934(x102881,a922)),x102883)) % 186.01/186.03 [10289]~P1(f335(f335(f337(x102892),x102894),x102896))+~P1(f335(f335(f337(x102892),x102895),x102896))+E(f335(f319(x102891,x102892,f335(f335(f7(x102891,x102892,x102892),f335(f335(f7(x102891,x102892,f934(x102892,x102892)),f335(f335(f8(a922,f934(x102892,f934(x102892,x102892)),x102891),f103(x102892)),f335(f335(f7(x102891,f934(x102891,a922),a922),f337(x102891)),x102893))),x102894)),x102895)),x102896),f250(f934(x102891,a922))) % 186.01/186.03 [8842]E(x88421,x88422)+~P58(x88424,x88425,x88423,x88426,x88427)+~E(f335(x88423,x88421),f335(x88423,x88422)) % 186.01/186.03 [8871]~P11(x88716,x88715,x88717,x88714,x88711)+E(f335(f335(x88711,x88712),x88713),x88714)+P1(f335(f67(x88715),x88713)) % 186.01/186.03 [9736]P43(x97361,x97362,x97363,x97364,x97365,f335(f335(x97363,x97366),x97367))+~E(f335(f335(x97363,x97366),x97367),x97364)+~E(x97365,f195(f934(x97361,a922))) % 186.01/186.03 [9916]~P1(f335(x99166,x99163))+~P1(f335(f335(f337(f933(x99162,x99162)),f335(f335(f260(x99162,x99162),x99164),x99165)),f335(x99167,x99163)))+P1(f335(f335(f337(f933(f933(x99161,x99162),f933(x99161,x99162))),f335(f335(f260(f933(x99161,x99162),f933(x99161,x99162)),f335(f335(f260(x99161,x99162),x99163),x99164)),f335(f335(f260(x99161,x99162),x99163),x99165))),f288(x99161,x99162,x99166,x99167))) % 186.01/186.03 [10351]~P43(x103512,x103517,x103513,x103516,x103511,f335(f335(x103513,x103515),x103514))+E(f335(f335(x103513,f520(x103514,x103515,x103511,x103516,x103513,x103517,x103512)),f530(x103514,x103515,x103511,x103516,x103513,x103517,x103512)),f335(f335(x103513,x103515),x103514))+E(x103511,f195(f934(x103512,a922))) % 186.01/186.03 [10352]~P43(x103527,x103526,x103521,x103524,x103525,f335(f335(x103521,x103522),x103523))+E(f335(f335(x103521,f520(x103523,x103522,x103525,x103524,x103521,x103526,x103527)),f530(x103523,x103522,x103525,x103524,x103521,x103526,x103527)),f335(f335(x103521,x103522),x103523))+E(f335(f335(x103521,x103522),x103523),x103524) % 186.01/186.03 [9418]~P35(x94181,x94182,x94183,x94185,x94187)+P35(x94181,x94182,x94183,f335(f335(f158(x94181),x94184),x94185),f335(f335(f158(x94182),x94186),x94187))+~P1(f335(f335(x94183,x94184),x94186)) % 186.01/186.03 [9434]P35(x94341,x94342,x94343,x94344,x94345)+~P35(x94341,x94342,x94343,f335(f335(f141(x94341),x94346),x94344),f335(f335(f141(x94342),x94347),x94345))+~E(f335(f196(f928(x94341)),x94346),f335(f196(f928(x94342)),x94347)) % 186.01/186.03 [9435]P35(x94351,x94352,x94353,x94354,x94355)+~P35(x94351,x94352,x94353,f335(f335(f141(x94351),x94354),x94356),f335(f335(f141(x94352),x94355),x94357))+~E(f335(f196(f928(x94351)),x94354),f335(f196(f928(x94352)),x94355)) % 186.01/186.03 [9643]~P35(x96431,x96432,x96433,x96435,x96437)+~P35(x96431,x96432,x96433,x96434,x96436)+P35(x96431,x96432,x96433,f335(f335(f141(x96431),x96434),x96435),f335(f335(f141(x96432),x96436),x96437)) % 186.01/186.03 [9992]~P1(f335(f72(x99921,x99924,x99925,x99926,x99923),x99927))+P1(f335(f72(x99921,x99924,x99925,x99926,f335(f335(f317(x99921),x99922),x99923)),f335(f335(x99925,x99922),x99927)))+P1(f335(f335(f337(x99921),x99922),x99923)) % 186.01/186.03 [10379]~P43(x103792,x103797,x103796,x103795,x103791,f335(f335(x103796,x103794),x103793))+E(x103791,f195(f934(x103792,a922)))+P1(f335(f335(f337(x103792),f520(x103793,x103794,x103791,x103795,x103796,x103797,x103792)),x103791)) % 186.01/186.03 [10380]~P43(x103805,x103807,x103801,x103804,x103806,f335(f335(x103801,x103802),x103803))+E(f335(f335(x103801,x103802),x103803),x103804)+P1(f335(f335(f337(x103805),f520(x103803,x103802,x103806,x103804,x103801,x103807,x103805)),x103806)) % 186.01/186.03 [10472]E(f335(f335(f260(x104721,x104722),x104723),x104724),f335(f335(f260(x104721,x104722),x104725),x104726))+P1(f335(f335(f337(f933(f933(x104721,x104722),f933(x104721,x104722))),f335(f335(f260(f933(x104721,x104722),f933(x104721,x104722)),f335(f335(f260(x104721,x104722),f859(x104727,x104724,x104723,x104726,x104725,x104722,x104721)),f860(x104727,x104724,x104723,x104726,x104725,x104722,x104721))),f335(f335(f260(x104721,x104722),x104723),x104724))),f315(f933(x104721,x104722),x104727)))+~P1(f335(f335(f337(f933(f933(x104721,x104722),f933(x104721,x104722))),f335(f335(f260(f933(x104721,x104722),f933(x104721,x104722)),f335(f335(f260(x104721,x104722),x104725),x104726)),f335(f335(f260(x104721,x104722),x104723),x104724))),f315(f933(x104721,x104722),x104727))) % 186.01/186.03 [9112]~P22(x91124,x91125,x91126,x91127,x91121)+~P1(f335(f67(x91125),x91123))+E(f335(f335(x91121,x91122),x91123),f335(f335(f335(f71(x91124,x91125,x91126),x91122),x91127),x91123)) % 186.01/186.03 [9113]~P11(x91134,x91135,x91136,x91137,x91131)+~P1(f335(f67(x91135),x91133))+E(f335(f335(x91131,x91132),x91133),f335(f335(f335(f71(x91134,x91135,x91136),x91132),x91137),x91133)) % 186.01/186.03 [9880]~P25(x98801,x98802,f335(f335(f317(f926(x98801)),f98(x98801,x98803,x98804,x98807)),f195(f934(f926(x98801),a922))))+P25(x98801,x98802,f335(f335(f317(f926(x98801)),f98(x98801,x98803,f32(x98804,x98805),x98806)),f195(f934(f926(x98801),a922))))+~P25(x98801,x98802,f335(f335(f317(f926(x98801)),f98(x98801,x98807,x98805,x98806)),f195(f934(f926(x98801),a922)))) % 186.01/186.03 [9889]~P24(x98893,x98894,x98895,x98897,x98896,x98891)+~P1(f335(f67(x98894),x98892))+E(f335(x98891,x98892),f335(f335(f335(f71(x98893,x98894,x98895),x98896),x98897),x98892)) % 186.01/186.03 [10041]P43(x100411,x100412,x100413,x100414,x100415,f335(f335(x100413,x100416),x100417))+~P43(x100411,x100412,x100413,x100414,f335(f335(f23(f934(x100411,a922)),x100415),f335(f335(f317(x100411),x100416),f195(f934(x100411,a922)))),x100417)+~P1(f335(f335(f337(x100411),x100416),x100415)) % 186.01/186.03 [10170]~P25(x101701,x101702,f335(f335(f317(f926(x101701)),f98(x101701,f99(x101701,x101703,x101704),x101705,x101707)),f195(f934(f926(x101701),a922))))+P25(x101701,x101702,f335(f335(f317(f926(x101701)),f98(x101701,x101703,f29(x101704,x101705,x101706),x101707)),f195(f934(f926(x101701),a922))))+~P25(x101701,x101702,f335(f335(f317(f926(x101701)),f98(x101701,f99(x101701,x101703,f335(f78(a922,a922,a923,a330),x101704)),x101706,x101707)),f195(f934(f926(x101701),a922)))) % 186.01/186.03 [10405]P1(f335(f335(x104057,f814(x104054,x104055,x104051,x104056,x104053,x104052,x104057)),f815(x104054,x104055,x104051,x104056,x104053,x104052,x104057)))+~P1(f335(f335(x104057,f335(f264(x104052,x104053),x104056)),f335(f259(x104052,x104053),x104056)))+P1(f335(x104051,f335(f335(f265(x104052,x104053,x104054),x104055),x104056))) % 186.01/186.03 [10406]P25(x104067,x104066,f335(f335(f317(f926(x104067)),f98(x104067,x104061,x104064,x104062)),f195(f934(f926(x104067),a922))))+~P25(x104067,x104066,f335(f335(f317(f926(x104067)),f98(x104067,x104065,x104064,x104063)),f195(f934(f926(x104067),a922))))+P1(f335(f335(x104061,f911(x104062,x104061,x104063,x104064,x104065,x104066,x104067)),f920(x104062,x104061,x104063,x104064,x104065,x104066,x104067))) % 186.01/186.03 [10417]~P43(x104172,x104173,x104174,x104175,x104171,f335(f335(x104174,x104177),x104176))+P43(x104172,x104173,x104174,x104175,f335(f335(f23(f934(x104172,a922)),x104171),f335(f335(f317(x104172),f520(x104176,x104177,x104171,x104175,x104174,x104173,x104172)),f195(f934(x104172,a922)))),f530(x104176,x104177,x104171,x104175,x104174,x104173,x104172))+E(x104171,f195(f934(x104172,a922))) % 186.01/186.03 [10418]~P43(x104185,x104186,x104181,x104184,x104187,f335(f335(x104181,x104182),x104183))+P43(x104185,x104186,x104181,x104184,f335(f335(f23(f934(x104185,a922)),x104187),f335(f335(f317(x104185),f520(x104183,x104182,x104187,x104184,x104181,x104186,x104185)),f195(f934(x104185,a922)))),f530(x104183,x104182,x104187,x104184,x104181,x104186,x104185))+E(f335(f335(x104181,x104182),x104183),x104184) % 186.01/186.03 [10419]~P25(x104191,x104192,f335(f335(f317(f926(x104191)),f98(x104191,x104197,x104194,x104196)),f195(f934(f926(x104191),a922))))+P25(x104191,x104192,f335(f335(f317(f926(x104191)),f98(x104191,x104193,x104194,x104195)),f195(f934(f926(x104191),a922))))+~P1(f335(f335(x104195,f911(x104195,x104193,x104196,x104194,x104197,x104192,x104191)),f353(x104195,x104193,x104196,x104194,x104197,x104192,x104191))) % 186.01/186.03 [10439]~P1(f335(x104391,f335(f335(x104395,f815(x104394,x104395,x104391,x104396,x104393,x104392,x104397)),f814(x104394,x104395,x104391,x104396,x104393,x104392,x104397))))+~P1(f335(f335(x104397,f335(f264(x104392,x104393),x104396)),f335(f259(x104392,x104393),x104396)))+P1(f335(x104391,f335(f335(f265(x104392,x104393,x104394),x104395),x104396))) % 186.01/186.03 [9721]P1(f335(f335(f243(f934(f933(x97211,x97212),a922)),f335(f335(f297(x97211,x97213,x97212),x97214),x97215)),f335(f335(f297(x97211,x97213,x97212),x97216),x97217)))+~P1(f335(f335(f243(f934(f933(x97213,x97212),a922)),x97215),x97217))+~P1(f335(f335(f243(f934(f933(x97211,x97213),a922)),x97214),x97216)) % 186.01/186.03 [10466]E(f335(f335(f260(x104661,x104662),x104663),x104664),f335(f335(f260(x104661,x104662),x104665),x104666))+~P1(f335(f335(f337(f933(f933(x104661,x104662),f933(x104661,x104662))),f335(f335(f260(f933(x104661,x104662),f933(x104661,x104662)),f335(f335(f260(x104661,x104662),x104663),x104664)),f335(f335(f260(x104661,x104662),x104665),x104666))),f315(f933(x104661,x104662),x104667)))+P1(f335(f335(f337(f933(f933(x104661,x104662),f933(x104661,x104662))),f335(f335(f260(f933(x104661,x104662),f933(x104661,x104662)),f335(f335(f260(x104661,x104662),x104663),x104664)),f335(f335(f260(x104661,x104662),f859(x104667,x104666,x104665,x104664,x104663,x104662,x104661)),f860(x104667,x104666,x104665,x104664,x104663,x104662,x104661)))),x104667)) % 186.01/186.03 [10053]~P1(f335(f335(f337(x100531),x100536),x100535))+P1(f335(f72(x100531,x100532,x100533,x100534,x100535),f335(f335(x100533,x100536),x100537)))+~P1(f335(f72(x100531,x100532,x100533,x100534,f335(f335(f23(f934(x100531,a922)),x100535),f335(f335(f317(x100531),x100536),f195(f934(x100531,a922))))),x100537)) % 186.01/186.03 [10479]~P145(x104791)+~P26(f933(x104792,x104793),x104791,f335(f265(x104792,x104793,x104791),f335(f335(f7(x104792,f934(x104793,x104791),f934(x104793,x104791)),f335(f335(f8(f934(x104791,x104791),f934(f934(x104793,x104791),f934(x104793,x104791)),x104792),f8(x104791,x104791,x104793)),f335(f335(f8(x104791,f934(x104791,x104791),x104792),f87(x104791)),x104794))),x104795)),f335(f335(f262(x104792,x104793),x104796),f335(f16(f934(x104793,a922),x104792),x104797)))+E(f335(f335(f6(x104791,x104791),f25(x104791)),f335(f270(x104791),f335(f335(f8(f934(x104792,a922),a922,x104791),f93(x104792)),f335(f335(f8(f934(x104792,f934(x104793,a922)),f934(x104792,a922),x104791),f335(f8(f934(x104793,a922),a922,x104792),f93(x104793))),f335(f335(f7(x104791,f934(x104792,f934(x104793,a922)),f934(x104792,f934(x104793,a922))),f335(f335(f8(f934(x104792,f934(f934(x104793,a922),f934(x104793,a922))),f934(f934(x104792,f934(x104793,a922)),f934(x104792,f934(x104793,a922))),x104791),f18(x104792,f934(x104793,a922),f934(x104793,a922))),f335(f335(f8(f934(x104792,f934(x104793,f934(a922,a922))),f934(x104792,f934(f934(x104793,a922),f934(x104793,a922))),x104791),f335(f8(f934(x104793,f934(a922,a922)),f934(f934(x104793,a922),f934(x104793,a922)),x104792),f18(x104793,a922,a922))),f335(f335(f8(f934(x104792,f934(x104793,a922)),f934(x104792,f934(x104793,f934(a922,a922))),x104791),f335(f8(f934(x104793,a922),f934(x104793,f934(a922,a922)),x104792),f335(f8(a922,f934(a922,a922),x104793),a333))),f335(f335(f7(x104791,f934(x104792,f934(x104793,x104791)),f934(x104792,f934(x104793,a922))),f335(f335(f8(f934(f934(x104793,x104791),f934(x104793,a922)),f934(f934(x104792,f934(x104793,x104791)),f934(x104792,f934(x104793,a922))),x104791),f8(f934(x104793,x104791),f934(x104793,a922),x104792)),f335(f335(f8(f934(x104791,a922),f934(f934(x104793,x104791),f934(x104793,a922)),x104791),f8(x104791,a922,x104793)),a332))),f335(f335(f7(x104792,f934(x104793,x104791),f934(x104793,x104791)),f335(f335(f8(f934(x104791,x104791),f934(f934(x104793,x104791),f934(x104793,x104791)),x104792),f8(x104791,x104791,x104793)),f335(f335(f8(x104791,f934(x104791,x104791),x104792),f87(x104791)),x104794))),x104795)))))),f335(f335(f7(x104792,f934(x104793,a922),f934(x104793,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x104793,a922),f934(x104793,a922)),x104792),f8(a922,a922,x104793)),f335(f335(f8(a922,f934(a922,a922),x104792),a333),f335(f335(f7(x104792,f934(x104792,a922),a922),f337(x104792)),x104796)))),f335(f335(f7(x104793,f934(x104793,a922),a922),f337(x104793)),x104797))))))),f335(f335(f87(x104791),f335(f335(f6(x104792,x104791),x104794),x104796)),f335(f335(f6(x104793,x104791),x104795),x104797))) % 186.01/186.03 [9725]~P27(x97251,x97253,x97255,x97256,x97258)+~P27(x97253,x97252,x97254,x97258,x97257)+P27(x97251,x97252,f335(f78(x97253,x97252,x97251,x97254),x97255),x97256,x97257) % 186.01/186.03 [9754]P27(x97541,x97542,x97543,x97544,x97545)+~P27(x97546,x97541,x97547,x97548,x97544)+~P27(x97546,x97542,f335(f78(x97541,x97542,x97546,x97543),x97547),x97548,x97545) % 186.01/186.03 [9887]~P1(f335(f335(x98874,x98876),x98878))+~P1(f335(f335(x98875,x98878),x98877))+P1(f335(f335(f261(x98871,x98872,x98873,x98874,x98875),x98876),x98877)) % 186.01/186.03 [9486]~P20(x94868,x94861,x94863,x94865)+~P1(f335(f67(x94868),x94866))+E(f335(f78(x94861,x94861,x94862,f335(x94863,x94864)),f335(f78(x94861,x94861,x94862,f335(x94865,x94866)),x94867)),f335(f78(x94861,x94861,x94862,f335(x94865,x94866)),f335(f78(x94861,x94861,x94862,f335(x94863,x94864)),x94867))) % 186.01/186.03 [9876]~P23(x98767,x98762,x98765,x98768,x98766,x98761)+~P1(f335(f67(x98762),x98764))+E(f335(x98761,f335(f335(f317(x98762),x98763),x98764)),f335(f335(x98765,f335(x98766,x98763)),f335(x98761,x98764))) % 186.01/186.03 [9997]~P26(x99972,x99974,x99976,x99978)+~P26(x99971,x99973,x99975,x99977)+P26(f933(x99971,x99972),f933(x99973,x99974),f266(x99971,x99973,x99972,x99974,x99975,x99976),f335(f335(f262(x99971,x99972),x99977),f335(f16(f934(x99972,a922),x99971),x99978))) % 186.01/186.03 [9669]P1(f335(f335(f337(f933(x96691,x96692)),f335(f335(f260(x96691,x96692),x96693),x96694)),f335(f335(f297(x96691,x96695,x96692),x96696),x96697)))+~P1(f335(f335(f337(f933(x96691,x96695)),f335(f335(f260(x96691,x96695),x96693),x96698)),x96696))+~P1(f335(f335(f337(f933(x96695,x96692)),f335(f335(f260(x96695,x96692),x96698),x96694)),x96697)) % 186.01/186.03 [9857]~P1(f335(f335(f243(f934(f933(x98573,x98572),a922)),x98575),f335(f335(f262(x98573,x98572),x98578),f335(f16(f934(x98572,a922),x98573),x98577))))+~P1(f335(f335(f243(f934(f933(x98571,x98573),a922)),x98574),f335(f335(f262(x98571,x98573),x98576),f335(f16(f934(x98573,a922),x98571),x98578))))+P1(f335(f335(f243(f934(f933(x98571,x98572),a922)),f335(f335(f297(x98571,x98573,x98572),x98574),x98575)),f335(f335(f262(x98571,x98572),x98576),f335(f16(f934(x98572,a922),x98571),x98577)))) % 186.01/186.03 [9911]~E(x99113,x99115)+P1(f335(f335(f337(f933(f933(x99111,x99112),f933(x99111,x99112))),f335(f335(f260(f933(x99111,x99112),f933(x99111,x99112)),f335(f335(f260(x99111,x99112),x99113),x99114)),f335(f335(f260(x99111,x99112),x99115),x99116))),f328(x99111,x99112,x99117,x99118)))+~P1(f335(f335(f337(f933(x99112,x99112)),f335(f335(f260(x99112,x99112),x99114),x99116)),x99118)) % 186.01/186.03 [10016]E(x100161,x100162)+~P1(f335(f335(f337(f933(f933(x100163,x100165),f933(x100163,x100165))),f335(f335(f260(f933(x100163,x100165),f933(x100163,x100165)),f335(f335(f260(x100163,x100165),x100161),x100166)),f335(f335(f260(x100163,x100165),x100162),x100167))),f328(x100163,x100165,x100164,x100168)))+P1(f335(f335(f337(f933(x100163,x100163)),f335(f335(f260(x100163,x100163),x100161),x100162)),x100164)) % 186.01/186.03 [10031]~P1(f335(f335(f337(f933(f933(x100311,x100315),f933(x100311,x100315))),f335(f335(f260(f933(x100311,x100315),f933(x100311,x100315)),f335(f335(f260(x100311,x100315),x100312),x100316)),f335(f335(f260(x100311,x100315),x100313),x100317))),f328(x100311,x100315,x100314,x100318)))+P1(f335(f335(f337(f933(x100311,x100311)),f335(f335(f260(x100311,x100311),x100312),x100313)),x100314))+P1(f335(f335(f337(f933(x100315,x100315)),f335(f335(f260(x100315,x100315),x100316),x100317)),x100318)) % 186.01/186.03 [9947]~P24(x99477,x99475,x99471,x99478,x99472,x99474)+~P1(f335(f67(x99475),x99476))+E(f335(f335(x99471,f335(x99472,x99473)),f335(x99474,f335(f335(f23(f934(x99475,a922)),x99476),f335(f335(f317(x99475),x99473),f195(f934(x99475,a922)))))),f335(x99474,f335(f335(f317(x99475),x99473),x99476))) % 186.01/186.03 [9440]~P1(f335(f335(f335(x94405,x94408),x94406),x94407))+~P1(f335(f335(f337(x94401),x94408),x94404))+P1(f335(f335(f335(f335(f45(x94401,f934(x94402,f934(x94403,a922))),x94404),x94405),x94406),x94407)) % 186.01/186.03 [9654]P1(f335(f335(f335(x96541,x96542),x96543),x96544))+~P1(f335(f335(f337(x96545),x96542),x96546))+~P1(f335(f335(f335(f335(f46(x96545,f934(x96547,f934(x96548,a922))),x96546),x96541),x96543),x96544)) % 186.01/186.03 [9850]~P22(x98503,x98502,x98504,x98508,x98501)+~P1(f335(f67(x98502),x98507))+E(f335(f335(x98501,f335(f335(f18(x98502,x98503,x98503),f335(f335(f8(x98503,f934(x98503,x98503),x98502),x98504),x98505)),x98506)),x98507),f335(f335(x98504,f335(f335(x98501,x98505),x98507)),f335(f335(x98501,x98506),x98507))) % 186.01/186.03 [10119]~E(f335(f318(x101192,x101194,x101196),x101198),x1011910)+~E(f335(f318(x101191,x101193,x101195),x101197),x101199)+E(f335(f318(f933(x101191,x101192),f933(x101193,x101194),f266(x101191,x101193,x101192,x101194,x101195,x101196)),f335(f335(f262(x101191,x101192),x101197),f335(f16(f934(x101192,a922),x101191),x101198))),f335(f335(f262(x101193,x101194),x101199),f335(f16(f934(x101194,a922),x101193),x1011910))) % 186.01/186.03 [5120]~P49(x51201,x51202)+~P51(x51201,x51202)+~P52(x51201,x51202)+P8(x51201,x51202) % 186.01/186.03 [5076]~P109(x50762)+~P14(x50762,x50761)+P14(x50762,f121(x50762,x50761))+E(x50761,f120(x50762)) % 186.01/186.03 [5077]~P109(x50772)+~P14(x50772,x50771)+P14(x50772,f731(x50771,x50772))+E(x50771,f120(x50772)) % 186.01/186.03 [5319]~P6(x53192)+E(f10(x53192,x53191),f44(x53192,x53191))+E(x53191,f195(f934(x53192,a922)))+~P1(f335(f67(x53192),x53191)) % 186.01/186.03 [5320]~P6(x53202)+E(f13(x53202,x53201),f43(x53202,x53201))+E(x53201,f195(f934(x53202,a922)))+~P1(f335(f67(x53202),x53201)) % 186.01/186.03 [5477]~P109(x54772)+~P14(x54772,x54771)+E(x54771,f120(x54772))+E(f335(f335(f158(x54772),f750(x54771,x54772)),f731(x54771,x54772)),x54771) % 186.01/186.03 [6282]~P98(x62822)+E(x62821,f195(f934(x62822,a922)))+P1(f335(f335(f243(x62822),f10(x62822,x62821)),f13(x62822,x62821)))+~P1(f335(f67(x62822),x62821)) % 186.01/186.03 [6293]~P41(x62932)+~P41(x62931)+E(x62931,x62932)+~E(f335(f318(a1,a927,a111),x62931),f335(f318(a1,a927,a111),x62932)) % 186.01/186.03 [9300]~P113(x93001)+~P1(f335(f335(f337(x93001),x93002),f116(x93001)))+P1(f335(f335(f244(x93001),f335(f335(f86(x93001),f335(f335(f86(x93001),f84(x93001)),x93002)),x93002)),f2(x93001)))+~P1(f335(f335(f244(x93001),x93002),f2(x93001))) % 186.01/186.03 [9539]~P113(x95391)+~P1(f335(f335(f337(x95391),x95392),f116(x95391)))+~P1(f335(f335(f244(x95391),f335(f335(f86(x95391),f335(f335(f86(x95391),f84(x95391)),x95392)),x95392)),f2(x95391)))+P1(f335(f335(f244(x95391),x95392),f2(x95391))) % 186.01/186.03 [5135]~P145(x51352)+~P117(x51352)+E(x51351,f2(a927))+E(f335(f335(f252(x51352),f2(x51352)),x51351),f2(x51352)) % 186.01/186.03 [5138]~P145(x51381)+~P117(x51381)+~E(x51382,f2(a927))+E(f335(f335(f252(x51381),f2(x51381)),x51382),f84(x51381)) % 186.01/186.03 [5305]~P139(x53052)+E(x53051,f84(x53052))+E(x53051,f335(f85(x53052),f84(x53052)))+~E(f335(f335(f87(x53052),x53051),x53051),f84(x53052)) % 186.01/186.03 [5557]~P90(x55572)+E(x55571,f2(x55572))+E(f88(x55572,x55571),f335(f85(x55572),f84(x55572)))+P1(f335(f335(f244(x55572),f2(x55572)),x55571)) % 186.01/186.03 [5796]~P90(x57962)+E(f88(x57962,x57961),f84(x57962))+E(x57961,f2(x57962))+~P1(f335(f335(f244(x57962),f2(x57962)),x57961)) % 186.01/186.03 [5805]E(x58051,x58052)+~E(f335(f110(a927),x58051),f335(f110(a927),x58052))+P1(f335(a200,f335(f110(a1),x58052)))+P1(f335(a200,f335(f110(a1),x58051))) % 186.01/186.03 [5855]~P93(x58551)+~E(x58552,f2(x58551))+E(f335(f335(f86(x58551),x58552),x58552),f2(x58551))+~P1(f335(f335(f337(x58551),x58552),f116(x58551))) % 186.01/186.03 [5894]E(x58941,f2(a1))+~E(f335(f335(f42(a1),x58942),x58941),f2(a1))+P1(f335(f335(f244(a1),x58941),x58942))+P1(f335(f335(f244(a1),x58942),x58941)) % 186.01/186.03 [5924]E(x59241,f2(a1))+~E(f335(f335(f42(a1),x59242),x59241),f2(a1))+P1(f335(f335(f243(a1),x59242),f2(a1)))+P1(f335(f335(f244(a1),x59242),x59241)) % 186.01/186.03 [5958]E(x59581,f2(a1))+~E(f335(f335(f42(a1),x59582),x59581),f2(a1))+P1(f335(f335(f243(a1),f2(a1)),x59582))+P1(f335(f335(f244(a1),x59581),x59582)) % 186.01/186.03 [5993]~P93(x59932)+E(x59931,f2(x59932))+~E(f335(f335(f86(x59932),x59931),x59931),f2(x59932))+~P1(f335(f335(f337(x59932),x59931),f116(x59932))) % 186.01/186.03 [6055]E(f335(f110(a927),x60551),f335(f110(a927),x60552))+~E(f335(f110(a1),x60552),f2(a1))+P1(f335(a200,f335(f110(a1),x60552)))+~P1(f335(a200,f335(f110(a1),x60551))) % 186.01/186.03 [6084]~E(f335(f110(a927),x60842),f335(f110(a927),x60841))+E(f335(f110(a1),x60841),f2(a1))+P1(f335(a200,f335(f110(a1),x60841)))+~P1(f335(a200,f335(f110(a1),x60842))) % 186.01/186.03 [6094]~P109(x60942)+E(x60941,f195(f934(x60942,a922)))+~P1(f335(f67(x60942),x60941))+P1(f335(f335(f337(x60942),f14(x60942,x60941)),x60941)) % 186.01/186.03 [6095]~P109(x60952)+E(x60951,f195(f934(x60952,a922)))+~P1(f335(f67(x60952),x60951))+P1(f335(f335(f337(x60952),f15(x60952,x60951)),x60951)) % 186.01/186.03 [6259]~P113(x62591)+~P94(x62591)+P1(f335(f335(f243(x62591),f2(x62591)),f335(f110(x62591),x62592)))+~P1(f335(f335(f243(a1),a89),x62592)) % 186.01/186.03 [6260]~P113(x62601)+~P94(x62601)+P1(f335(f335(f244(x62601),f2(x62601)),f335(f110(x62601),x62602)))+~P1(f335(f335(f244(a1),a89),x62602)) % 186.01/186.03 [6281]~P113(x62811)+~P94(x62811)+E(f335(f81(x62811),f335(f110(x62811),x62812)),f335(f110(x62811),x62812))+P1(f335(f335(f244(x62811),f335(f110(x62811),x62812)),f2(x62811))) % 186.01/186.03 [6317]E(x63171,x63172)+~E(f335(a111,x63171),f335(a111,x63172))+~P1(f335(f335(f243(a1),f2(a1)),x63172))+~P1(f335(f335(f243(a1),f2(a1)),x63171)) % 186.01/186.03 [6510]~P94(x65102)+~P113(x65102)+~P1(f335(f335(f243(x65102),f2(x65102)),f335(f110(x65102),x65101)))+P1(f335(f335(f243(a1),a89),x65101)) % 186.01/186.03 [6511]~P94(x65112)+~P113(x65112)+~P1(f335(f335(f244(x65112),f2(x65112)),f335(f110(x65112),x65111)))+P1(f335(f335(f244(a1),a89),x65111)) % 186.01/186.03 [6516]~P113(x65161)+~P94(x65161)+P1(f335(f335(f243(x65161),f335(f110(x65161),x65162)),f2(x65161)))+~P1(f335(f335(f243(a1),x65162),a89)) % 186.01/186.03 [6517]~P113(x65171)+~P94(x65171)+P1(f335(f335(f244(x65171),f335(f110(x65171),x65172)),f2(x65171)))+~P1(f335(f335(f244(a1),x65172),a89)) % 186.01/186.04 [6830]~P94(x68302)+~P113(x68302)+~P1(f335(f335(f243(x68302),f335(f110(x68302),x68301)),f2(x68302)))+P1(f335(f335(f243(a1),x68301),a89)) % 186.01/186.04 [6831]~P94(x68312)+~P113(x68312)+~P1(f335(f335(f244(x68312),f335(f110(x68312),x68311)),f2(x68312)))+P1(f335(f335(f244(a1),x68311),a89)) % 186.01/186.04 [6923]~P113(x69231)+~P94(x69231)+E(f335(f81(x69231),f335(f110(x69231),x69232)),f335(f85(x69231),f335(f110(x69231),x69232)))+~P1(f335(f335(f244(x69231),f335(f110(x69231),x69232)),f2(x69231))) % 186.01/186.04 [6941]E(f335(f110(a927),x69411),f335(f110(a927),x69412))+~E(f335(f110(a1),x69412),f2(a1))+~P1(f335(f335(f243(a1),f335(f110(a1),x69411)),f2(a1)))+~P1(f335(a200,f335(f110(a1),x69411))) % 186.01/186.04 [7810]~P109(x78102)+E(x78101,f195(f934(x78102,a922)))+~P1(f335(f67(x78102),x78101))+P1(f335(f335(f243(x78102),f12(x78102,f241(x78102),x78101)),f11(x78102,f242(x78102),x78101))) % 186.01/186.04 [8121]~P41(x81212)+~P7(x81211)+P1(f335(f335(f337(a1),x81211),x81212))+~P1(f335(f335(f337(a927),f335(a111,x81211)),f335(f318(a1,a927,a111),x81212))) % 186.01/186.04 [6090]~P140(x60902)+E(x60901,f2(a1))+E(f335(f85(x60902),f335(f109(x60902),f335(f85(a1),x60901))),f335(f109(x60902),x60901))+~P1(f335(f335(f244(a1),x60901),f2(a1))) % 186.01/186.04 [6164]~P93(x61641)+~P94(x61641)+~P29(x61641,f335(f110(x61641),x61642))+P29(x61641,f335(f110(x61641),f335(f335(f86(a1),x61642),x61642))) % 186.01/186.04 [6499]~P78(x64992)+E(x64991,f195(f934(x64992,a922)))+E(f15(x64992,f335(f318(x64992,x64992,f85(x64992)),x64991)),f335(f85(x64992),f14(x64992,x64991)))+~P1(f335(f67(x64992),x64991)) % 186.01/186.04 [6500]~P78(x65002)+E(x65001,f195(f934(x65002,a922)))+E(f14(x65002,f335(f318(x65002,x65002,f85(x65002)),x65001)),f335(f85(x65002),f15(x65002,x65001)))+~P1(f335(f67(x65002),x65001)) % 186.01/186.04 [6533]~P93(x65331)+~P94(x65331)+P29(x65331,f335(f110(x65331),x65332))+~P29(x65331,f335(f110(x65331),f335(f335(f86(a1),x65332),x65332))) % 186.01/186.04 [6623]E(x66231,f2(a1))+E(f335(a57,f56(f335(f85(a1),x66231),f335(f85(a1),x66232))),f52(x66231,x66232))+P1(f335(f335(f243(a1),f2(a1)),x66232))+~P1(f335(f335(f243(a1),f2(a1)),x66231)) % 186.01/186.04 [8899]~P41(x88992)+~P41(x88991)+P1(f335(f335(f244(f934(a927,a922)),f335(f318(a1,a927,a111),x88991)),f335(f318(a1,a927,a111),x88992)))+~P1(f335(f335(f244(f934(a1,a922)),x88991),x88992)) % 186.01/186.04 [9132]~E(f752(x91322,x91321),f753(x91322,x91321))+~P1(f335(f144(x91321),f754(x91322,x91321)))+~P1(f335(f144(f928(x91321)),x91322))+P1(f335(f144(x91321),f335(f149(f928(x91321),f928(x91321),f141(x91321),f120(x91321)),x91322))) % 186.01/186.04 [9220]~P41(x92202)+~P41(x92201)+~P1(f335(f335(f243(f934(a927,a922)),f335(f318(a1,a927,a111),x92201)),f335(f318(a1,a927,a111),x92202)))+P1(f335(f335(f243(f934(a1,a922)),x92201),x92202)) % 186.01/186.04 [9221]~P41(x92212)+~P41(x92211)+~P1(f335(f335(f244(f934(a927,a922)),f335(f318(a1,a927,a111),x92211)),f335(f318(a1,a927,a111),x92212)))+P1(f335(f335(f244(f934(a1,a922)),x92211),x92212)) % 186.01/186.04 [9227]~E(f752(x92272,x92271),f753(x92272,x92271))+~P1(f335(f144(f928(x92271)),x92272))+P1(f335(f144(x92271),f335(f149(f928(x92271),f928(x92271),f141(x92271),f120(x92271)),x92272)))+P1(f335(f335(f337(f928(x92271)),f754(x92272,x92271)),f335(f179(f928(x92271)),x92272))) % 186.01/186.04 [9268]~P1(f335(f144(x92681),f754(x92682,x92681)))+~P1(f335(f144(f928(x92681)),x92682))+P1(f335(f144(x92681),f335(f149(f928(x92681),f928(x92681),f141(x92681),f120(x92681)),x92682)))+P1(f335(f335(f337(f928(x92681)),f753(x92682,x92681)),f335(f179(f928(x92681)),x92682))) % 186.01/186.04 [9269]~P1(f335(f144(x92691),f754(x92692,x92691)))+~P1(f335(f144(f928(x92691)),x92692))+P1(f335(f144(x92691),f335(f149(f928(x92691),f928(x92691),f141(x92691),f120(x92691)),x92692)))+P1(f335(f335(f337(f928(x92691)),f752(x92692,x92691)),f335(f179(f928(x92691)),x92692))) % 186.01/186.04 [9347]~P1(f335(f144(f928(x93471)),x93472))+P1(f335(f144(x93471),f335(f149(f928(x93471),f928(x93471),f141(x93471),f120(x93471)),x93472)))+P1(f335(f335(f337(f928(x93471)),f753(x93472,x93471)),f335(f179(f928(x93471)),x93472)))+P1(f335(f335(f337(f928(x93471)),f754(x93472,x93471)),f335(f179(f928(x93471)),x93472))) % 186.01/186.04 [9348]~P1(f335(f144(f928(x93481)),x93482))+P1(f335(f144(x93481),f335(f149(f928(x93481),f928(x93481),f141(x93481),f120(x93481)),x93482)))+P1(f335(f335(f337(f928(x93481)),f752(x93482,x93481)),f335(f179(f928(x93481)),x93482)))+P1(f335(f335(f337(f928(x93481)),f754(x93482,x93481)),f335(f179(f928(x93481)),x93482))) % 186.01/186.04 [9362]~E(f335(f335(f108(f934(x93621,a922)),f335(f179(x93621),f753(x93622,x93621))),f335(f179(x93621),f752(x93622,x93621))),f195(f934(x93621,a922)))+~P1(f335(f144(x93621),f754(x93622,x93621)))+~P1(f335(f144(f928(x93621)),x93622))+P1(f335(f144(x93621),f335(f149(f928(x93621),f928(x93621),f141(x93621),f120(x93621)),x93622))) % 186.01/186.04 [9422]~E(f335(f335(f108(f934(x94221,a922)),f335(f179(x94221),f753(x94222,x94221))),f335(f179(x94221),f752(x94222,x94221))),f195(f934(x94221,a922)))+~P1(f335(f144(f928(x94221)),x94222))+P1(f335(f144(x94221),f335(f149(f928(x94221),f928(x94221),f141(x94221),f120(x94221)),x94222)))+P1(f335(f335(f337(f928(x94221)),f754(x94222,x94221)),f335(f179(f928(x94221)),x94222))) % 186.01/186.04 [9694]E(x96941,f2(a1))+E(x96942,f2(a1))+E(f335(f335(f92(a1,f933(a1,a1)),f335(f335(a226,x96942),x96941)),f335(f335(f18(a1,a1,f933(a1,a1)),f335(f335(f8(a1,f934(a1,f933(a1,a1)),a1),f260(a1,a1)),f335(f42(a1),x96942))),f335(f42(a1),x96941))),f224(x96942,x96941))+P1(f335(f335(f244(a1),x96941),f2(a1))) % 186.01/186.04 [8443]~P94(x84432)+~P113(x84432)+~P1(f335(f335(f243(x84432),f335(f110(x84432),x84431)),f84(x84432)))+P1(f335(f335(f243(a1),x84431),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))) % 186.01/186.04 [8444]~P94(x84442)+~P113(x84442)+~P1(f335(f335(f244(x84442),f335(f110(x84442),x84441)),f84(x84442)))+P1(f335(f335(f244(a1),x84441),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))) % 186.01/186.04 [8715]~P113(x87151)+~P94(x87151)+P1(f335(f335(f243(x87151),f335(f110(x87151),x87152)),f84(x87151)))+~P1(f335(f335(f243(a1),x87152),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))) % 186.01/186.04 [8716]~P113(x87161)+~P94(x87161)+P1(f335(f335(f244(x87161),f335(f110(x87161),x87162)),f84(x87161)))+~P1(f335(f335(f244(a1),x87162),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))) % 186.01/186.04 [8927]~P94(x89272)+~P113(x89272)+~P1(f335(f335(f243(x89272),f84(x89272)),f335(f110(x89272),x89271)))+P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),x89271)) % 186.01/186.04 [8928]~P94(x89282)+~P113(x89282)+~P1(f335(f335(f244(x89282),f84(x89282)),f335(f110(x89282),x89281)))+P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),x89281)) % 186.01/186.04 [9306]~P113(x93061)+~P94(x93061)+P1(f335(f335(f243(x93061),f84(x93061)),f335(f110(x93061),x93062)))+~P1(f335(f335(f243(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),x93062)) % 186.01/186.04 [9307]~P113(x93071)+~P94(x93071)+P1(f335(f335(f244(x93071),f84(x93071)),f335(f110(x93071),x93072)))+~P1(f335(f335(f244(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),x93072)) % 186.01/186.04 [9823]~P139(x98232)+E(x98231,f84(x98232))+E(x98231,f335(f85(x98232),f84(x98232)))+~E(f335(f335(f252(x98232),x98231),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f84(x98232)) % 186.01/186.04 [10094]~P94(x100941)+~P68(x100941)+~P1(f335(f335(f244(x100941),f2(x100941)),x100942))+P1(f335(f335(f244(x100941),f2(x100941)),f335(f335(f299(x100941),x100942),f335(f110(x100941),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.04 [10149]~P94(x101491)+~P68(x101491)+P1(f335(f335(f244(x101491),f2(x101491)),x101492))+~P1(f335(f335(f244(x101491),f2(x101491)),f335(f335(f299(x101491),x101492),f335(f110(x101491),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.04 [10446]~P140(x104462)+E(x104461,f2(a1))+P1(f335(f335(f244(a1),x104461),f2(a1)))+E(f335(f335(f265(a1,a1,x104462),f335(f335(f7(a1,f934(a1,f934(x104462,x104462)),f934(a1,x104462)),f335(f335(f8(f934(f934(x104462,x104462),x104462),f934(f934(a1,f934(x104462,x104462)),f934(a1,x104462)),a1),f8(f934(x104462,x104462),x104462,a1)),f335(f335(f8(x104462,f934(f934(x104462,x104462),x104462),a1),f92(x104462,x104462)),f109(x104462)))),f335(f335(f7(a1,f934(x104462,x104462),f934(x104462,x104462)),f335(f335(f8(f934(x104462,f934(x104462,x104462)),f934(f934(x104462,x104462),f934(x104462,x104462)),a1),f18(x104462,x104462,x104462)),f335(f335(f7(a1,f934(x104462,x104462),f934(x104462,f934(x104462,x104462))),f335(f335(f8(f934(x104462,f934(x104462,x104462)),f934(f934(x104462,x104462),f934(x104462,f934(x104462,x104462))),a1),f8(x104462,f934(x104462,x104462),x104462)),f335(f335(f8(a922,f934(x104462,f934(x104462,x104462)),a1),f103(x104462)),f335(f335(f7(a1,a1,a922),a332),f2(a1))))),f335(f335(f18(x104462,x104462,x104462),f86(x104462)),f5(x104462))))),f335(f335(f7(x104462,x104462,x104462),f335(f335(f8(x104462,f934(x104462,x104462),x104462),f86(x104462)),f335(f335(f18(x104462,x104462,x104462),f86(x104462)),f5(x104462)))),f84(x104462))))),f52(x104461,f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f109(x104462),x104461)) % 186.01/186.04 [5566]~P39(x55661,x55663)+~P53(x55661,x55663)+~P54(x55661,x55662,x55663)+P9(x55661,x55662,x55663) % 186.01/186.04 [5104]~P93(x51043)+~P94(x51043)+E(x51041,x51042)+~E(f335(f110(x51043),x51041),f335(f110(x51043),x51042)) % 186.01/186.04 [5576]~P51(x55761,x55762)+~P52(x55761,x55762)+P16(x55761,x55762)+~P1(f335(f335(x55762,x55763),x55763)) % 186.01/186.04 [6070]P16(x60702,x60701)+E(f335(x60701,f831(x60701)),f335(x60701,f832(x60701)))+P1(f335(f335(x60701,f831(x60701)),f832(x60701)))+~P1(f335(f335(x60701,x60703),x60703)) % 186.01/186.04 [6269]~P1(f335(x62691,x62692))+~P1(f335(x62691,x62693))+~P1(f335(f335(f243(a927),x62693),f536(x62692,x62691)))+P1(f335(x62691,f2(a927))) % 186.01/186.04 [6336]P16(x63361,x63362)+P1(f335(f335(x63362,f831(x63362)),f831(x63362)))+P1(f335(f335(x63362,f831(x63362)),f832(x63362)))+~P1(f335(f335(x63362,x63363),x63363)) % 186.01/186.04 [6337]P16(x63371,x63372)+P1(f335(f335(x63372,f831(x63372)),f832(x63372)))+P1(f335(f335(x63372,f832(x63372)),f832(x63372)))+~P1(f335(f335(x63372,x63373),x63373)) % 186.01/186.04 [6687]P148(x66872,x66871,x66873)+E(x66871,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f868(x66873,x66871,x66872)))+P1(f335(f335(f244(a1),x66871),f2(a1))) % 186.01/186.04 [6688]P147(x66882,x66881,x66883)+E(x66881,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f874(x66883,x66881,x66882)))+P1(f335(f335(f244(a1),x66881),f2(a1))) % 186.01/186.04 [6811]P147(x68111,x68112,x68113)+~P1(f335(x68111,x68113))+P1(f335(f335(f243(a1),f2(a1)),f874(x68113,x68112,x68111)))+P1(f335(f335(f244(a1),x68112),f2(a1))) % 186.01/186.04 [6836]P148(x68361,x68362,x68363)+P1(f335(f335(f243(a1),f2(a1)),f868(x68363,x68362,x68361)))+~P1(f335(x68361,f2(a1)))+P1(f335(f335(f244(a1),x68362),f2(a1))) % 186.01/186.04 [6866]P148(x68662,x68661,x68663)+E(x68661,f2(a1))+~P1(f335(x68662,f869(x68663,x68661,x68662)))+P1(f335(f335(f244(a1),x68661),f2(a1))) % 186.01/186.04 [6867]P147(x68672,x68671,x68673)+E(x68671,f2(a1))+~P1(f335(x68672,f874(x68673,x68671,x68672)))+P1(f335(f335(f244(a1),x68671),f2(a1))) % 186.01/186.04 [6967]~P109(x69671)+~P6(x69671)+~P1(f335(f335(f244(x69671),x69672),f43(x69671,x69673)))+P1(f335(f335(f244(x69671),x69672),f580(x69673,x69672,x69671))) % 186.01/186.04 [6976]P147(x69761,x69762,x69763)+~P1(f335(x69761,x69763))+~P1(f335(x69761,f874(x69763,x69762,x69761)))+P1(f335(f335(f244(a1),x69762),f2(a1))) % 186.01/186.04 [7006]P148(x70061,x70062,x70063)+~P1(f335(x70061,f869(x70063,x70062,x70061)))+~P1(f335(x70061,f2(a1)))+P1(f335(f335(f244(a1),x70062),f2(a1))) % 186.01/186.04 [7251]P148(x72512,x72511,x72513)+E(x72511,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f868(x72513,x72511,x72512)))+P1(f335(f335(f244(a1),x72511),f867(x72513,x72511,x72512))) % 186.01/186.04 [7252]P147(x72522,x72521,x72523)+E(x72521,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f874(x72523,x72521,x72522)))+P1(f335(f335(f244(a1),x72521),f873(x72523,x72521,x72522))) % 186.01/186.04 [7371]P147(x73711,x73712,x73713)+~P1(f335(x73711,x73713))+P1(f335(f335(f243(a1),f2(a1)),f874(x73713,x73712,x73711)))+P1(f335(f335(f244(a1),x73712),f873(x73713,x73712,x73711))) % 186.01/186.04 [7390]P148(x73901,x73902,x73903)+P1(f335(f335(f243(a1),f2(a1)),f868(x73903,x73902,x73901)))+P1(f335(f335(f244(a1),x73902),f867(x73903,x73902,x73901)))+~P1(f335(x73901,f2(a1))) % 186.01/186.04 [7422]P148(x74222,x74221,x74223)+E(x74221,f2(a1))+~P1(f335(x74222,f869(x74223,x74221,x74222)))+P1(f335(f335(f244(a1),x74221),f867(x74223,x74221,x74222))) % 186.01/186.04 [7423]P147(x74232,x74231,x74233)+E(x74231,f2(a1))+~P1(f335(x74232,f874(x74233,x74231,x74232)))+P1(f335(f335(f244(a1),x74231),f873(x74233,x74231,x74232))) % 186.01/186.04 [7467]P148(x74672,x74671,x74673)+E(x74671,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f868(x74673,x74671,x74672)))+~P1(f335(x74672,f872(x74673,x74671,x74672))) % 186.01/186.04 [7468]P147(x74682,x74681,x74683)+E(x74681,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f874(x74683,x74681,x74682)))+~P1(f335(x74682,f873(x74683,x74681,x74682))) % 186.01/186.04 [7567]P147(x75671,x75672,x75673)+~P1(f335(x75671,x75673))+~P1(f335(x75671,f874(x75673,x75672,x75671)))+P1(f335(f335(f244(a1),x75672),f873(x75673,x75672,x75671))) % 186.01/186.04 [7582]P148(x75821,x75822,x75823)+~P1(f335(x75821,f869(x75823,x75822,x75821)))+P1(f335(f335(f244(a1),x75822),f867(x75823,x75822,x75821)))+~P1(f335(x75821,f2(a1))) % 186.01/186.04 [7585]P147(x75851,x75852,x75853)+~P1(f335(x75851,x75853))+P1(f335(f335(f243(a1),f2(a1)),f874(x75853,x75852,x75851)))+~P1(f335(x75851,f873(x75853,x75852,x75851))) % 186.01/186.04 [7601]P148(x76011,x76012,x76013)+P1(f335(f335(f243(a1),f2(a1)),f868(x76013,x76012,x76011)))+~P1(f335(x76011,f872(x76013,x76012,x76011)))+~P1(f335(x76011,f2(a1))) % 186.01/186.04 [7622]P148(x76222,x76221,x76223)+E(x76221,f2(a1))+~P1(f335(x76222,f869(x76223,x76221,x76222)))+~P1(f335(x76222,f872(x76223,x76221,x76222))) % 186.01/186.04 [7623]P147(x76232,x76231,x76233)+E(x76231,f2(a1))+~P1(f335(x76232,f874(x76233,x76231,x76232)))+~P1(f335(x76232,f873(x76233,x76231,x76232))) % 186.01/186.04 [7709]P147(x77091,x77092,x77093)+~P1(f335(x77091,x77093))+~P1(f335(x77091,f874(x77093,x77092,x77091)))+~P1(f335(x77091,f873(x77093,x77092,x77091))) % 186.01/186.04 [7726]P148(x77261,x77262,x77263)+~P1(f335(x77261,f869(x77263,x77262,x77261)))+~P1(f335(x77261,f872(x77263,x77262,x77261)))+~P1(f335(x77261,f2(a1))) % 186.01/186.04 [7769]P148(x77692,x77691,x77693)+E(x77691,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f868(x77693,x77691,x77692)))+P1(f335(f335(f243(a1),f867(x77693,x77691,x77692)),f2(a1))) % 186.01/186.04 [7770]P147(x77702,x77701,x77703)+E(x77701,f2(a1))+P1(f335(f335(f243(a1),f2(a1)),f874(x77703,x77701,x77702)))+P1(f335(f335(f243(a1),f873(x77703,x77701,x77702)),f2(a1))) % 186.01/186.04 [7771]~P140(x77711)+~P1(f335(f335(f337(x77711),x77713),f116(x77711)))+~P1(f335(f335(f337(x77711),x77712),f116(x77711)))+P1(f335(f335(f337(x77711),f335(f335(f23(x77711),x77712),x77713)),f116(x77711))) % 186.01/186.04 [7772]~P140(x77721)+~P1(f335(f335(f337(x77721),x77723),f116(x77721)))+~P1(f335(f335(f337(x77721),x77722),f116(x77721)))+P1(f335(f335(f337(x77721),f335(f335(f87(x77721),x77722),x77723)),f116(x77721))) % 186.01/186.04 [7773]~P146(x77731)+~P1(f335(f335(f337(x77731),x77733),f193(x77731)))+~P1(f335(f335(f337(x77731),x77732),f193(x77731)))+P1(f335(f335(f337(x77731),f335(f335(f87(x77731),x77732),x77733)),f193(x77731))) % 186.01/186.04 [7774]~P140(x77741)+~P1(f335(f335(f337(x77741),x77743),f116(x77741)))+~P1(f335(f335(f337(x77741),x77742),f116(x77741)))+P1(f335(f335(f337(x77741),f335(f335(f86(x77741),x77742),x77743)),f116(x77741))) % 186.01/186.04 [7775]~P146(x77751)+~P1(f335(f335(f337(x77751),x77753),f193(x77751)))+~P1(f335(f335(f337(x77751),x77752),f193(x77751)))+P1(f335(f335(f337(x77751),f335(f335(f86(x77751),x77752),x77753)),f193(x77751))) % 186.01/186.04 [7776]~P89(x77761)+~P1(f335(f335(f243(x77761),x77763),f2(x77761)))+~P1(f335(f335(f243(x77761),x77762),f2(x77761)))+P1(f335(f335(f243(x77761),f335(f335(f86(x77761),x77762),x77763)),f2(x77761))) % 186.01/186.04 [7777]~P89(x77771)+~P1(f335(f335(f243(x77771),x77773),f2(x77771)))+~P1(f335(f335(f244(x77771),x77772),f2(x77771)))+P1(f335(f335(f244(x77771),f335(f335(f86(x77771),x77772),x77773)),f2(x77771))) % 186.01/186.04 [7778]~P89(x77781)+~P1(f335(f335(f243(x77781),x77782),f2(x77781)))+~P1(f335(f335(f244(x77781),x77783),f2(x77781)))+P1(f335(f335(f244(x77781),f335(f335(f86(x77781),x77782),x77783)),f2(x77781))) % 186.01/186.04 [7779]~P89(x77791)+~P1(f335(f335(f244(x77791),x77793),f2(x77791)))+~P1(f335(f335(f244(x77791),x77792),f2(x77791)))+P1(f335(f335(f244(x77791),f335(f335(f86(x77791),x77792),x77793)),f2(x77791))) % 186.01/186.04 [7806]P148(x78063,x78061,x78062)+E(x78061,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x78061),f869(x78062,x78061,x78063))),f868(x78062,x78061,x78063)),x78062)+P1(f335(f335(f244(a1),x78061),f2(a1))) % 186.01/186.04 [7807]P147(x78073,x78071,x78072)+E(x78071,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x78071),f875(x78072,x78071,x78073))),f874(x78072,x78071,x78073)),x78072)+P1(f335(f335(f244(a1),x78071),f2(a1))) % 186.01/186.04 [7888]P147(x78881,x78882,x78883)+~P1(f335(x78881,x78883))+P1(f335(f335(f243(a1),f2(a1)),f874(x78883,x78882,x78881)))+P1(f335(f335(f243(a1),f873(x78883,x78882,x78881)),f2(a1))) % 186.01/186.04 [7917]P148(x79171,x79172,x79173)+P1(f335(f335(f243(a1),f2(a1)),f868(x79173,x79172,x79171)))+~P1(f335(x79171,f2(a1)))+P1(f335(f335(f243(a1),f867(x79173,x79172,x79171)),f2(a1))) % 186.01/186.04 [7926]P147(x79263,x79261,x79262)+~P1(f335(x79263,x79262))+E(f335(f335(f86(a1),f335(f335(f87(a1),x79261),f875(x79262,x79261,x79263))),f874(x79262,x79261,x79263)),x79262)+P1(f335(f335(f244(a1),x79261),f2(a1))) % 186.01/186.04 [7932]P148(x79322,x79321,x79323)+E(x79321,f2(a1))+~P1(f335(x79322,f869(x79323,x79321,x79322)))+P1(f335(f335(f243(a1),f867(x79323,x79321,x79322)),f2(a1))) % 186.01/186.04 [7933]P147(x79332,x79331,x79333)+E(x79331,f2(a1))+~P1(f335(x79332,f874(x79333,x79331,x79332)))+P1(f335(f335(f243(a1),f873(x79333,x79331,x79332)),f2(a1))) % 186.01/186.04 [7938]P148(x79383,x79381,x79382)+E(f335(f335(f86(a1),f335(f335(f87(a1),x79381),f869(x79382,x79381,x79383))),f868(x79382,x79381,x79383)),x79382)+~P1(f335(x79383,f2(a1)))+P1(f335(f335(f244(a1),x79381),f2(a1))) % 186.01/186.04 [7994]P147(x79941,x79942,x79943)+~P1(f335(x79941,x79943))+~P1(f335(x79941,f874(x79943,x79942,x79941)))+P1(f335(f335(f243(a1),f873(x79943,x79942,x79941)),f2(a1))) % 186.01/186.04 [7998]P148(x79981,x79982,x79983)+~P1(f335(x79981,f869(x79983,x79982,x79981)))+~P1(f335(x79981,f2(a1)))+P1(f335(f335(f243(a1),f867(x79983,x79982,x79981)),f2(a1))) % 186.01/186.04 [8063]~P127(x80631)+~P1(f335(f335(f243(x80631),f335(f335(f87(x80631),x80633),x80632)),f2(x80631)))+P1(f335(f335(f243(x80631),x80632),f2(x80631)))+P1(f335(f335(f243(x80631),x80633),f2(x80631))) % 186.01/186.04 [8064]~P68(x80641)+~P1(f335(f335(f243(x80641),f335(f335(f299(x80641),x80643),x80642)),f2(x80641)))+P1(f335(f335(f243(x80641),x80642),f2(x80641)))+P1(f335(f335(f243(x80641),x80643),f2(x80641))) % 186.01/186.04 [8065]~P68(x80651)+~P1(f335(f335(f244(x80651),f335(f335(f299(x80651),x80653),x80652)),f2(x80651)))+P1(f335(f335(f244(x80651),x80652),f2(x80651)))+P1(f335(f335(f244(x80651),x80653),f2(x80651))) % 186.01/186.04 [8177]P148(x81773,x81771,x81772)+E(x81771,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x81771),f869(x81772,x81771,x81773))),f868(x81772,x81771,x81773)),x81772)+P1(f335(f335(f244(a1),x81771),f867(x81772,x81771,x81773))) % 186.01/186.04 [8178]P147(x81783,x81781,x81782)+E(x81781,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x81781),f875(x81782,x81781,x81783))),f874(x81782,x81781,x81783)),x81782)+P1(f335(f335(f244(a1),x81781),f873(x81782,x81781,x81783))) % 186.01/186.04 [8191]P148(x81913,x81911,x81912)+E(x81911,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x81911),f872(x81912,x81911,x81913))),f867(x81912,x81911,x81913)),x81912)+P1(f335(f335(f243(a1),f2(a1)),f868(x81912,x81911,x81913))) % 186.01/186.04 [8192]P147(x81923,x81921,x81922)+E(x81921,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x81921),f877(x81922,x81921,x81923))),f873(x81922,x81921,x81923)),x81922)+P1(f335(f335(f243(a1),f2(a1)),f874(x81922,x81921,x81923))) % 186.01/186.04 [8234]P147(x82343,x82341,x82342)+~P1(f335(x82343,x82342))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82341),f875(x82342,x82341,x82343))),f874(x82342,x82341,x82343)),x82342)+P1(f335(f335(f244(a1),x82341),f873(x82342,x82341,x82343))) % 186.01/186.04 [8243]P148(x82433,x82431,x82432)+E(f335(f335(f86(a1),f335(f335(f87(a1),x82431),f869(x82432,x82431,x82433))),f868(x82432,x82431,x82433)),x82432)+P1(f335(f335(f244(a1),x82431),f867(x82432,x82431,x82433)))+~P1(f335(x82433,f2(a1))) % 186.01/186.04 [8249]P147(x82493,x82491,x82492)+~P1(f335(x82493,x82492))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82491),f877(x82492,x82491,x82493))),f873(x82492,x82491,x82493)),x82492)+P1(f335(f335(f243(a1),f2(a1)),f874(x82492,x82491,x82493))) % 186.01/186.04 [8255]P148(x82553,x82551,x82552)+E(f335(f335(f86(a1),f335(f335(f87(a1),x82551),f872(x82552,x82551,x82553))),f867(x82552,x82551,x82553)),x82552)+P1(f335(f335(f243(a1),f2(a1)),f868(x82552,x82551,x82553)))+~P1(f335(x82553,f2(a1))) % 186.01/186.04 [8266]P148(x82663,x82661,x82662)+E(x82661,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82661),f869(x82662,x82661,x82663))),f868(x82662,x82661,x82663)),x82662)+~P1(f335(x82663,f872(x82662,x82661,x82663))) % 186.01/186.04 [8267]P147(x82673,x82671,x82672)+E(x82671,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82671),f875(x82672,x82671,x82673))),f874(x82672,x82671,x82673)),x82672)+~P1(f335(x82673,f873(x82672,x82671,x82673))) % 186.01/186.04 [8268]P148(x82683,x82681,x82682)+E(x82681,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82681),f872(x82682,x82681,x82683))),f867(x82682,x82681,x82683)),x82682)+~P1(f335(x82683,f869(x82682,x82681,x82683))) % 186.01/186.04 [8269]P147(x82693,x82691,x82692)+E(x82691,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x82691),f877(x82692,x82691,x82693))),f873(x82692,x82691,x82693)),x82692)+~P1(f335(x82693,f874(x82692,x82691,x82693))) % 186.01/186.04 [8328]P147(x83283,x83281,x83282)+~P1(f335(x83283,x83282))+E(f335(f335(f86(a1),f335(f335(f87(a1),x83281),f875(x83282,x83281,x83283))),f874(x83282,x83281,x83283)),x83282)+~P1(f335(x83283,f873(x83282,x83281,x83283))) % 186.01/186.04 [8329]P147(x83293,x83291,x83292)+~P1(f335(x83293,x83292))+E(f335(f335(f86(a1),f335(f335(f87(a1),x83291),f877(x83292,x83291,x83293))),f873(x83292,x83291,x83293)),x83292)+~P1(f335(x83293,f874(x83292,x83291,x83293))) % 186.01/186.04 [8339]P148(x83393,x83391,x83392)+E(f335(f335(f86(a1),f335(f335(f87(a1),x83391),f869(x83392,x83391,x83393))),f868(x83392,x83391,x83393)),x83392)+~P1(f335(x83393,f872(x83392,x83391,x83393)))+~P1(f335(x83393,f2(a1))) % 186.01/186.04 [8340]P148(x83403,x83401,x83402)+E(f335(f335(f86(a1),f335(f335(f87(a1),x83401),f872(x83402,x83401,x83403))),f867(x83402,x83401,x83403)),x83402)+~P1(f335(x83403,f869(x83402,x83401,x83403)))+~P1(f335(x83403,f2(a1))) % 186.01/186.04 [8436]P148(x84363,x84361,x84362)+E(x84361,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84361),f869(x84362,x84361,x84363))),f868(x84362,x84361,x84363)),x84362)+P1(f335(f335(f243(a1),f867(x84362,x84361,x84363)),f2(a1))) % 186.01/186.04 [8437]P147(x84373,x84371,x84372)+E(x84371,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84371),f875(x84372,x84371,x84373))),f874(x84372,x84371,x84373)),x84372)+P1(f335(f335(f243(a1),f873(x84372,x84371,x84373)),f2(a1))) % 186.01/186.04 [8477]P147(x84773,x84771,x84772)+~P1(f335(x84773,x84772))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84771),f875(x84772,x84771,x84773))),f874(x84772,x84771,x84773)),x84772)+P1(f335(f335(f243(a1),f873(x84772,x84771,x84773)),f2(a1))) % 186.01/186.04 [8482]P148(x84823,x84821,x84822)+E(f335(f335(f86(a1),f335(f335(f87(a1),x84821),f869(x84822,x84821,x84823))),f868(x84822,x84821,x84823)),x84822)+~P1(f335(x84823,f2(a1)))+P1(f335(f335(f243(a1),f867(x84822,x84821,x84823)),f2(a1))) % 186.01/186.04 [8617]P148(x86173,x86171,x86172)+E(x86171,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x86171),f872(x86172,x86171,x86173))),f867(x86172,x86171,x86173)),x86172)+E(f335(f335(f86(a1),f335(f335(f87(a1),x86171),f869(x86172,x86171,x86173))),f868(x86172,x86171,x86173)),x86172) % 186.01/186.04 [8618]P147(x86183,x86181,x86182)+E(x86181,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x86181),f877(x86182,x86181,x86183))),f873(x86182,x86181,x86183)),x86182)+E(f335(f335(f86(a1),f335(f335(f87(a1),x86181),f875(x86182,x86181,x86183))),f874(x86182,x86181,x86183)),x86182) % 186.01/186.04 [8638]P147(x86383,x86381,x86382)+~P1(f335(x86383,x86382))+E(f335(f335(f86(a1),f335(f335(f87(a1),x86381),f877(x86382,x86381,x86383))),f873(x86382,x86381,x86383)),x86382)+E(f335(f335(f86(a1),f335(f335(f87(a1),x86381),f875(x86382,x86381,x86383))),f874(x86382,x86381,x86383)),x86382) % 186.01/186.04 [8649]P148(x86493,x86491,x86492)+E(f335(f335(f86(a1),f335(f335(f87(a1),x86491),f872(x86492,x86491,x86493))),f867(x86492,x86491,x86493)),x86492)+E(f335(f335(f86(a1),f335(f335(f87(a1),x86491),f869(x86492,x86491,x86493))),f868(x86492,x86491,x86493)),x86492)+~P1(f335(x86493,f2(a1))) % 186.01/186.04 [9315]~P127(x93151)+~E(x93153,f2(x93151))+~E(x93152,f2(x93151))+P1(f335(f335(f243(x93151),f335(f335(f86(x93151),f335(f335(f87(x93151),x93152),x93152)),f335(f335(f87(x93151),x93153),x93153))),f2(x93151))) % 186.01/186.04 [10382]~P113(x103821)+~E(x103823,f2(x103821))+~E(x103822,f2(x103821))+P1(f335(f335(f243(x103821),f335(f335(f86(x103821),f335(f335(f252(x103821),x103822),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103821),x103823),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))),f2(x103821))) % 186.01/186.04 [5052]~E(x50523,x50521)+~P121(x50522)+E(x50521,f2(x50522))+E(f335(f335(f299(x50522),x50523),x50521),f84(x50522)) % 186.01/186.04 [5105]~P101(x51051)+~E(x51053,f250(x51051))+~E(x51052,f250(x51051))+E(f335(f335(f108(x51051),x51052),x51053),f250(x51051)) % 186.01/186.04 [5106]~P99(x51061)+~E(x51063,f195(x51061))+~E(x51062,f195(x51061))+E(f335(f335(f117(x51061),x51062),x51063),f195(x51061)) % 186.01/186.04 [5199]~P121(x51993)+E(x51991,x51992)+E(x51992,f2(x51993))+~E(f335(f335(f299(x51993),x51991),x51992),f84(x51993)) % 186.01/186.04 [5217]~P129(x52172)+E(x52171,f2(x52172))+E(x52173,f2(x52172))+~E(f335(f335(f87(x52172),x52173),x52171),f2(x52172)) % 186.01/186.04 [5218]~P142(x52182)+E(x52181,f2(x52182))+E(x52183,f2(x52182))+~E(f335(f335(f87(x52182),x52183),x52181),f2(x52182)) % 186.01/186.04 [5595]~P114(x55953)+E(x55951,x55952)+E(x55951,f335(f85(x55953),x55952))+~E(f335(f335(f87(x55953),x55951),x55951),f335(f335(f87(x55953),x55952),x55952)) % 186.01/186.04 [5633]~P83(x56331)+E(f335(f85(x56331),x56332),x56333)+~E(f335(f335(f108(x56331),x56332),x56333),f195(x56331))+~E(f335(f335(f117(x56331),x56332),x56333),f250(x56331)) % 186.01/186.04 [5713]~P113(x57133)+E(x57131,x57132)+P1(f335(f335(f244(x57133),x57132),x57131))+P1(f335(f335(f244(x57133),x57131),x57132)) % 186.01/186.04 [5714]~P109(x57143)+E(x57141,x57142)+P1(f335(f335(f244(x57143),x57142),x57141))+P1(f335(f335(f244(x57143),x57141),x57142)) % 186.01/186.04 [5715]~E(x57152,x57153)+~P109(x57151)+P1(f335(f335(f244(x57151),x57152),x57153))+P1(f335(f335(f243(x57151),x57152),x57153)) % 186.01/186.04 [5974]~P110(x59743)+E(x59741,x59742)+~P1(f335(f335(f243(x59743),x59742),x59741))+P1(f335(f335(f244(x59743),x59742),x59741)) % 186.01/186.04 [5976]~P109(x59763)+E(x59761,x59762)+~P1(f335(f335(f243(x59763),x59761),x59762))+P1(f335(f335(f244(x59763),x59761),x59762)) % 186.01/186.04 [5982]~P110(x59823)+E(x59821,x59822)+~P1(f335(f335(f243(x59823),x59821),x59822))+P1(f335(f335(f244(x59823),x59821),x59822)) % 186.01/186.04 [6087]P147(x60871,x60872,x60873)+~P1(f335(x60871,x60873))+P1(f335(f335(f244(a1),x60872),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x60872)) % 186.01/186.04 [6137]P148(x61371,x61372,x61373)+~P1(f335(x61371,f2(a1)))+P1(f335(f335(f244(a1),x61372),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x61372)) % 186.01/186.04 [6142]~P98(x61421)+E(f335(f335(f108(x61421),x61422),f13(x61421,x61423)),x61422)+~P1(f335(f67(x61421),x61423))+~P1(f335(f335(f337(x61421),x61422),x61423)) % 186.01/186.04 [6143]~P98(x61431)+E(f335(f335(f117(x61431),x61432),f10(x61431,x61433)),x61432)+~P1(f335(f67(x61431),x61433))+~P1(f335(f335(f337(x61431),x61432),x61433)) % 186.01/186.04 [6180]~P98(x61801)+E(f335(f335(f108(x61801),x61802),f10(x61801,x61803)),f10(x61801,x61803))+~P1(f335(f67(x61801),x61803))+~P1(f335(f335(f337(x61801),x61802),x61803)) % 186.01/186.04 [6181]~P98(x61811)+E(f335(f335(f117(x61811),x61812),f13(x61811,x61813)),f13(x61811,x61813))+~P1(f335(f67(x61811),x61813))+~P1(f335(f335(f337(x61811),x61812),x61813)) % 186.01/186.04 [6182]~P109(x61821)+E(f335(f335(f241(x61821),x61822),f15(x61821,x61823)),f15(x61821,x61823))+~P1(f335(f67(x61821),x61823))+~P1(f335(f335(f337(x61821),x61822),x61823)) % 186.01/186.04 [6183]~P109(x61831)+E(f335(f335(f242(x61831),x61832),f14(x61831,x61833)),f14(x61831,x61833))+~P1(f335(f67(x61831),x61833))+~P1(f335(f335(f337(x61831),x61832),x61833)) % 186.01/186.04 [6222]E(x62221,x62222)+~P110(x62223)+~P1(f335(f335(f243(x62223),x62222),x62221))+~P1(f335(f335(f243(x62223),x62221),x62222)) % 186.01/186.04 [6364]~P107(x63641)+P1(f335(f335(f244(x63641),x63643),x63642))+~P1(f335(f335(f243(x63641),x63643),x63642))+P1(f335(f335(f243(x63641),x63642),x63643)) % 186.01/186.04 [6391]~P109(x63911)+~P1(f335(f67(x63911),x63913))+P1(f335(f335(f243(x63911),x63912),f14(x63911,x63913)))+~P1(f335(f335(f337(x63911),x63912),x63913)) % 186.01/186.04 [6436]~P109(x64361)+E(f335(f335(f241(x64361),x64362),f11(x64361,f242(x64361),x64363)),x64362)+~P1(f335(f67(x64361),x64363))+~P1(f335(f335(f337(x64361),x64362),x64363)) % 186.01/186.04 [6437]~P109(x64371)+E(f335(f335(f242(x64371),x64372),f12(x64371,f241(x64371),x64373)),x64372)+~P1(f335(f67(x64371),x64373))+~P1(f335(f335(f337(x64371),x64372),x64373)) % 186.01/186.04 [6576]E(x65761,x65762)+~E(f335(f335(f23(a927),x65761),x65763),f335(f335(f23(a927),x65762),x65763))+~P1(f335(f335(f243(a927),x65763),x65761))+~P1(f335(f335(f243(a927),x65763),x65762)) % 186.01/186.04 [6602]~P109(x66021)+~P1(f335(f67(x66021),x66022))+~P1(f335(f335(f337(x66021),x66023),x66022))+P1(f335(f335(f243(x66021),f15(x66021,x66022)),x66023)) % 186.01/186.04 [6666]P148(x66662,x66661,x66663)+E(x66661,f2(a1))+P1(f335(f335(f244(a1),x66661),f867(x66663,x66661,x66662)))+P1(f335(f335(f244(a1),f2(a1)),x66661)) % 186.01/186.04 [6667]P147(x66672,x66671,x66673)+E(x66671,f2(a1))+P1(f335(f335(f244(a1),x66671),f873(x66673,x66671,x66672)))+P1(f335(f335(f244(a1),f2(a1)),x66671)) % 186.01/186.04 [6668]~P109(x66681)+E(f335(f335(f241(x66681),x66682),f12(x66681,f241(x66681),x66683)),f12(x66681,f241(x66681),x66683))+~P1(f335(f67(x66681),x66683))+~P1(f335(f335(f337(x66681),x66682),x66683)) % 186.01/186.04 [6669]~P109(x66691)+E(f335(f335(f242(x66691),x66692),f11(x66691,f242(x66691),x66693)),f11(x66691,f242(x66691),x66693))+~P1(f335(f67(x66691),x66693))+~P1(f335(f335(f337(x66691),x66692),x66693)) % 186.01/186.04 [6674]~P1(f335(x66741,x66742))+P1(f335(x66741,f609(x66742,x66741,x66743)))+P1(f335(x66741,f2(a927)))+~P1(f335(f335(f244(a927),x66742),x66743)) % 186.01/186.04 [6730]~P1(f335(x67301,x67302))+~P1(f335(f67(x67303),x67302))+P1(f335(x67301,f351(x67301,x67302,x67303)))+P1(f335(x67301,f195(f934(x67303,a922)))) % 186.01/186.04 [6743]~P113(x67431)+~P94(x67431)+P1(f335(f335(f243(x67431),f335(f110(x67431),x67432)),f335(f110(x67431),x67433)))+~P1(f335(f335(f243(a1),x67432),x67433)) % 186.01/186.04 [6744]~P113(x67441)+~P94(x67441)+P1(f335(f335(f244(x67441),f335(f110(x67441),x67442)),f335(f110(x67441),x67443)))+~P1(f335(f335(f244(a1),x67442),x67443)) % 186.01/186.04 [6747]~P1(f335(x67471,x67473))+~P1(f335(f67(x67472),x67473))+P1(f335(f67(x67472),f351(x67471,x67473,x67472)))+P1(f335(x67471,f195(f934(x67472,a922)))) % 186.01/186.04 [6781]P147(x67811,x67812,x67813)+~P1(f335(x67811,x67813))+P1(f335(f335(f244(a1),x67812),f873(x67813,x67812,x67811)))+P1(f335(f335(f244(a1),f2(a1)),x67812)) % 186.01/186.04 [6817]P148(x68171,x68172,x68173)+P1(f335(f335(f244(a1),x68172),f867(x68173,x68172,x68171)))+~P1(f335(x68171,f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x68172)) % 186.01/186.04 [6847]~P108(x68471)+~P95(x68471)+E(f335(f335(f241(x68471),f335(f110(x68471),x68472)),f335(f110(x68471),x68473)),f335(f110(x68471),x68473))+P1(f335(f335(f243(x68471),f335(f110(x68471),x68472)),f335(f110(x68471),x68473))) % 186.01/186.04 [6848]~P108(x68481)+~P95(x68481)+E(f335(f335(f242(x68481),f335(f110(x68481),x68482)),f335(f110(x68481),x68483)),f335(f110(x68481),x68482))+P1(f335(f335(f243(x68481),f335(f110(x68481),x68482)),f335(f110(x68481),x68483))) % 186.01/186.04 [6906]P148(x69062,x69061,x69063)+E(x69061,f2(a1))+~P1(f335(x69062,f872(x69063,x69061,x69062)))+P1(f335(f335(f244(a1),f2(a1)),x69061)) % 186.01/186.04 [6907]P147(x69072,x69071,x69073)+E(x69071,f2(a1))+~P1(f335(x69072,f873(x69073,x69071,x69072)))+P1(f335(f335(f244(a1),f2(a1)),x69071)) % 186.01/186.04 [6911]P1(f335(x69111,x69112))+~P1(f335(f67(x69113),x69112))+P1(f335(x69111,f782(x69111,x69112,x69113)))+~P1(f335(x69111,f195(f934(x69113,a922)))) % 186.01/186.04 [6932]P1(f335(x69321,x69322))+P1(f335(f67(x69323),f782(x69321,x69322,x69323)))+~P1(f335(f67(x69323),x69322))+~P1(f335(x69321,f195(f934(x69323,a922)))) % 186.01/186.04 [6995]P147(x69951,x69952,x69953)+~P1(f335(x69951,x69953))+~P1(f335(x69951,f873(x69953,x69952,x69951)))+P1(f335(f335(f244(a1),f2(a1)),x69952)) % 186.01/186.04 [7025]P148(x70251,x70252,x70253)+~P1(f335(x70251,f872(x70253,x70252,x70251)))+~P1(f335(x70251,f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x70252)) % 186.01/186.04 [7129]~P94(x71293)+~P113(x71293)+~P1(f335(f335(f243(x71293),f335(f110(x71293),x71291)),f335(f110(x71293),x71292)))+P1(f335(f335(f243(a1),x71291),x71292)) % 186.01/186.04 [7130]~P94(x71303)+~P113(x71303)+~P1(f335(f335(f244(x71303),f335(f110(x71303),x71301)),f335(f110(x71303),x71302)))+P1(f335(f335(f244(a1),x71301),x71302)) % 186.01/186.04 [7157]~P109(x71571)+~P14(x71571,x71573)+P14(x71571,f335(f335(f158(x71571),x71572),x71573))+~P1(f335(f335(f243(x71571),x71572),f734(x71573,x71572,x71571))) % 186.01/186.04 [7158]~P109(x71581)+~P14(x71581,x71583)+P14(x71581,f335(f335(f158(x71581),x71582),x71583))+~P1(f335(f335(f243(x71581),x71582),f736(x71583,x71582,x71581))) % 186.01/186.04 [7159]~P109(x71591)+~P14(x71591,x71593)+P14(x71591,f335(f335(f158(x71591),x71592),x71593))+~P1(f335(f335(f243(x71591),x71592),f774(x71592,x71593,x71591))) % 186.01/186.04 [7244]P148(x72442,x72441,x72443)+E(x72441,f2(a1))+P1(f335(f335(f244(a1),x72441),f2(a1)))+P1(f335(f335(f244(a1),f868(x72443,x72441,x72442)),x72441)) % 186.01/186.04 [7245]P147(x72452,x72451,x72453)+E(x72451,f2(a1))+P1(f335(f335(f244(a1),x72451),f2(a1)))+P1(f335(f335(f244(a1),f874(x72453,x72451,x72452)),x72451)) % 186.01/186.04 [7281]P148(x72812,x72811,x72813)+E(x72811,f2(a1))+P1(f335(f335(f243(a1),f867(x72813,x72811,x72812)),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x72811)) % 186.01/186.04 [7282]P147(x72822,x72821,x72823)+E(x72821,f2(a1))+P1(f335(f335(f243(a1),f873(x72823,x72821,x72822)),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x72821)) % 186.01/186.04 [7307]~P109(x73071)+~P14(x73071,x73073)+E(f335(f335(f155(x73071,x73071,f5(x73071)),x73072),f177(x73071,x73072,x73073)),x73073)+~P1(f335(f335(f337(x73071),x73072),f335(f179(x73071),x73073))) % 186.01/186.04 [7354]P147(x73541,x73542,x73543)+~P1(f335(x73541,x73543))+P1(f335(f335(f244(a1),x73542),f2(a1)))+P1(f335(f335(f244(a1),f874(x73543,x73542,x73541)),x73542)) % 186.01/186.04 [7360]~P108(x73601)+~P95(x73601)+E(f335(f335(f241(x73601),f335(f110(x73601),x73602)),f335(f110(x73601),x73603)),f335(f110(x73601),x73602))+~P1(f335(f335(f243(x73601),f335(f110(x73601),x73602)),f335(f110(x73601),x73603))) % 186.01/186.04 [7361]~P108(x73611)+~P95(x73611)+E(f335(f335(f242(x73611),f335(f110(x73611),x73612)),f335(f110(x73611),x73613)),f335(f110(x73611),x73613))+~P1(f335(f335(f243(x73611),f335(f110(x73611),x73612)),f335(f110(x73611),x73613))) % 186.01/186.04 [7375]P148(x73751,x73752,x73753)+~P1(f335(x73751,f2(a1)))+P1(f335(f335(f244(a1),x73752),f2(a1)))+P1(f335(f335(f244(a1),f868(x73753,x73752,x73751)),x73752)) % 186.01/186.04 [7383]P147(x73831,x73832,x73833)+~P1(f335(x73831,x73833))+P1(f335(f335(f243(a1),f873(x73833,x73832,x73831)),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x73832)) % 186.01/186.04 [7407]P148(x74071,x74072,x74073)+~P1(f335(x74071,f2(a1)))+P1(f335(f335(f243(a1),f867(x74073,x74072,x74071)),f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x74072)) % 186.01/186.04 [7434]~P1(f335(x74341,x74342))+P1(f335(x74341,f2(a927)))+~P1(f335(f335(f244(a927),x74342),x74343))+P1(f335(f335(f244(a927),f609(x74342,x74341,x74343)),x74343)) % 186.01/186.04 [7451]~P109(x74511)+~P14(x74511,x74513)+P14(x74511,f335(f335(f158(x74511),x74512),x74513))+P1(f335(f335(f337(x74511),f734(x74513,x74512,x74511)),f335(f179(x74511),x74513))) % 186.01/186.04 [7452]~P109(x74521)+~P14(x74521,x74523)+P14(x74521,f335(f335(f158(x74521),x74522),x74523))+P1(f335(f335(f337(x74521),f736(x74523,x74522,x74521)),f335(f179(x74521),x74523))) % 186.01/186.04 [7453]~P109(x74531)+~P14(x74531,x74533)+P14(x74531,f335(f335(f158(x74531),x74532),x74533))+P1(f335(f335(f337(x74531),f774(x74532,x74533,x74531)),f335(f179(x74531),x74533))) % 186.01/186.04 [7571]~P109(x75711)+~P6(x75711)+~P1(f335(f335(f244(x75711),x75713),f43(x75711,x75712)))+P1(f335(f335(f337(x75711),f580(x75712,x75713,x75711)),x75712)) % 186.01/186.04 [7724]~P109(x77241)+~P6(x77241)+~P1(f335(f335(f244(x77241),f44(x77241,x77243)),x77242))+P1(f335(f335(f337(x77241),f897(x77242,x77243,x77241)),x77243)) % 186.01/186.04 [7725]~P109(x77251)+~P6(x77251)+~P1(f335(f335(f244(x77251),f44(x77251,x77253)),x77252))+P1(f335(f335(f244(x77251),f897(x77252,x77253,x77251)),x77252)) % 186.01/186.04 [7737]P148(x77372,x77371,x77373)+E(x77371,f2(a1))+P1(f335(f335(f244(a1),x77371),f867(x77373,x77371,x77372)))+P1(f335(f335(f244(a1),f868(x77373,x77371,x77372)),x77371)) % 186.01/186.04 [7738]P147(x77382,x77381,x77383)+E(x77381,f2(a1))+P1(f335(f335(f244(a1),x77381),f873(x77383,x77381,x77382)))+P1(f335(f335(f244(a1),f874(x77383,x77381,x77382)),x77381)) % 186.01/186.04 [7827]P148(x78273,x78271,x78272)+E(x78271,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x78271),f872(x78272,x78271,x78273))),f867(x78272,x78271,x78273)),x78272)+P1(f335(f335(f244(a1),f2(a1)),x78271)) % 186.01/186.04 [7828]P147(x78283,x78281,x78282)+E(x78281,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x78281),f877(x78282,x78281,x78283))),f873(x78282,x78281,x78283)),x78282)+P1(f335(f335(f244(a1),f2(a1)),x78281)) % 186.01/186.04 [7830]~P127(x78301)+~P1(f335(f335(f243(x78301),x78303),f2(x78301)))+P1(f335(f335(f243(x78301),f335(f335(f87(x78301),x78302),x78303)),f2(x78301)))+~P1(f335(f335(f243(x78301),f2(x78301)),x78302)) % 186.01/186.04 [7831]~P127(x78311)+~P1(f335(f335(f243(x78311),x78312),f2(x78311)))+P1(f335(f335(f243(x78311),f335(f335(f87(x78311),x78312),x78313)),f2(x78311)))+~P1(f335(f335(f243(x78311),f2(x78311)),x78313)) % 186.01/186.04 [7833]~P135(x78331)+~P1(f335(f335(f243(x78331),x78333),f2(x78331)))+P1(f335(f335(f243(x78331),f335(f335(f87(x78331),x78332),x78333)),f2(x78331)))+~P1(f335(f335(f243(x78331),f2(x78331)),x78332)) % 186.01/186.04 [7835]~P135(x78351)+~P1(f335(f335(f243(x78351),x78352),f2(x78351)))+P1(f335(f335(f243(x78351),f335(f335(f87(x78351),x78352),x78353)),f2(x78351)))+~P1(f335(f335(f243(x78351),f2(x78351)),x78353)) % 186.01/186.04 [7836]~P68(x78361)+~P1(f335(f335(f243(x78361),x78363),f2(x78361)))+P1(f335(f335(f243(x78361),f335(f335(f299(x78361),x78362),x78363)),f2(x78361)))+~P1(f335(f335(f243(x78361),f2(x78361)),x78362)) % 186.01/186.04 [7837]~P68(x78371)+~P1(f335(f335(f243(x78371),x78372),f2(x78371)))+P1(f335(f335(f243(x78371),f335(f335(f299(x78371),x78372),x78373)),f2(x78371)))+~P1(f335(f335(f243(x78371),f2(x78371)),x78373)) % 186.01/186.04 [7838]~P69(x78381)+~P1(f335(f335(f243(x78381),x78382),f2(x78381)))+P1(f335(f335(f243(x78381),f335(f335(f299(x78381),x78382),x78383)),f2(x78381)))+~P1(f335(f335(f244(x78381),f2(x78381)),x78383)) % 186.01/186.04 [7839]~P69(x78391)+~P1(f335(f335(f244(x78391),x78393),f2(x78391)))+P1(f335(f335(f243(x78391),f335(f335(f299(x78391),x78392),x78393)),f2(x78391)))+~P1(f335(f335(f243(x78391),f2(x78391)),x78392)) % 186.01/186.04 [7841]~P131(x78411)+~P1(f335(f335(f244(x78411),x78413),f2(x78411)))+P1(f335(f335(f244(x78411),f335(f335(f87(x78411),x78412),x78413)),f2(x78411)))+~P1(f335(f335(f244(x78411),f2(x78411)),x78412)) % 186.01/186.04 [7842]~P131(x78421)+~P1(f335(f335(f244(x78421),x78422),f2(x78421)))+P1(f335(f335(f244(x78421),f335(f335(f87(x78421),x78422),x78423)),f2(x78421)))+~P1(f335(f335(f244(x78421),f2(x78421)),x78423)) % 186.01/186.04 [7843]~P68(x78431)+~P1(f335(f335(f244(x78431),x78433),f2(x78431)))+P1(f335(f335(f244(x78431),f335(f335(f299(x78431),x78432),x78433)),f2(x78431)))+~P1(f335(f335(f244(x78431),f2(x78431)),x78432)) % 186.01/186.04 [7844]~P68(x78441)+~P1(f335(f335(f244(x78441),x78442),f2(x78441)))+P1(f335(f335(f244(x78441),f335(f335(f299(x78441),x78442),x78443)),f2(x78441)))+~P1(f335(f335(f244(x78441),f2(x78441)),x78443)) % 186.01/186.04 [7845]~P69(x78451)+~P1(f335(f335(f244(x78451),x78453),f2(x78451)))+P1(f335(f335(f244(x78451),f335(f335(f299(x78451),x78452),x78453)),f2(x78451)))+~P1(f335(f335(f244(x78451),f2(x78451)),x78452)) % 186.01/186.04 [7846]~P69(x78461)+~P1(f335(f335(f244(x78461),x78462),f2(x78461)))+P1(f335(f335(f244(x78461),f335(f335(f299(x78461),x78462),x78463)),f2(x78461)))+~P1(f335(f335(f244(x78461),f2(x78461)),x78463)) % 186.01/186.04 [7861]P147(x78611,x78612,x78613)+~P1(f335(x78611,x78613))+P1(f335(f335(f244(a1),x78612),f873(x78613,x78612,x78611)))+P1(f335(f335(f244(a1),f874(x78613,x78612,x78611)),x78612)) % 186.01/186.04 [7874]P148(x78741,x78742,x78743)+P1(f335(f335(f244(a1),x78742),f867(x78743,x78742,x78741)))+~P1(f335(x78741,f2(a1)))+P1(f335(f335(f244(a1),f868(x78743,x78742,x78741)),x78742)) % 186.01/186.04 [7924]P148(x79242,x79241,x79243)+E(x79241,f2(a1))+~P1(f335(x79242,f872(x79243,x79241,x79242)))+P1(f335(f335(f244(a1),f868(x79243,x79241,x79242)),x79241)) % 186.01/186.04 [7925]P147(x79252,x79251,x79253)+E(x79251,f2(a1))+~P1(f335(x79252,f873(x79253,x79251,x79252)))+P1(f335(f335(f244(a1),f874(x79253,x79251,x79252)),x79251)) % 186.01/186.04 [7935]P147(x79353,x79351,x79352)+~P1(f335(x79353,x79352))+E(f335(f335(f86(a1),f335(f335(f87(a1),x79351),f877(x79352,x79351,x79353))),f873(x79352,x79351,x79353)),x79352)+P1(f335(f335(f244(a1),f2(a1)),x79351)) % 186.01/186.04 [7950]P148(x79503,x79501,x79502)+E(f335(f335(f86(a1),f335(f335(f87(a1),x79501),f872(x79502,x79501,x79503))),f867(x79502,x79501,x79503)),x79502)+~P1(f335(x79503,f2(a1)))+P1(f335(f335(f244(a1),f2(a1)),x79501)) % 186.01/186.04 [7978]~P1(f335(x79781,x79783))+~P1(f335(f67(x79782),x79783))+P1(f335(f335(f337(x79782),f352(x79781,x79783,x79782)),f351(x79781,x79783,x79782)))+P1(f335(x79781,f195(f934(x79782,a922)))) % 186.01/186.04 [7989]P147(x79891,x79892,x79893)+~P1(f335(x79891,x79893))+~P1(f335(x79891,f873(x79893,x79892,x79891)))+P1(f335(f335(f244(a1),f874(x79893,x79892,x79891)),x79892)) % 186.01/186.04 [7995]P148(x79951,x79952,x79953)+~P1(f335(x79951,f872(x79953,x79952,x79951)))+~P1(f335(x79951,f2(a1)))+P1(f335(f335(f244(a1),f868(x79953,x79952,x79951)),x79952)) % 186.01/186.04 [8094]~P127(x80941)+~P1(f335(f335(f243(x80941),f335(f335(f87(x80941),x80943),x80942)),f2(x80941)))+P1(f335(f335(f243(x80941),x80942),f2(x80941)))+P1(f335(f335(f243(x80941),f2(x80941)),x80942)) % 186.01/186.04 [8095]~P127(x80951)+~P1(f335(f335(f243(x80951),f335(f335(f87(x80951),x80952),x80953)),f2(x80951)))+P1(f335(f335(f243(x80951),x80952),f2(x80951)))+P1(f335(f335(f243(x80951),f2(x80951)),x80952)) % 186.01/186.04 [8096]~P68(x80961)+~P1(f335(f335(f243(x80961),f335(f335(f299(x80961),x80963),x80962)),f2(x80961)))+P1(f335(f335(f243(x80961),x80962),f2(x80961)))+P1(f335(f335(f243(x80961),f2(x80961)),x80962)) % 186.01/186.04 [8097]~P68(x80971)+~P1(f335(f335(f243(x80971),f335(f335(f299(x80971),x80972),x80973)),f2(x80971)))+P1(f335(f335(f243(x80971),x80972),f2(x80971)))+P1(f335(f335(f243(x80971),f2(x80971)),x80972)) % 186.01/186.04 [8098]~P68(x80981)+~P1(f335(f335(f244(x80981),f335(f335(f299(x80981),x80983),x80982)),f2(x80981)))+P1(f335(f335(f244(x80981),x80982),f2(x80981)))+P1(f335(f335(f244(x80981),f2(x80981)),x80982)) % 186.01/186.04 [8099]~P68(x80991)+~P1(f335(f335(f244(x80991),f335(f335(f299(x80991),x80992),x80993)),f2(x80991)))+P1(f335(f335(f244(x80991),x80992),f2(x80991)))+P1(f335(f335(f244(x80991),f2(x80991)),x80992)) % 186.01/186.04 [8122]~P127(x81221)+~P1(f335(f335(f243(x81221),f335(f335(f87(x81221),x81222),x81223)),f2(x81221)))+P1(f335(f335(f243(x81221),f2(x81221)),x81222))+P1(f335(f335(f243(x81221),f2(x81221)),x81223)) % 186.01/186.04 [8123]~P68(x81231)+~P1(f335(f335(f243(x81231),f335(f335(f299(x81231),x81232),x81233)),f2(x81231)))+P1(f335(f335(f243(x81231),f2(x81231)),x81232))+P1(f335(f335(f243(x81231),f2(x81231)),x81233)) % 186.01/186.04 [8124]~P68(x81241)+~P1(f335(f335(f244(x81241),f335(f335(f299(x81241),x81242),x81243)),f2(x81241)))+P1(f335(f335(f244(x81241),f2(x81241)),x81242))+P1(f335(f335(f244(x81241),f2(x81241)),x81243)) % 186.01/186.04 [8146]P148(x81462,x81461,x81463)+E(x81461,f2(a1))+P1(f335(f335(f243(a1),f867(x81463,x81461,x81462)),f2(a1)))+P1(f335(f335(f244(a1),f868(x81463,x81461,x81462)),x81461)) % 186.01/186.04 [8147]P147(x81472,x81471,x81473)+E(x81471,f2(a1))+P1(f335(f335(f243(a1),f873(x81473,x81471,x81472)),f2(a1)))+P1(f335(f335(f244(a1),f874(x81473,x81471,x81472)),x81471)) % 186.01/186.04 [8154]~P125(x81541)+~P1(f335(f335(f244(x81541),x81542),f84(x81541)))+P1(f335(f335(f244(x81541),f335(f335(f252(x81541),x81542),f335(a119,x81543))),f84(x81541)))+~P1(f335(f335(f244(x81541),f2(x81541)),x81542)) % 186.01/186.04 [8208]~P109(x82081)+~E(x82083,f120(x82081))+~P14(x82081,f335(f175(x82081),x82083))+E(f335(f149(x82081,x82081,f335(f7(x82081,x82081,x82081),f242(x82081)),x82082),f335(f175(x82081),x82083)),x82082) % 186.01/186.04 [8211]P147(x82111,x82112,x82113)+~P1(f335(x82111,x82113))+P1(f335(f335(f243(a1),f873(x82113,x82112,x82111)),f2(a1)))+P1(f335(f335(f244(a1),f874(x82113,x82112,x82111)),x82112)) % 186.01/186.04 [8218]P148(x82181,x82182,x82183)+~P1(f335(x82181,f2(a1)))+P1(f335(f335(f243(a1),f867(x82183,x82182,x82181)),f2(a1)))+P1(f335(f335(f244(a1),f868(x82183,x82182,x82181)),x82182)) % 186.01/186.04 [8431]P148(x84313,x84311,x84312)+E(x84311,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84311),f872(x84312,x84311,x84313))),f867(x84312,x84311,x84313)),x84312)+P1(f335(f335(f244(a1),f868(x84312,x84311,x84313)),x84311)) % 186.01/186.04 [8432]P147(x84323,x84321,x84322)+E(x84321,f2(a1))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84321),f877(x84322,x84321,x84323))),f873(x84322,x84321,x84323)),x84322)+P1(f335(f335(f244(a1),f874(x84322,x84321,x84323)),x84321)) % 186.01/186.04 [8468]P147(x84683,x84681,x84682)+~P1(f335(x84683,x84682))+E(f335(f335(f86(a1),f335(f335(f87(a1),x84681),f877(x84682,x84681,x84683))),f873(x84682,x84681,x84683)),x84682)+P1(f335(f335(f244(a1),f874(x84682,x84681,x84683)),x84681)) % 186.01/186.04 [8469]~P72(x84691)+~P76(x84691)+~P41(x84693)+E(f335(f335(f6(a927,x84691),f335(f335(f8(a1,x84691,a927),x84692),f107(a1))),f335(f318(a1,a927,a111),x84693)),f335(f335(f6(a1,x84691),x84692),x84693)) % 186.01/186.04 [8470]~P72(x84701)+~P76(x84701)+~P41(x84703)+E(f335(f335(f9(a927,x84701),f335(f335(f8(a1,x84701,a927),x84702),f107(a1))),f335(f318(a1,a927,a111),x84703)),f335(f335(f9(a1,x84701),x84702),x84703)) % 186.01/186.04 [8479]P148(x84793,x84791,x84792)+E(f335(f335(f86(a1),f335(f335(f87(a1),x84791),f872(x84792,x84791,x84793))),f867(x84792,x84791,x84793)),x84792)+~P1(f335(x84793,f2(a1)))+P1(f335(f335(f244(a1),f868(x84792,x84791,x84793)),x84791)) % 186.01/186.04 [8502]~E(x85022,f2(a927))+~E(f335(f259(a927,a927),x85023),f2(a927))+~E(x85021,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x85023)),x85022)),f335(f264(a927,a927),x85023)))+P1(f335(f54(x85021,x85022),x85023)) % 186.01/186.04 [8558]P1(f335(x85581,x85582))+~P1(f335(f335(f337(x85583),f788(x85581,x85582,x85583)),f782(x85581,x85582,x85583)))+~P1(f335(f67(x85583),x85582))+~P1(f335(x85581,f195(f934(x85583,a922)))) % 186.01/186.04 [9186]P1(f335(x91861,x91862))+~P1(f335(f67(x91863),x91862))+~P1(f335(x91861,f335(f335(f317(x91863),f788(x91861,x91862,x91863)),f782(x91861,x91862,x91863))))+~P1(f335(x91861,f195(f934(x91863,a922)))) % 186.01/186.04 [9417]P1(f335(f335(f243(a1),x94171),f2(a1)))+~P1(f335(f335(f244(a1),f335(f335(f86(a1),f335(f335(f87(a1),x94173),x94171)),x94172)),f2(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x94172))+~P1(f335(f335(f244(a1),f2(a1)),x94173)) % 186.01/186.04 [6044]~P98(x60442)+E(x60441,f195(f934(x60442,a922)))+~P1(f335(f67(x60442),x60441))+E(f13(x60442,f335(f335(f317(x60442),x60443),x60441)),f335(f335(f117(x60442),x60443),f13(x60442,x60441))) % 186.01/186.04 [6045]~P98(x60452)+E(x60451,f195(f934(x60452,a922)))+~P1(f335(f67(x60452),x60451))+E(f10(x60452,f335(f335(f317(x60452),x60453),x60451)),f335(f335(f108(x60452),x60453),f10(x60452,x60451))) % 186.01/186.04 [6046]~P109(x60462)+E(x60461,f195(f934(x60462,a922)))+~P1(f335(f67(x60462),x60461))+E(f14(x60462,f335(f335(f317(x60462),x60463),x60461)),f335(f335(f242(x60462),x60463),f14(x60462,x60461))) % 186.01/186.04 [6047]~P109(x60472)+E(x60471,f195(f934(x60472,a922)))+~P1(f335(f67(x60472),x60471))+E(f15(x60472,f335(f335(f317(x60472),x60473),x60471)),f335(f335(f241(x60472),x60473),f15(x60472,x60471))) % 186.01/186.04 [6361]~P127(x63611)+~E(x63613,f2(x63611))+~E(x63612,f2(x63611))+E(f335(f335(f86(x63611),f335(f335(f87(x63611),x63612),x63612)),f335(f335(f87(x63611),x63613),x63613)),f2(x63611)) % 186.01/186.04 [6429]~P96(x64292)+E(x64291,f195(f934(x64292,a922)))+~P1(f335(f67(x64292),x64291))+E(f335(f69(x64292,f87(x64292)),f335(f335(f317(x64292),x64293),x64291)),f335(f335(f87(x64292),x64293),f335(f69(x64292,f87(x64292)),x64291))) % 186.01/186.04 [6553]~P109(x65532)+E(x65531,f195(f934(x65532,a922)))+~P1(f335(f67(x65532),x65531))+E(f11(x65532,f242(x65532),f335(f335(f317(x65532),x65533),x65531)),f335(f335(f242(x65532),x65533),f11(x65532,f242(x65532),x65531))) % 186.01/186.04 [6554]~P109(x65542)+E(x65541,f195(f934(x65542,a922)))+~P1(f335(f67(x65542),x65541))+E(f12(x65542,f241(x65542),f335(f335(f317(x65542),x65543),x65541)),f335(f335(f241(x65542),x65543),f12(x65542,f241(x65542),x65541))) % 186.01/186.04 [7059]~P70(x70591)+~P1(f335(f67(x70591),x70593))+E(f335(f69(x70591,f87(x70591)),f335(f335(f317(x70591),x70592),x70593)),f335(f335(f70(x70591,x70591,f87(x70591)),x70592),x70593))+P1(f335(f335(f337(x70591),x70592),x70593)) % 186.01/186.04 [7136]~E(f335(f335(f86(a1),x71362),f335(f335(f87(a1),x71363),x71361)),x71363)+~P1(f335(f335(f244(a1),f2(a1)),x71363))+P1(f335(f335(f243(a1),f84(a1)),x71361))+~P1(f335(f335(f244(a1),x71362),x71363)) % 186.01/186.04 [7164]~E(f335(f335(f86(a1),x71642),f335(f335(f87(a1),x71643),x71641)),x71643)+P1(f335(f335(f243(a1),x71641),f84(a1)))+~P1(f335(f335(f243(a1),f2(a1)),x71642))+~P1(f335(f335(f244(a1),f2(a1)),x71643)) % 186.01/186.04 [7180]E(x71801,f2(a927))+~P1(f335(f54(x71803,x71801),x71802))+~P1(f335(f335(f244(a927),f2(a927)),x71801))+P1(f335(f335(f244(a927),f335(f264(a927,a927),x71802)),x71801)) % 186.01/186.04 [7212]~P138(x72121)+~P1(f335(f335(f243(x72121),x72122),f2(x72121)))+~P1(f335(f335(f243(x72121),x72123),f2(x72121)))+E(f335(f335(f87(x72121),f335(f81(x72121),x72122)),f335(f81(x72121),x72123)),f335(f81(x72121),f335(f335(f87(x72121),x72122),x72123))) % 186.01/186.04 [7258]~P138(x72581)+~P1(f335(f335(f243(x72581),x72582),f2(x72581)))+E(f335(f335(f87(x72581),f335(f81(x72581),x72582)),f335(f81(x72581),x72583)),f335(f81(x72581),f335(f335(f87(x72581),x72582),x72583)))+~P1(f335(f335(f243(x72581),f2(x72581)),x72583)) % 186.01/186.04 [7259]~P138(x72591)+~P1(f335(f335(f243(x72591),x72593),f2(x72591)))+E(f335(f335(f87(x72591),f335(f81(x72591),x72592)),f335(f81(x72591),x72593)),f335(f81(x72591),f335(f335(f87(x72591),x72592),x72593)))+~P1(f335(f335(f243(x72591),f2(x72591)),x72592)) % 186.01/186.04 [7315]~P138(x73151)+E(f335(f335(f87(x73151),f335(f81(x73151),x73152)),f335(f81(x73151),x73153)),f335(f81(x73151),f335(f335(f87(x73151),x73152),x73153)))+~P1(f335(f335(f243(x73151),f2(x73151)),x73152))+~P1(f335(f335(f243(x73151),f2(x73151)),x73153)) % 186.01/186.04 [7332]~P128(x73321)+~P1(f335(f335(f243(x73321),x73323),f2(x73321)))+~P1(f335(f335(f243(x73321),x73322),f2(x73321)))+P1(f335(f335(f243(x73321),f2(x73321)),f335(f335(f87(x73321),x73322),x73323))) % 186.01/186.04 [7333]~P127(x73331)+~P1(f335(f335(f243(x73331),x73333),f2(x73331)))+~P1(f335(f335(f243(x73331),x73332),f2(x73331)))+P1(f335(f335(f243(x73331),f2(x73331)),f335(f335(f87(x73331),x73332),x73333))) % 186.01/186.04 [7334]~P68(x73341)+~P1(f335(f335(f243(x73341),x73343),f2(x73341)))+~P1(f335(f335(f243(x73341),x73342),f2(x73341)))+P1(f335(f335(f243(x73341),f2(x73341)),f335(f335(f299(x73341),x73342),x73343))) % 186.01/186.04 [7335]~P69(x73351)+~P1(f335(f335(f244(x73351),x73353),f2(x73351)))+~P1(f335(f335(f243(x73351),x73352),f2(x73351)))+P1(f335(f335(f243(x73351),f2(x73351)),f335(f335(f299(x73351),x73352),x73353))) % 186.01/186.04 [7336]~P127(x73361)+~P1(f335(f335(f244(x73361),x73363),f2(x73361)))+~P1(f335(f335(f244(x73361),x73362),f2(x73361)))+P1(f335(f335(f244(x73361),f2(x73361)),f335(f335(f87(x73361),x73362),x73363))) % 186.01/186.04 [7337]~P68(x73371)+~P1(f335(f335(f244(x73371),x73373),f2(x73371)))+~P1(f335(f335(f244(x73371),x73372),f2(x73371)))+P1(f335(f335(f244(x73371),f2(x73371)),f335(f335(f299(x73371),x73372),x73373))) % 186.01/186.04 [7338]~P69(x73381)+~P1(f335(f335(f244(x73381),x73383),f2(x73381)))+~P1(f335(f335(f244(x73381),x73382),f2(x73381)))+P1(f335(f335(f244(x73381),f2(x73381)),f335(f335(f299(x73381),x73382),x73383))) % 186.01/186.04 [7339]~P125(x73391)+~P1(f335(f335(f244(a927),f2(a927)),x73393))+~P1(f335(f335(f244(x73391),f84(x73391)),x73392))+P1(f335(f335(f244(x73391),f84(x73391)),f335(f335(f252(x73391),x73392),x73393))) % 186.01/186.04 [7435]~P128(x74351)+~P1(f335(f335(f243(x74351),f2(x74351)),x74353))+~P1(f335(f335(f243(x74351),f2(x74351)),x74352))+P1(f335(f335(f243(x74351),f2(x74351)),f335(f335(f87(x74351),x74352),x74353))) % 186.01/186.04 [7436]~P127(x74361)+~P1(f335(f335(f243(x74361),f2(x74361)),x74363))+~P1(f335(f335(f243(x74361),f2(x74361)),x74362))+P1(f335(f335(f243(x74361),f2(x74361)),f335(f335(f87(x74361),x74362),x74363))) % 186.01/186.04 [7437]~P135(x74371)+~P1(f335(f335(f243(x74371),f2(x74371)),x74373))+~P1(f335(f335(f243(x74371),f2(x74371)),x74372))+P1(f335(f335(f243(x74371),f2(x74371)),f335(f335(f87(x74371),x74372),x74373))) % 186.01/186.04 [7439]~P68(x74391)+~P1(f335(f335(f243(x74391),f2(x74391)),x74393))+~P1(f335(f335(f243(x74391),f2(x74391)),x74392))+P1(f335(f335(f243(x74391),f2(x74391)),f335(f335(f299(x74391),x74392),x74393))) % 186.01/186.04 [7440]~P69(x74401)+~P1(f335(f335(f244(x74401),f2(x74401)),x74403))+~P1(f335(f335(f243(x74401),f2(x74401)),x74402))+P1(f335(f335(f243(x74401),f2(x74401)),f335(f335(f299(x74401),x74402),x74403))) % 186.01/186.04 [7441]~P125(x74411)+~P1(f335(f335(f244(x74411),f84(x74411)),x74413))+~P1(f335(f335(f244(x74411),f84(x74411)),x74412))+P1(f335(f335(f244(x74411),f84(x74411)),f335(f335(f87(x74411),x74412),x74413))) % 186.01/186.04 [7442]~P131(x74421)+~P1(f335(f335(f244(x74421),f2(x74421)),x74423))+~P1(f335(f335(f244(x74421),f2(x74421)),x74422))+P1(f335(f335(f244(x74421),f2(x74421)),f335(f335(f87(x74421),x74422),x74423))) % 186.01/186.04 [7445]~P89(x74451)+~P1(f335(f335(f244(x74451),f2(x74451)),x74453))+~P1(f335(f335(f244(x74451),f2(x74451)),x74452))+P1(f335(f335(f244(x74451),f2(x74451)),f335(f335(f86(x74451),x74452),x74453))) % 186.01/186.04 [7446]~P68(x74461)+~P1(f335(f335(f244(x74461),f2(x74461)),x74463))+~P1(f335(f335(f244(x74461),f2(x74461)),x74462))+P1(f335(f335(f244(x74461),f2(x74461)),f335(f335(f299(x74461),x74462),x74463))) % 186.01/186.04 [7447]~P69(x74471)+~P1(f335(f335(f244(x74471),f2(x74471)),x74473))+~P1(f335(f335(f244(x74471),f2(x74471)),x74472))+P1(f335(f335(f244(x74471),f2(x74471)),f335(f335(f299(x74471),x74472),x74473))) % 186.01/186.04 [7528]~P98(x75281)+~P1(f335(f67(x75281),x75283))+E(f13(x75281,f335(f335(f317(x75281),x75282),x75283)),x75282)+~E(f335(f335(f23(f934(x75281,a922)),x75283),f335(f335(f317(x75281),x75282),f195(f934(x75281,a922)))),f195(f934(x75281,a922))) % 186.01/186.04 [7529]~P98(x75291)+~P1(f335(f67(x75291),x75293))+E(f10(x75291,f335(f335(f317(x75291),x75292),x75293)),x75292)+~E(f335(f335(f23(f934(x75291,a922)),x75293),f335(f335(f317(x75291),x75292),f195(f934(x75291,a922)))),f195(f934(x75291,a922))) % 186.01/186.04 [7530]~P109(x75301)+~P1(f335(f67(x75301),x75303))+E(f14(x75301,f335(f335(f317(x75301),x75302),x75303)),x75302)+~E(f335(f335(f23(f934(x75301,a922)),x75303),f335(f335(f317(x75301),x75302),f195(f934(x75301,a922)))),f195(f934(x75301,a922))) % 186.01/186.04 [7531]~P109(x75311)+~P1(f335(f67(x75311),x75313))+E(f15(x75311,f335(f335(f317(x75311),x75312),x75313)),x75312)+~E(f335(f335(f23(f934(x75311,a922)),x75313),f335(f335(f317(x75311),x75312),f195(f934(x75311,a922)))),f195(f934(x75311,a922))) % 186.01/186.04 [7533]~P127(x75331)+P1(f335(f335(f243(x75331),x75332),f2(x75331)))+P1(f335(f335(f243(x75331),f2(x75331)),x75333))+~P1(f335(f335(f243(x75331),f2(x75331)),f335(f335(f87(x75331),x75333),x75332))) % 186.01/186.04 [7534]~P127(x75341)+P1(f335(f335(f243(x75341),x75342),f2(x75341)))+P1(f335(f335(f243(x75341),f2(x75341)),x75343))+~P1(f335(f335(f243(x75341),f2(x75341)),f335(f335(f87(x75341),x75342),x75343))) % 186.01/186.04 [7535]~P68(x75351)+P1(f335(f335(f243(x75351),x75352),f2(x75351)))+P1(f335(f335(f243(x75351),f2(x75351)),x75353))+~P1(f335(f335(f243(x75351),f2(x75351)),f335(f335(f299(x75351),x75353),x75352))) % 186.01/186.04 [7536]~P68(x75361)+P1(f335(f335(f243(x75361),x75362),f2(x75361)))+P1(f335(f335(f243(x75361),f2(x75361)),x75363))+~P1(f335(f335(f243(x75361),f2(x75361)),f335(f335(f299(x75361),x75362),x75363))) % 186.01/186.04 [7537]~P127(x75371)+P1(f335(f335(f243(x75371),x75372),f2(x75371)))+P1(f335(f335(f243(x75371),f2(x75371)),x75372))+~P1(f335(f335(f243(x75371),f2(x75371)),f335(f335(f87(x75371),x75373),x75372))) % 186.01/186.04 [7538]~P127(x75381)+P1(f335(f335(f243(x75381),x75382),f2(x75381)))+P1(f335(f335(f243(x75381),f2(x75381)),x75382))+~P1(f335(f335(f243(x75381),f2(x75381)),f335(f335(f87(x75381),x75382),x75383))) % 186.01/186.04 [7539]~P68(x75391)+P1(f335(f335(f243(x75391),x75392),f2(x75391)))+P1(f335(f335(f243(x75391),f2(x75391)),x75392))+~P1(f335(f335(f243(x75391),f2(x75391)),f335(f335(f299(x75391),x75393),x75392))) % 186.01/186.04 [7540]~P68(x75401)+P1(f335(f335(f243(x75401),x75402),f2(x75401)))+P1(f335(f335(f243(x75401),f2(x75401)),x75402))+~P1(f335(f335(f243(x75401),f2(x75401)),f335(f335(f299(x75401),x75402),x75403))) % 186.01/186.04 [7541]~P68(x75411)+P1(f335(f335(f244(x75411),x75412),f2(x75411)))+P1(f335(f335(f244(x75411),f2(x75411)),x75413))+~P1(f335(f335(f244(x75411),f2(x75411)),f335(f335(f299(x75411),x75413),x75412))) % 186.01/186.04 [7542]~P68(x75421)+P1(f335(f335(f244(x75421),x75422),f2(x75421)))+P1(f335(f335(f244(x75421),f2(x75421)),x75423))+~P1(f335(f335(f244(x75421),f2(x75421)),f335(f335(f299(x75421),x75422),x75423))) % 186.01/186.04 [7543]~P68(x75431)+P1(f335(f335(f244(x75431),x75432),f2(x75431)))+P1(f335(f335(f244(x75431),f2(x75431)),x75432))+~P1(f335(f335(f244(x75431),f2(x75431)),f335(f335(f299(x75431),x75433),x75432))) % 186.01/186.04 [7544]~P68(x75441)+P1(f335(f335(f244(x75441),x75442),f2(x75441)))+P1(f335(f335(f244(x75441),f2(x75441)),x75442))+~P1(f335(f335(f244(x75441),f2(x75441)),f335(f335(f299(x75441),x75442),x75443))) % 186.01/186.04 [7630]~E(f335(f335(f108(f934(x76301,a922)),f335(f179(x76301),x76302)),f335(f179(x76301),x76303)),f195(f934(x76301,a922)))+~P1(f335(f144(x76301),x76303))+~P1(f335(f144(x76301),x76302))+P1(f335(f144(x76301),f335(f335(f141(x76301),x76302),x76303))) % 186.01/186.04 [7631]~P109(x76311)+~P1(f335(f67(x76311),x76313))+E(f11(x76311,f242(x76311),f335(f335(f317(x76311),x76312),x76313)),x76312)+~E(f335(f335(f23(f934(x76311,a922)),x76313),f335(f335(f317(x76311),x76312),f195(f934(x76311,a922)))),f195(f934(x76311,a922))) % 186.01/186.04 [7632]~P109(x76321)+~P1(f335(f67(x76321),x76323))+E(f12(x76321,f241(x76321),f335(f335(f317(x76321),x76322),x76323)),x76322)+~E(f335(f335(f23(f934(x76321,a922)),x76323),f335(f335(f317(x76321),x76322),f195(f934(x76321,a922)))),f195(f934(x76321,a922))) % 186.01/186.04 [7646]~P87(x76461)+~P1(f335(f335(f243(x76461),x76462),x76463))+~P1(f335(f335(f243(x76461),f335(f85(x76461),x76462)),x76463))+P1(f335(f335(f243(x76461),f335(f81(x76461),x76462)),x76463)) % 186.01/186.04 [7647]~P113(x76471)+~P1(f335(f335(f244(x76471),x76472),x76473))+~P1(f335(f335(f244(x76471),f335(f85(x76471),x76472)),x76473))+P1(f335(f335(f244(x76471),f335(f81(x76471),x76472)),x76473)) % 186.01/186.04 [7714]~P131(x77141)+P1(f335(f335(f244(x77141),f2(x77141)),x77142))+~P1(f335(f335(f244(x77141),f2(x77141)),x77143))+~P1(f335(f335(f244(x77141),f2(x77141)),f335(f335(f87(x77141),x77143),x77142))) % 186.01/186.04 [7715]~P131(x77151)+P1(f335(f335(f244(x77151),f2(x77151)),x77152))+~P1(f335(f335(f244(x77151),f2(x77151)),x77153))+~P1(f335(f335(f244(x77151),f2(x77151)),f335(f335(f87(x77151),x77152),x77153))) % 186.01/186.04 [8009]E(x80091,x80092)+~P1(f335(f67(x80093),x80091))+~P1(f335(f335(f243(a927),f335(f41(x80093),x80091)),f335(f41(x80093),x80092)))+~P1(f335(f335(f243(f934(x80093,a922)),x80092),x80091)) % 186.01/186.04 [8151]~P1(f335(f335(f244(a1),x81511),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x81512))+~P1(f335(f335(f243(a1),x81512),x81513))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x81511),x81512)),f335(f335(f42(a1),x81511),x81513))) % 186.01/186.04 [8161]~P1(f335(f335(f243(a1),f2(a1)),x81611))+~P1(f335(f335(f244(a1),f2(a1)),x81613))+~P1(f335(f335(f243(a1),x81613),x81612))+P1(f335(f335(f243(a1),f335(f335(f42(a1),x81611),x81612)),f335(f335(f42(a1),x81611),x81613))) % 186.01/186.04 [8296]E(f335(x82961,f559(x82962,x82961,x82963)),x82962)+~P1(f335(f335(f243(a1),x82962),f335(x82961,x82963)))+P1(f335(f335(f244(a927),f560(x82962,x82961,x82963)),x82963))+~P1(f335(f335(f243(a1),f335(x82961,f2(a927))),x82962)) % 186.01/186.04 [8297]E(f335(x82971,f564(x82972,x82971,x82973)),x82972)+~P1(f335(f335(f243(a1),x82972),f335(x82971,x82973)))+P1(f335(f335(f244(a927),f565(x82972,x82971,x82973)),x82973))+~P1(f335(f335(f243(a1),f335(x82971,f2(a927))),x82972)) % 186.01/186.04 [8394]~P1(f335(f67(x83941),x83943))+~P1(f335(f335(f244(a927),f335(f41(x83941),x83942)),f335(f41(x83941),x83943)))+~P1(f335(f335(f243(f934(x83941,a922)),x83942),x83943))+P1(f335(f335(f244(f934(x83941,a922)),x83942),x83943)) % 186.01/186.04 [8421]E(f335(f335(f86(a1),f508(x84213,x84211,x84212)),f509(x84213,x84211,x84212)),x84211)+E(f335(f335(f23(a1),x84211),x84212),x84211)+~P1(f335(f335(f244(a1),f2(a1)),x84212))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x84211),f84(a1))),x84213)) % 186.01/186.04 [8422]E(f335(f335(f23(a1),f512(x84223,x84221,x84222)),f513(x84223,x84221,x84222)),x84221)+E(f335(f335(f86(a1),x84221),x84222),x84221)+~P1(f335(f335(f244(a1),f2(a1)),x84222))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x84221),f84(a1))),x84223)) % 186.01/186.04 [8474]~P1(f335(f335(f243(a927),x84743),x84741))+P1(f335(f335(f243(a927),x84741),x84742))+~P1(f335(f335(f243(a927),x84743),x84742))+~P1(f335(f335(f243(a927),f335(f335(f23(a927),x84741),x84743)),f335(f335(f23(a927),x84742),x84743))) % 186.01/186.04 [8475]~P1(f335(f335(f243(a927),x84753),x84751))+P1(f335(f335(f244(a927),x84751),x84752))+~P1(f335(f335(f243(a927),x84753),x84752))+~P1(f335(f335(f244(a927),f335(f335(f23(a927),x84751),x84753)),f335(f335(f23(a927),x84752),x84753))) % 186.01/186.04 [8494]~P109(x84942)+E(x84941,f120(x84942))+~P14(x84942,f335(f175(x84942),x84941))+E(f335(f149(x84942,x84942,f335(f7(x84942,x84942,x84942),f242(x84942)),x84943),f335(f175(x84942),x84941)),f335(f335(f242(x84942),f335(f335(f171(x84942),x84941),f2(a927))),x84943)) % 186.01/186.04 [8563]E(f335(f335(f23(a1),x85631),x85632),x85631)+~P1(f335(f335(f244(a1),f2(a1)),x85632))+P1(f335(f335(f337(a1),f508(x85633,x85631,x85632)),x85633))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x85631),f84(a1))),x85633)) % 186.01/186.04 [8564]E(f335(f335(f86(a1),x85641),x85642),x85641)+~P1(f335(f335(f244(a1),f2(a1)),x85642))+P1(f335(f335(f337(a1),f512(x85643,x85641,x85642)),x85643))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x85641),f84(a1))),x85643)) % 186.01/186.04 [8636]~P1(f335(f335(f243(a1),x86361),f335(x86362,x86363)))+P1(f335(f335(f244(a927),f560(x86361,x86362,x86363)),x86363))+P1(f335(f335(f243(a927),f559(x86361,x86362,x86363)),x86363))+~P1(f335(f335(f243(a1),f335(x86362,f2(a927))),x86361)) % 186.01/186.04 [8637]~P1(f335(f335(f243(a1),x86371),f335(x86372,x86373)))+P1(f335(f335(f244(a927),f565(x86371,x86372,x86373)),x86373))+P1(f335(f335(f243(a927),f564(x86371,x86372,x86373)),x86373))+~P1(f335(f335(f243(a1),f335(x86372,f2(a927))),x86371)) % 186.01/186.04 [8709]E(f335(f335(f23(a1),x87091),x87092),x87091)+~P1(f335(f335(f244(a1),f2(a1)),x87092))+P1(f335(f335(f337(a1),f509(x87093,x87091,x87092)),f311(a1,f84(a1),x87092)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x87091),f84(a1))),x87093)) % 186.01/186.04 [8710]E(f335(f335(f86(a1),x87101),x87102),x87101)+~P1(f335(f335(f244(a1),f2(a1)),x87102))+P1(f335(f335(f337(a1),f513(x87103,x87101,x87102)),f311(a1,f84(a1),x87102)))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x87101),f84(a1))),x87103)) % 186.01/186.04 [8843]~P125(x88431)+~P1(f335(f335(f244(x88431),x88432),f84(x88431)))+~P1(f335(f335(f244(x88431),f2(x88431)),x88432))+P1(f335(f335(f244(x88431),f335(f335(f87(x88431),x88432),f335(f335(f252(x88431),x88432),x88433))),f335(f335(f252(x88431),x88432),x88433))) % 186.01/186.04 [8936]~P1(f335(x89361,x89362))+P1(f335(x89361,f2(a927)))+~P1(f335(f335(f244(a927),x89362),x89363))+~P1(f335(x89361,f51(a927,f335(a119,f609(x89362,x89361,x89363)),x89363))) % 186.01/186.04 [9088]E(f554(x90881,x90882,x90883),f2(a927))+P1(f335(f335(x90881,x90883),x90882))+P1(f335(f335(x90881,f554(x90881,x90882,x90883)),f51(a927,f552(x90881,x90882,x90883),f554(x90881,x90882,x90883))))+~P1(f335(f323(f933(a927,a927),a228),f335(f335(f260(a927,a927),x90883),x90882))) % 186.01/186.04 [9126]~P26(x91261,x91261,x91262,x91263)+E(f335(f318(x91261,x91261,x91262),x91263),x91263)+~P1(f335(f67(x91261),x91263))+~P1(f335(f335(f243(f934(x91261,a922)),f335(f318(x91261,x91261,x91262),x91263)),x91263)) % 186.01/186.04 [9344]P1(f335(f335(x93441,x93442),x93443))+P1(f335(f335(f244(a1),f798(x93441,x93443,x93442)),f800(x93441,x93443,x93442)))+P1(f335(f335(x93441,f798(x93441,x93443,x93442)),f335(f335(f86(a1),f800(x93441,x93443,x93442)),f84(a1))))+~P1(f335(f323(f933(a1,a1),a140),f335(f335(f260(a1,a1),x93442),x93443))) % 186.01/186.04 [9361]P1(f335(f335(x93611,x93612),x93613))+~P1(f335(f335(f244(a1),f476(x93611,x93613,x93612)),f2(a1)))+P1(f335(f335(x93611,f335(f85(a1),f475(x93611,x93613,x93612))),f335(f85(a1),f476(x93611,x93613,x93612))))+~P1(f335(f323(f933(a1,a1),a230),f335(f335(f260(a1,a1),x93612),x93613))) % 186.01/186.04 [9545]P1(f335(f335(x95451,x95452),x95453))+P1(f335(f335(x95451,f335(f335(f86(a1),f701(x95451,x95453,x95452)),f84(a1))),f703(x95451,x95453,x95452)))+~P1(f335(f335(f243(a1),f701(x95451,x95453,x95452)),f703(x95451,x95453,x95452)))+~P1(f335(f323(f933(a1,a1),a189),f335(f335(f260(a1,a1),x95452),x95453))) % 186.01/186.04 [9979]~P65(x99792)+~P65(x99791)+~P1(f335(f62(f933(x99791,x99792)),x99793))+P1(f335(f62(x99791),f335(f335(f8(f934(x99792,a922),a922,x99791),f62(x99792)),f335(f335(f8(f934(x99792,f933(x99791,x99792)),f934(x99792,a922),x99791),f335(f8(f933(x99791,x99792),a922,x99792),x99793)),f260(x99791,x99792))))) % 186.01/186.04 [9980]~P65(x99802)+~P65(x99801)+~P1(f335(f63(f933(x99801,x99802)),x99803))+P1(f335(f63(x99801),f335(f335(f8(f934(x99802,a922),a922,x99801),f63(x99802)),f335(f335(f8(f934(x99802,f933(x99801,x99802)),f934(x99802,a922),x99801),f335(f8(f933(x99801,x99802),a922,x99802),x99803)),f260(x99801,x99802))))) % 186.01/186.04 [10075]~P65(x100752)+~P65(x100751)+P1(f335(f62(f933(x100751,x100752)),x100753))+~P1(f335(f62(x100751),f335(f335(f8(f934(x100752,a922),a922,x100751),f62(x100752)),f335(f335(f8(f934(x100752,f933(x100751,x100752)),f934(x100752,a922),x100751),f335(f8(f933(x100751,x100752),a922,x100752),x100753)),f260(x100751,x100752))))) % 186.01/186.04 [10076]~P65(x100762)+~P65(x100761)+P1(f335(f63(f933(x100761,x100762)),x100763))+~P1(f335(f63(x100761),f335(f335(f8(f934(x100762,a922),a922,x100761),f63(x100762)),f335(f335(f8(f934(x100762,f933(x100761,x100762)),f934(x100762,a922),x100761),f335(f8(f933(x100761,x100762),a922,x100762),x100763)),f260(x100761,x100762))))) % 186.01/186.04 [10252]E(f335(x102521,f559(x102522,x102521,x102523)),x102522)+~P1(f335(f335(f243(a1),x102522),f335(x102521,x102523)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x102521,f335(f335(f86(a927),f560(x102522,x102521,x102523)),f84(a927)))),f335(x102521,f560(x102522,x102521,x102523))))),f84(a1)))+~P1(f335(f335(f243(a1),f335(x102521,f2(a927))),x102522)) % 186.01/186.04 [10253]E(f335(x102531,f564(x102532,x102531,x102533)),x102532)+~P1(f335(f335(f243(a1),x102532),f335(x102531,x102533)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x102531,f335(f335(f86(a927),f565(x102532,x102531,x102533)),f84(a927)))),f335(x102531,f565(x102532,x102531,x102533))))),f84(a1)))+~P1(f335(f335(f243(a1),f335(x102531,f2(a927))),x102532)) % 186.01/186.04 [10256]~P1(f335(f335(f243(a1),x102561),f335(x102562,x102563)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x102562,f335(f335(f86(a927),f560(x102561,x102562,x102563)),f84(a927)))),f335(x102562,f560(x102561,x102562,x102563))))),f84(a1)))+P1(f335(f335(f243(a927),f559(x102561,x102562,x102563)),x102563))+~P1(f335(f335(f243(a1),f335(x102562,f2(a927))),x102561)) % 186.01/186.04 [10257]~P1(f335(f335(f243(a1),x102571),f335(x102572,x102573)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x102572,f335(f335(f86(a927),f565(x102571,x102572,x102573)),f84(a927)))),f335(x102572,f565(x102571,x102572,x102573))))),f84(a1)))+P1(f335(f335(f243(a927),f564(x102571,x102572,x102573)),x102573))+~P1(f335(f335(f243(a1),f335(x102572,f2(a927))),x102571)) % 186.01/186.04 [10316]E(x103161,x103162)+~E(f335(f149(f928(x103163),f928(x103163),f141(x103163),f120(x103163)),x103161),f335(f149(f928(x103163),f928(x103163),f141(x103163),f120(x103163)),x103162))+~E(f335(f196(f928(f928(x103163))),x103161),f335(f196(f928(f928(x103163))),x103162))+~P1(f335(f335(f265(f928(x103163),f928(x103163),a922),f335(f335(f7(f928(x103163),f934(f928(x103163),a927),f934(f928(x103163),a922)),f335(f335(f8(f934(a927,a922),f934(f934(f928(x103163),a927),f934(f928(x103163),a922)),f928(x103163)),f8(a927,a922,f928(x103163))),f335(f335(f8(a927,f934(a927,a922),f928(x103163)),a332),f196(f928(x103163))))),f196(f928(x103163)))),f726(x103161,x103162,x103163))) % 186.01/186.04 [10317]E(x103171,x103172)+~E(f335(f149(f928(x103173),f928(x103173),f141(x103173),f120(x103173)),x103171),f335(f149(f928(x103173),f928(x103173),f141(x103173),f120(x103173)),x103172))+~E(f335(f196(f928(f928(x103173))),x103171),f335(f196(f928(f928(x103173))),x103172))+~P1(f335(f335(f265(f928(x103173),f928(x103173),a922),f335(f335(f7(f928(x103173),f934(f928(x103173),a927),f934(f928(x103173),a922)),f335(f335(f8(f934(a927,a922),f934(f934(f928(x103173),a927),f934(f928(x103173),a922)),f928(x103173)),f8(a927,a922,f928(x103173))),f335(f335(f8(a927,f934(a927,a922),f928(x103173)),a332),f196(f928(x103173))))),f196(f928(x103173)))),f727(x103172,x103171,x103173))) % 186.01/186.04 [7047]~E(f84(a927),f2(a927))+~P1(f335(f67(x70471),x70473))+~P1(f335(f67(x70471),x70472))+E(f335(f335(f86(a927),f335(f41(x70471),x70472)),f335(f41(x70471),x70473)),f335(f41(x70471),f335(f335(f117(f934(x70471,a922)),x70472),x70473))) % 186.01/186.04 [7454]~P97(x74541)+~P1(f335(f67(x74541),x74542))+~P1(f335(f335(f337(x74541),x74543),x74542))+P1(f335(f335(f243(x74541),f335(f69(x74541,f108(x74541)),x74542)),x74543)) % 186.01/186.04 [7455]~P109(x74551)+~P1(f335(f67(x74551),x74552))+~P1(f335(f335(f337(x74551),x74553),x74552))+P1(f335(f335(f243(x74551),f335(f69(x74551,f241(x74551)),x74552)),x74553)) % 186.01/186.04 [7708]~P1(f335(f67(x77081),x77083))+~P1(f335(f67(x77081),x77082))+~E(f335(f335(f108(f934(x77081,a922)),x77082),x77083),f195(f934(x77081,a922)))+E(f335(f335(f86(a927),f335(f41(x77081),x77082)),f335(f41(x77081),x77083)),f335(f41(x77081),f335(f335(f117(f934(x77081,a922)),x77082),x77083))) % 186.01/186.04 [8480]~P38(x84801,x84803)+~P38(x84801,x84802)+~E(f335(f335(f108(f934(x84801,a922)),f335(f272(x84801,x84801),x84802)),f335(f292(x84801,x84801),x84803)),f195(f934(x84801,a922)))+P38(x84801,f335(f335(f117(f934(f933(x84801,x84801),a922)),x84802),x84803)) % 186.01/186.04 [8575]E(x85751,f335(f335(f42(a927),x85752),x85753))+~P1(f335(f335(f244(a927),f2(a927)),x85753))+~P1(f335(f335(f244(a927),x85752),f335(f335(f87(a927),x85753),f335(a119,x85751))))+~P1(f335(f335(f243(a927),f335(f335(f87(a927),x85753),x85751)),x85752)) % 186.01/186.04 [8707]~P1(f335(f67(x87071),x87072))+~P1(f335(f67(x87071),x87073))+E(f335(f335(f86(a927),f335(f41(x87071),x87072)),f335(f41(x87071),x87073)),f335(f41(x87071),f335(f335(f117(f934(x87071,a922)),x87072),x87073)))+P1(f335(f335(f337(x87071),f398(x87073,x87072,x87071)),f335(f335(f108(f934(x87071,a922)),x87072),x87073))) % 186.01/186.04 [9100]~P127(x91002)+~E(x91001,f2(x91002))+~E(x91003,f2(x91002))+~P1(f335(f335(f244(x91002),f2(x91002)),f335(f335(f86(x91002),f335(f335(f87(x91002),x91003),x91003)),f335(f335(f87(x91002),x91001),x91001)))) % 186.01/186.04 [9624]~P38(x96241,x96243)+~P38(x96241,x96242)+P38(x96241,f335(f335(f117(f934(f933(x96241,x96241),a922)),x96242),x96243))+~P1(f335(f335(f243(f934(f933(x96241,x96241),a922)),f335(f335(f297(x96241,x96241,x96241),x96242),x96243)),x96242)) % 186.01/186.04 [9752]~P1(f335(x97521,x97523))+~P1(f335(f67(x97522),x97523))+P1(f335(x97521,f195(f934(x97522,a922))))+~P1(f335(x97521,f335(f335(f23(f934(x97522,a922)),f351(x97521,x97523,x97522)),f335(f335(f317(x97522),f352(x97521,x97523,x97522)),f195(f934(x97522,a922)))))) % 186.01/186.04 [8883]~P1(f335(f335(f244(a1),f2(a1)),x88833))+P1(f335(f335(f243(a1),f2(a1)),x88831))+~P1(f335(f335(f244(a1),x88832),x88833))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),f335(f335(f87(a1),x88833),x88831)),x88832))) % 186.01/186.04 [8907]~P98(x89071)+~P1(f335(f67(x89071),x89072))+E(f335(f335(f23(f934(x89071,a922)),x89072),f335(f335(f317(x89071),x89073),f195(f934(x89071,a922)))),f195(f934(x89071,a922)))+E(f335(f335(f117(x89071),x89073),f13(x89071,f335(f335(f23(f934(x89071,a922)),x89072),f335(f335(f317(x89071),x89073),f195(f934(x89071,a922)))))),f13(x89071,f335(f335(f317(x89071),x89073),x89072))) % 186.01/186.04 [8908]~P98(x89081)+~P1(f335(f67(x89081),x89082))+E(f335(f335(f23(f934(x89081,a922)),x89082),f335(f335(f317(x89081),x89083),f195(f934(x89081,a922)))),f195(f934(x89081,a922)))+E(f335(f335(f108(x89081),x89083),f10(x89081,f335(f335(f23(f934(x89081,a922)),x89082),f335(f335(f317(x89081),x89083),f195(f934(x89081,a922)))))),f10(x89081,f335(f335(f317(x89081),x89083),x89082))) % 186.01/186.04 [8909]~P109(x89091)+~P1(f335(f67(x89091),x89092))+E(f335(f335(f23(f934(x89091,a922)),x89092),f335(f335(f317(x89091),x89093),f195(f934(x89091,a922)))),f195(f934(x89091,a922)))+E(f335(f335(f242(x89091),x89093),f14(x89091,f335(f335(f23(f934(x89091,a922)),x89092),f335(f335(f317(x89091),x89093),f195(f934(x89091,a922)))))),f14(x89091,f335(f335(f317(x89091),x89093),x89092))) % 186.01/186.04 [8910]~P109(x89101)+~P1(f335(f67(x89101),x89102))+E(f335(f335(f23(f934(x89101,a922)),x89102),f335(f335(f317(x89101),x89103),f195(f934(x89101,a922)))),f195(f934(x89101,a922)))+E(f335(f335(f241(x89101),x89103),f15(x89101,f335(f335(f23(f934(x89101,a922)),x89102),f335(f335(f317(x89101),x89103),f195(f934(x89101,a922)))))),f15(x89101,f335(f335(f317(x89101),x89103),x89102))) % 186.01/186.04 [8982]~P109(x89821)+~P1(f335(f67(x89821),x89822))+E(f335(f335(f23(f934(x89821,a922)),x89822),f335(f335(f317(x89821),x89823),f195(f934(x89821,a922)))),f195(f934(x89821,a922)))+E(f335(f335(f242(x89821),x89823),f11(x89821,f242(x89821),f335(f335(f23(f934(x89821,a922)),x89822),f335(f335(f317(x89821),x89823),f195(f934(x89821,a922)))))),f11(x89821,f242(x89821),f335(f335(f317(x89821),x89823),x89822))) % 186.01/186.04 [8983]~P109(x89831)+~P1(f335(f67(x89831),x89832))+E(f335(f335(f23(f934(x89831,a922)),x89832),f335(f335(f317(x89831),x89833),f195(f934(x89831,a922)))),f195(f934(x89831,a922)))+E(f335(f335(f241(x89831),x89833),f12(x89831,f241(x89831),f335(f335(f23(f934(x89831,a922)),x89832),f335(f335(f317(x89831),x89833),f195(f934(x89831,a922)))))),f12(x89831,f241(x89831),f335(f335(f317(x89831),x89833),x89832))) % 186.01/186.04 [9564]E(x95641,x95642)+~E(f335(f149(f928(x95643),f928(x95643),f141(x95643),f120(x95643)),x95641),f335(f149(f928(x95643),f928(x95643),f141(x95643),f120(x95643)),x95642))+~E(f335(f196(f928(f928(x95643))),x95641),f335(f196(f928(f928(x95643))),x95642))+P1(f335(f335(f337(f933(f928(x95643),f928(x95643))),f726(x95641,x95642,x95643)),f335(f179(f933(f928(x95643),f928(x95643))),f335(f335(f188(f928(x95643),f928(x95643)),x95642),x95641)))) % 186.01/186.04 [9565]E(x95651,x95652)+~E(f335(f149(f928(x95653),f928(x95653),f141(x95653),f120(x95653)),x95651),f335(f149(f928(x95653),f928(x95653),f141(x95653),f120(x95653)),x95652))+~E(f335(f196(f928(f928(x95653))),x95651),f335(f196(f928(f928(x95653))),x95652))+P1(f335(f335(f337(f933(f928(x95653),f928(x95653))),f727(x95652,x95651,x95653)),f335(f179(f933(f928(x95653),f928(x95653))),f335(f335(f188(f928(x95653),f928(x95653)),x95651),x95652)))) % 186.01/186.04 [10426]~P102(x104262)+E(x104261,f195(f934(x104262,a922)))+~P1(f335(f67(x104262),x104261))+E(f13(x104262,f335(f270(x104262),f335(f335(f8(f934(x104262,a922),a922,x104262),f93(x104262)),f335(f335(f7(x104262,f934(x104262,a922),f934(x104262,a922)),f335(f335(f8(f934(x104262,f934(a922,a922)),f934(f934(x104262,a922),f934(x104262,a922)),x104262),f18(x104262,a922,a922)),f335(f335(f8(f934(x104262,a922),f934(x104262,f934(a922,a922)),x104262),f335(f8(a922,f934(a922,a922),x104262),a333)),f335(f335(f7(x104262,f934(x104262,x104262),f934(x104262,a922)),f335(f335(f8(f934(x104262,a922),f934(f934(x104262,x104262),f934(x104262,a922)),x104262),f8(x104262,a922,x104262)),a332)),f335(f108(x104262),x104263))))),f335(f335(f7(x104262,f934(x104262,a922),a922),f337(x104262)),x104261))))),f335(f335(f108(x104262),x104263),f13(x104262,x104261))) % 186.01/186.04 [10427]~P102(x104272)+E(x104271,f195(f934(x104272,a922)))+~P1(f335(f67(x104272),x104271))+E(f10(x104272,f335(f270(x104272),f335(f335(f8(f934(x104272,a922),a922,x104272),f93(x104272)),f335(f335(f7(x104272,f934(x104272,a922),f934(x104272,a922)),f335(f335(f8(f934(x104272,f934(a922,a922)),f934(f934(x104272,a922),f934(x104272,a922)),x104272),f18(x104272,a922,a922)),f335(f335(f8(f934(x104272,a922),f934(x104272,f934(a922,a922)),x104272),f335(f8(a922,f934(a922,a922),x104272),a333)),f335(f335(f7(x104272,f934(x104272,x104272),f934(x104272,a922)),f335(f335(f8(f934(x104272,a922),f934(f934(x104272,x104272),f934(x104272,a922)),x104272),f8(x104272,a922,x104272)),a332)),f335(f117(x104272),x104273))))),f335(f335(f7(x104272,f934(x104272,a922),a922),f337(x104272)),x104271))))),f335(f335(f117(x104272),x104273),f10(x104272,x104271))) % 186.01/186.04 [10428]~P77(x104282)+E(x104281,f195(f934(x104282,a922)))+~P1(f335(f67(x104282),x104281))+E(f14(x104282,f335(f270(x104282),f335(f335(f8(f934(x104282,a922),a922,x104282),f93(x104282)),f335(f335(f7(x104282,f934(x104282,a922),f934(x104282,a922)),f335(f335(f8(f934(x104282,f934(a922,a922)),f934(f934(x104282,a922),f934(x104282,a922)),x104282),f18(x104282,a922,a922)),f335(f335(f8(f934(x104282,a922),f934(x104282,f934(a922,a922)),x104282),f335(f8(a922,f934(a922,a922),x104282),a333)),f335(f335(f7(x104282,f934(x104282,x104282),f934(x104282,a922)),f335(f335(f8(f934(x104282,a922),f934(f934(x104282,x104282),f934(x104282,a922)),x104282),f8(x104282,a922,x104282)),a332)),f335(f86(x104282),x104283))))),f335(f335(f7(x104282,f934(x104282,a922),a922),f337(x104282)),x104281))))),f335(f335(f86(x104282),x104283),f14(x104282,x104281))) % 186.01/186.04 [10429]~P77(x104292)+E(x104291,f195(f934(x104292,a922)))+~P1(f335(f67(x104292),x104291))+E(f15(x104292,f335(f270(x104292),f335(f335(f8(f934(x104292,a922),a922,x104292),f93(x104292)),f335(f335(f7(x104292,f934(x104292,a922),f934(x104292,a922)),f335(f335(f8(f934(x104292,f934(a922,a922)),f934(f934(x104292,a922),f934(x104292,a922)),x104292),f18(x104292,a922,a922)),f335(f335(f8(f934(x104292,a922),f934(x104292,f934(a922,a922)),x104292),f335(f8(a922,f934(a922,a922),x104292),a333)),f335(f335(f7(x104292,f934(x104292,x104292),f934(x104292,a922)),f335(f335(f8(f934(x104292,a922),f934(f934(x104292,x104292),f934(x104292,a922)),x104292),f8(x104292,a922,x104292)),a332)),f335(f86(x104292),x104293))))),f335(f335(f7(x104292,f934(x104292,a922),a922),f337(x104292)),x104291))))),f335(f335(f86(x104292),x104293),f15(x104292,x104291))) % 186.01/186.04 [10430]~P109(x104302)+E(x104301,f195(f934(x104302,a922)))+~P1(f335(f67(x104302),x104301))+E(f11(x104302,f242(x104302),f335(f270(x104302),f335(f335(f8(f934(x104302,a922),a922,x104302),f93(x104302)),f335(f335(f7(x104302,f934(x104302,a922),f934(x104302,a922)),f335(f335(f8(f934(x104302,f934(a922,a922)),f934(f934(x104302,a922),f934(x104302,a922)),x104302),f18(x104302,a922,a922)),f335(f335(f8(f934(x104302,a922),f934(x104302,f934(a922,a922)),x104302),f335(f8(a922,f934(a922,a922),x104302),a333)),f335(f335(f7(x104302,f934(x104302,x104302),f934(x104302,a922)),f335(f335(f8(f934(x104302,a922),f934(f934(x104302,x104302),f934(x104302,a922)),x104302),f8(x104302,a922,x104302)),a332)),f335(f241(x104302),x104303))))),f335(f335(f7(x104302,f934(x104302,a922),a922),f337(x104302)),x104301))))),f335(f335(f241(x104302),x104303),f11(x104302,f242(x104302),x104301))) % 186.01/186.04 [10431]~P109(x104312)+E(x104311,f195(f934(x104312,a922)))+~P1(f335(f67(x104312),x104311))+E(f12(x104312,f241(x104312),f335(f270(x104312),f335(f335(f8(f934(x104312,a922),a922,x104312),f93(x104312)),f335(f335(f7(x104312,f934(x104312,a922),f934(x104312,a922)),f335(f335(f8(f934(x104312,f934(a922,a922)),f934(f934(x104312,a922),f934(x104312,a922)),x104312),f18(x104312,a922,a922)),f335(f335(f8(f934(x104312,a922),f934(x104312,f934(a922,a922)),x104312),f335(f8(a922,f934(a922,a922),x104312),a333)),f335(f335(f7(x104312,f934(x104312,x104312),f934(x104312,a922)),f335(f335(f8(f934(x104312,a922),f934(f934(x104312,x104312),f934(x104312,a922)),x104312),f8(x104312,a922,x104312)),a332)),f335(f242(x104312),x104313))))),f335(f335(f7(x104312,f934(x104312,a922),a922),f337(x104312)),x104311))))),f335(f335(f242(x104312),x104313),f12(x104312,f241(x104312),x104311))) % 186.01/186.04 [10140]~P113(x101401)+~E(x101403,f2(x101401))+~E(x101402,f2(x101401))+E(f335(f335(f86(x101401),f335(f335(f252(x101401),x101402),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x101401),x101403),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f2(x101401)) % 186.01/186.04 [10297]~P125(x102971)+~P1(f335(f335(f243(x102971),f2(x102971)),x102973))+P1(f335(f335(f243(x102971),x102972),x102973))+~P1(f335(f335(f243(x102971),f335(f335(f252(x102971),x102972),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x102971),x102973),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))))) % 186.01/186.04 [10354]~P113(x103542)+~E(x103541,f2(x103542))+~E(x103543,f2(x103542))+~P1(f335(f335(f244(x103542),f2(x103542)),f335(f335(f86(x103542),f335(f335(f252(x103542),x103543),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))),f335(f335(f252(x103542),x103541),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))))) % 186.01/186.04 [6930]~P8(x69303,x69302)+~P1(f335(x69301,x69304))+~P1(f335(f335(f337(x69303),x69304),f278(x69303,x69302)))+P1(f335(x69301,f846(x69301,x69302,x69303))) % 186.01/186.04 [8818]P27(x88181,x88182,f358(x88183,x88182,x88184,x88181),x88184,x88183)+~E(f335(f41(x88181),x88184),f335(f41(x88182),x88183))+~P1(f335(f67(x88182),x88183))+~P1(f335(f67(x88181),x88184)) % 186.01/186.04 [9527]E(x95271,x95272)+~E(f672(x95271,x95272,x95274,x95273),f674(x95271,x95272,x95274,x95273))+P1(f335(f335(f337(f933(f928(x95273),f928(x95273))),f335(f335(f260(f928(x95273),f928(x95273)),x95272),x95271)),f154(x95273,x95274)))+P1(f335(f335(f337(f933(f928(x95273),f928(x95273))),f335(f335(f260(f928(x95273),f928(x95273)),x95271),x95272)),f154(x95273,x95274))) % 186.01/186.04 [5090]~P66(x50902)+~E(x50904,f2(x50902))+~E(x50901,f2(x50902))+E(x50901,f335(f335(f299(x50902),x50903),x50904)) % 186.01/186.04 [5091]~P66(x50911)+~E(x50913,f2(x50911))+~E(x50914,f2(x50911))+E(f335(f335(f299(x50911),x50912),x50913),x50914) % 186.01/186.04 [5207]~P66(x52072)+E(x52071,f2(x52072))+~E(x52073,f2(x52072))+~E(x52071,f335(f335(f299(x52072),x52074),x52073)) % 186.01/186.04 [5208]~P66(x52082)+E(x52081,f2(x52082))+~E(x52083,f2(x52082))+~E(f335(f335(f299(x52082),x52084),x52083),x52081) % 186.01/186.04 [5390]~P121(x53902)+E(x53901,f2(x53902))+~E(f335(f335(f299(x53902),x53903),x53901),x53904)+E(x53903,f335(f335(f87(x53902),x53904),x53901)) % 186.01/186.04 [5392]~P121(x53922)+E(x53921,f2(x53922))+~E(f335(f335(f87(x53922),x53923),x53921),x53924)+E(x53923,f335(f335(f299(x53922),x53924),x53921)) % 186.01/186.04 [5393]~P66(x53932)+E(x53931,f2(x53932))+~E(f335(f335(f299(x53932),x53933),x53931),x53934)+E(x53933,f335(f335(f87(x53932),x53934),x53931)) % 186.01/186.04 [5394]~P66(x53942)+E(x53941,f2(x53942))+~E(f335(f335(f87(x53942),x53943),x53941),x53944)+E(x53943,f335(f335(f299(x53942),x53944),x53941)) % 186.01/186.04 [5395]~P121(x53952)+E(x53951,f2(x53952))+~E(x53953,f335(f335(f299(x53952),x53954),x53951))+E(f335(f335(f87(x53952),x53953),x53951),x53954) % 186.01/186.04 [5397]~P121(x53972)+E(x53971,f2(x53972))+~E(x53973,f335(f335(f87(x53972),x53974),x53971))+E(f335(f335(f299(x53972),x53973),x53971),x53974) % 186.01/186.04 [5398]~P66(x53982)+E(x53981,f2(x53982))+~E(x53983,f335(f335(f299(x53982),x53984),x53981))+E(f335(f335(f87(x53982),x53983),x53981),x53984) % 186.01/186.04 [5399]~P66(x53992)+E(x53991,f2(x53992))+~E(x53993,f335(f335(f87(x53992),x53994),x53991))+E(f335(f335(f299(x53992),x53993),x53991),x53994) % 186.01/186.04 [5423]~P66(x54232)+~E(x54231,f2(x54232))+~E(f335(f335(f87(x54232),x54231),x54234),x54233)+E(x54231,f335(f335(f299(x54232),x54233),x54234)) % 186.01/186.04 [5424]~P66(x54241)+~E(x54244,f2(x54241))+~E(x54242,f335(f335(f87(x54241),x54244),x54243))+E(f335(f335(f299(x54241),x54242),x54243),x54244) % 186.01/186.04 [5498]~E(x54983,x54984)+~E(x54982,x54983)+~P110(x54981)+E(f311(x54981,x54982,x54983),f335(f335(f317(x54981),x54984),f195(f934(x54981,a922)))) % 186.01/186.04 [5703]~E(f121(x57032,x57031),x57033)+~E(f151(x57032,x57031),x57034)+E(x57031,f120(x57032))+E(f335(f335(f141(x57032),x57033),f335(f335(f158(x57032),x57034),f120(x57032))),x57031) % 186.01/186.04 [6327]~P125(x63273)+E(x63271,x63272)+~E(f335(f335(f252(x63273),x63274),x63271),f335(f335(f252(x63273),x63274),x63272))+~P1(f335(f335(f244(x63273),f84(x63273)),x63274)) % 186.01/186.04 [6328]E(x63281,x63282)+~E(f335(f335(f317(x63283),x63284),x63281),f335(f335(f317(x63283),x63284),x63282))+P1(f335(f335(f337(x63283),x63284),x63282))+P1(f335(f335(f337(x63283),x63284),x63281)) % 186.01/186.04 [6370]E(f335(x63701,x63702),f84(a927))+~E(f335(f335(f9(x63703,a927),x63701),x63704),f84(a927))+~P1(f335(f67(x63703),x63704))+~P1(f335(f335(f337(x63703),x63702),x63704)) % 186.01/186.04 [6371]E(f335(x63711,x63712),f2(a927))+~E(f335(f335(f6(x63713,a927),x63711),x63714),f2(a927))+~P1(f335(f67(x63713),x63714))+~P1(f335(f335(f337(x63713),x63712),x63714)) % 186.01/186.04 [6587]~P110(x65871)+~P1(f335(f335(f243(x65871),x65874),x65873))+P1(f335(f335(f243(x65871),x65872),x65873))+~P1(f335(f335(f243(x65871),x65872),x65874)) % 186.01/186.04 [6588]~P107(x65881)+~P1(f335(f335(f243(x65881),x65882),x65884))+P1(f335(f335(f243(x65881),x65882),x65883))+~P1(f335(f335(f243(x65881),x65884),x65883)) % 186.01/186.04 [6589]~P110(x65891)+~P1(f335(f335(f244(x65891),x65894),x65893))+P1(f335(f335(f244(x65891),x65892),x65893))+~P1(f335(f335(f243(x65891),x65892),x65894)) % 186.01/186.04 [6590]~P110(x65901)+~P1(f335(f335(f244(x65901),x65902),x65904))+P1(f335(f335(f244(x65901),x65902),x65903))+~P1(f335(f335(f243(x65901),x65904),x65903)) % 186.01/186.04 [6591]~P110(x65911)+~P1(f335(f335(f244(x65911),x65914),x65913))+P1(f335(f335(f244(x65911),x65912),x65913))+~P1(f335(f335(f244(x65911),x65912),x65914)) % 186.01/186.04 [6592]~P107(x65921)+~P1(f335(f335(f244(x65921),x65922),x65924))+P1(f335(f335(f244(x65921),x65922),x65923))+~P1(f335(f335(f243(x65921),x65924),x65923)) % 186.01/186.04 [6593]~P107(x65931)+~P1(f335(f335(f244(x65931),x65934),x65933))+P1(f335(f335(f244(x65931),x65932),x65933))+~P1(f335(f335(f243(x65931),x65932),x65934)) % 186.01/186.04 [6594]~P107(x65941)+~P1(f335(f335(f244(x65941),x65942),x65944))+P1(f335(f335(f244(x65941),x65942),x65943))+~P1(f335(f335(f244(x65941),x65944),x65943)) % 186.01/186.04 [6675]~P36(x66754,x66753,x66752)+E(x66751,f780(x66752,x66753,x66754))+~P1(f335(x66753,x66751))+~P1(f335(f335(f337(x66754),x66751),f335(f179(x66754),x66752))) % 186.01/186.04 [6676]~P36(x66764,x66763,x66762)+E(x66761,f793(x66762,x66763,x66764))+~P1(f335(x66763,x66761))+~P1(f335(f335(f337(x66764),x66761),f335(f179(x66764),x66762))) % 186.01/186.04 [6823]~P6(x68231)+~P1(f335(f335(f243(x68231),x68232),f44(x68231,x68234)))+P1(f335(f335(f243(x68231),x68232),x68233))+~P1(f335(f335(f337(x68231),x68233),x68234)) % 186.01/186.04 [6970]~P109(x69701)+~P14(x69701,f335(f335(f158(x69701),x69702),x69704))+~P1(f335(f335(f337(x69701),x69703),f335(f179(x69701),x69704)))+P1(f335(f335(f243(x69701),x69702),x69703)) % 186.01/186.04 [7057]~P6(x70571)+~P1(f335(f335(f243(x70571),f43(x70571,x70574)),x70573))+P1(f335(f335(f243(x70571),x70572),x70573))+~P1(f335(f335(f337(x70571),x70572),x70574)) % 186.01/186.04 [7194]~P63(x71941)+P1(f335(f335(f295(x71941),x71942),f51(x71941,x71943,x71944)))+~P1(f335(f335(f295(x71941),x71942),x71944))+~P1(f335(f335(f295(x71941),x71942),x71943)) % 186.01/186.04 [7457]~P109(x74571)+E(f335(f335(f117(f934(x74571,a922)),f335(f310(x74571,x74572),x74573)),f335(f310(x74571,x74573),x74574)),f335(f310(x74571,x74572),x74574))+~P1(f335(f335(f243(x74571),x74573),x74574))+~P1(f335(f335(f243(x74571),x74572),x74573)) % 186.01/186.04 [7504]P36(x75041,x75042,x75043)+~E(f795(x75043,x75042,x75041,x75044),x75044)+~P1(f335(x75042,x75044))+~P1(f335(f335(f337(x75041),x75044),f335(f179(x75041),x75043))) % 186.01/186.04 [7505]P36(x75051,x75052,x75053)+~E(f803(x75053,x75052,x75051,x75054),x75054)+~P1(f335(x75052,x75054))+~P1(f335(f335(f337(x75051),x75054),f335(f179(x75051),x75053))) % 186.01/186.04 [7547]~P63(x75471)+~P1(f335(f335(f295(x75471),x75472),f51(x75471,x75473,x75474)))+P1(f335(f335(f295(x75471),x75472),x75473))+~P1(f335(f335(f295(x75471),x75472),x75474)) % 186.01/186.04 [7581]~P109(x75811)+E(f335(f335(f117(f934(x75811,a922)),f335(f310(x75811,x75812),x75813)),f311(x75811,x75813,x75814)),f311(x75811,x75812,x75814))+~P1(f335(f335(f243(x75811),x75813),x75814))+~P1(f335(f335(f243(x75811),x75812),x75813)) % 186.01/186.04 [7641]~P109(x76411)+E(f335(f335(f117(f934(x76411,a922)),f314(x76411,x76412,x76413)),f335(f310(x76411,x76413),x76414)),f314(x76411,x76412,x76414))+~P1(f335(f335(f243(x76411),x76413),x76414))+~P1(f335(f335(f244(x76411),x76412),x76413)) % 186.01/186.04 [7658]~P109(x76581)+E(f335(f335(f117(f934(x76581,a922)),f311(x76581,x76582,x76583)),f314(x76581,x76583,x76584)),f335(f310(x76581,x76582),x76584))+~P1(f335(f335(f243(x76581),x76582),x76583))+~P1(f335(f335(f244(x76581),x76583),x76584)) % 186.01/186.04 [7689]~P109(x76891)+E(f335(f335(f117(f934(x76891,a922)),f314(x76891,x76892,x76893)),f311(x76891,x76893,x76894)),f313(x76891,x76892,x76894))+~P1(f335(f335(f243(x76891),x76893),x76894))+~P1(f335(f335(f244(x76891),x76892),x76893)) % 186.01/186.04 [7690]~P109(x76901)+E(f335(f335(f117(f934(x76901,a922)),f313(x76901,x76902,x76903)),f314(x76901,x76903,x76904)),f314(x76901,x76902,x76904))+~P1(f335(f335(f243(x76901),x76902),x76903))+~P1(f335(f335(f244(x76901),x76903),x76904)) % 186.01/186.04 [7691]~P109(x76911)+E(f335(f335(f117(f934(x76911,a922)),f313(x76911,x76912,x76913)),f313(x76911,x76913,x76914)),f313(x76911,x76912,x76914))+~P1(f335(f335(f243(x76911),x76913),x76914))+~P1(f335(f335(f243(x76911),x76912),x76913)) % 186.01/186.04 [7692]~P109(x76921)+E(f335(f335(f117(f934(x76921,a922)),f311(x76921,x76922,x76923)),f313(x76921,x76923,x76924)),f311(x76921,x76922,x76924))+~P1(f335(f335(f243(x76921),x76923),x76924))+~P1(f335(f335(f243(x76921),x76922),x76923)) % 186.01/186.04 [8464]P26(x84641,x84642,f365(x84643,x84642,x84644,x84641),x84644)+~P1(f335(f67(x84642),x84643))+~P1(f335(f67(x84641),x84644))+~P1(f335(f335(f243(a927),f335(f41(x84641),x84644)),f335(f41(x84642),x84643))) % 186.01/186.04 [8485]P36(x84851,x84852,x84853)+~P1(f335(x84852,x84854))+P1(f335(x84852,f795(x84853,x84852,x84851,x84854)))+~P1(f335(f335(f337(x84851),x84854),f335(f179(x84851),x84853))) % 186.01/186.04 [8486]P36(x84861,x84862,x84863)+~P1(f335(x84862,x84864))+P1(f335(x84862,f803(x84863,x84862,x84861,x84864)))+~P1(f335(f335(f337(x84861),x84864),f335(f179(x84861),x84863))) % 186.01/186.04 [8541]~P72(x85411)+~E(f335(x85413,f607(x85413,x85414,x85412,x85411)),f84(x85411))+E(f335(f335(f335(f71(x85411,x85412,f87(x85411)),x85413),f84(x85411)),x85414),f84(x85411))+~P1(f335(f67(x85412),x85414)) % 186.01/186.04 [8807]~P125(x88071)+~P1(f335(f335(f243(x88071),f2(x88071)),x88073))+P1(f335(f335(f243(x88071),x88072),x88073))+~P1(f335(f335(f243(x88071),f335(f335(f252(x88071),x88072),f335(a119,x88074))),f335(f335(f252(x88071),x88073),f335(a119,x88074)))) % 186.01/186.04 [9127]P36(x91271,x91272,x91273)+~P1(f335(x91272,x91274))+~P1(f335(f335(f337(x91271),x91274),f335(f179(x91271),x91273)))+P1(f335(f335(f337(x91271),f795(x91273,x91272,x91271,x91274)),f335(f179(x91271),x91273))) % 186.01/186.04 [9128]P36(x91281,x91282,x91283)+~P1(f335(x91282,x91284))+~P1(f335(f335(f337(x91281),x91284),f335(f179(x91281),x91283)))+P1(f335(f335(f337(x91281),f803(x91283,x91282,x91281,x91284)),f335(f179(x91281),x91283))) % 186.01/186.04 [9206]~P72(x92061)+E(f335(f335(f335(f71(x92061,x92062,f87(x92061)),x92063),f84(x92061)),x92064),f84(x92061))+~P1(f335(f67(x92062),x92064))+P1(f335(f335(f337(x92062),f607(x92063,x92064,x92062,x92061)),x92064)) % 186.01/186.04 [9695]~P1(f335(f335(f243(a1),x96954),f2(a1)))+P1(f335(f335(f243(a1),f335(f335(f86(a1),f335(f335(f87(a1),x96951),f51(a1,x96952,x96953))),x96954)),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x96953))+~P1(f335(f335(f244(a1),x96951),x96954)) % 186.01/186.04 [10133]~P1(f335(f67(x101331),x101332))+~P1(f335(f335(f337(x101331),x101334),x101332))+~P1(f335(f335(f337(x101331),x101333),x101332))+P1(f335(f335(f244(a927),f335(f41(x101331),f335(f335(f23(f934(x101331,a922)),f335(f335(f23(f934(x101331,a922)),x101332),f335(f335(f317(x101331),x101333),f195(f934(x101331,a922))))),f335(f335(f317(x101331),x101334),f195(f934(x101331,a922)))))),f335(f41(x101331),x101332))) % 186.01/186.04 [7168]~P97(x71681)+~P1(f335(f335(f243(x71681),x71682),x71684))+~P1(f335(f335(f243(x71681),x71682),x71683))+P1(f335(f335(f243(x71681),x71682),f335(f335(f108(x71681),x71683),x71684))) % 186.01/186.04 [7171]~P109(x71711)+~P1(f335(f335(f243(x71711),x71712),x71714))+~P1(f335(f335(f243(x71711),x71712),x71713))+P1(f335(f335(f243(x71711),x71712),f335(f335(f241(x71711),x71713),x71714))) % 186.01/186.04 [7172]~P109(x71721)+~P1(f335(f335(f244(x71721),x71722),x71724))+~P1(f335(f335(f244(x71721),x71722),x71723))+P1(f335(f335(f244(x71721),x71722),f335(f335(f241(x71721),x71723),x71724))) % 186.01/186.04 [7192]~P67(x71922)+E(x71921,f2(x71922))+E(f335(f335(f299(x71922),f335(f335(f252(x71922),x71921),x71923)),f335(f335(f252(x71922),x71921),x71924)),f335(f335(f252(x71922),x71921),f335(f335(f23(a927),x71923),x71924)))+~P1(f335(f335(f243(a927),x71924),x71923)) % 186.01/186.04 [7238]~P109(x72381)+~P14(x72381,f335(f335(f158(x72381),x72383),x72384))+P14(x72381,f335(f335(f158(x72381),x72382),f335(f335(f158(x72381),x72383),x72384)))+~P1(f335(f335(f243(x72381),x72382),x72383)) % 186.01/186.04 [7274]~P89(x72741)+~P1(f335(f335(f243(x72741),f2(x72741)),x72744))+~P1(f335(f335(f243(x72741),x72742),x72743))+P1(f335(f335(f243(x72741),x72742),f335(f335(f86(x72741),x72743),x72744))) % 186.01/186.04 [7275]~P89(x72751)+~P1(f335(f335(f243(x72751),f2(x72751)),x72753))+~P1(f335(f335(f243(x72751),x72752),x72754))+P1(f335(f335(f243(x72751),x72752),f335(f335(f86(x72751),x72753),x72754))) % 186.01/186.04 [7276]~P125(x72761)+~P1(f335(f335(f244(x72761),f2(x72761)),x72763))+~P1(f335(f335(f244(x72761),x72762),x72764))+P1(f335(f335(f244(x72761),x72762),f335(f335(f86(x72761),x72763),x72764))) % 186.01/186.04 [7277]~P89(x72771)+~P1(f335(f335(f243(x72771),x72772),x72774))+~P1(f335(f335(f244(x72771),f2(x72771)),x72773))+P1(f335(f335(f244(x72771),x72772),f335(f335(f86(x72771),x72773),x72774))) % 186.01/186.04 [7278]~P89(x72781)+~P1(f335(f335(f243(x72781),f2(x72781)),x72783))+~P1(f335(f335(f244(x72781),x72782),x72784))+P1(f335(f335(f244(x72781),x72782),f335(f335(f86(x72781),x72783),x72784))) % 186.01/186.04 [7319]~P109(x73191)+P1(f335(f335(f243(x73191),x73192),x73193))+P1(f335(f335(f243(x73191),x73192),x73194))+~P1(f335(f335(f243(x73191),x73192),f335(f335(f242(x73191),x73194),x73193))) % 186.01/186.04 [7320]~P109(x73201)+P1(f335(f335(f244(x73201),x73202),x73203))+P1(f335(f335(f244(x73201),x73202),x73204))+~P1(f335(f335(f244(x73201),x73202),f335(f335(f242(x73201),x73204),x73203))) % 186.01/186.04 [7614]~P110(x76142)+~P65(x76141)+~P1(f335(f335(f244(f934(x76141,x76142)),x76143),x76144))+P1(f335(f335(f243(f934(x76141,x76142)),x76143),x76144)) % 186.01/186.04 [7971]~P69(x79711)+~P1(f335(f335(f244(x79711),x79714),f2(x79711)))+~P1(f335(f335(f243(x79711),x79713),f335(f335(f299(x79711),x79712),x79714)))+P1(f335(f335(f243(x79711),x79712),f335(f335(f87(x79711),x79713),x79714))) % 186.01/186.04 [7972]~P69(x79721)+~P1(f335(f335(f244(x79721),x79724),f2(x79721)))+~P1(f335(f335(f243(x79721),x79723),f335(f335(f87(x79721),x79722),x79724)))+P1(f335(f335(f243(x79721),x79722),f335(f335(f299(x79721),x79723),x79724))) % 186.01/186.04 [7973]~P69(x79731)+~P1(f335(f335(f244(x79731),x79734),f2(x79731)))+~P1(f335(f335(f244(x79731),x79733),f335(f335(f299(x79731),x79732),x79734)))+P1(f335(f335(f244(x79731),x79732),f335(f335(f87(x79731),x79733),x79734))) % 186.01/186.04 [7974]~P69(x79741)+~P1(f335(f335(f244(x79741),x79744),f2(x79741)))+~P1(f335(f335(f244(x79741),x79743),f335(f335(f87(x79741),x79742),x79744)))+P1(f335(f335(f244(x79741),x79742),f335(f335(f299(x79741),x79743),x79744))) % 186.01/186.04 [8077]~P128(x80771)+~P1(f335(f335(f243(x80771),x80772),f2(x80771)))+~P1(f335(f335(f243(x80771),x80774),x80773))+P1(f335(f335(f243(x80771),f335(f335(f87(x80771),x80772),x80773)),f335(f335(f87(x80771),x80772),x80774))) % 186.01/186.04 [8078]~P127(x80781)+~P1(f335(f335(f244(x80781),x80782),f2(x80781)))+~P1(f335(f335(f243(x80781),x80784),x80783))+P1(f335(f335(f243(x80781),f335(f335(f87(x80781),x80782),x80783)),f335(f335(f87(x80781),x80782),x80784))) % 186.01/186.04 [8079]~P128(x80791)+~P1(f335(f335(f243(x80791),x80793),f2(x80791)))+~P1(f335(f335(f243(x80791),x80794),x80792))+P1(f335(f335(f243(x80791),f335(f335(f87(x80791),x80792),x80793)),f335(f335(f87(x80791),x80794),x80793))) % 186.01/186.04 [8080]~P68(x80801)+~P1(f335(f335(f243(x80801),x80803),f2(x80801)))+~P1(f335(f335(f243(x80801),x80804),x80802))+P1(f335(f335(f243(x80801),f335(f335(f299(x80801),x80802),x80803)),f335(f335(f299(x80801),x80804),x80803))) % 186.01/186.04 [8084]~P127(x80841)+~P1(f335(f335(f244(x80841),x80843),f2(x80841)))+~P1(f335(f335(f244(x80841),x80844),x80842))+P1(f335(f335(f244(x80841),f335(f335(f87(x80841),x80842),x80843)),f335(f335(f87(x80841),x80844),x80843))) % 186.01/186.04 [8085]~P127(x80851)+~P1(f335(f335(f244(x80851),x80852),f2(x80851)))+~P1(f335(f335(f244(x80851),x80854),x80853))+P1(f335(f335(f244(x80851),f335(f335(f87(x80851),x80852),x80853)),f335(f335(f87(x80851),x80852),x80854))) % 186.01/186.04 [8086]~P69(x80861)+~P1(f335(f335(f244(x80861),x80863),f2(x80861)))+~P1(f335(f335(f244(x80861),x80864),x80862))+P1(f335(f335(f244(x80861),f335(f335(f299(x80861),x80862),x80863)),f335(f335(f299(x80861),x80864),x80863))) % 186.01/186.04 [8087]~P125(x80871)+~P1(f335(f335(f244(x80871),f84(x80871)),x80872))+~P1(f335(f335(f243(a927),x80873),x80874))+P1(f335(f335(f243(x80871),f335(f335(f252(x80871),x80872),x80873)),f335(f335(f252(x80871),x80872),x80874))) % 186.01/186.04 [8088]~P125(x80881)+~P1(f335(f335(f243(x80881),f84(x80881)),x80882))+~P1(f335(f335(f243(a927),x80883),x80884))+P1(f335(f335(f243(x80881),f335(f335(f252(x80881),x80882),x80883)),f335(f335(f252(x80881),x80882),x80884))) % 186.01/186.04 [8090]~P125(x80901)+~P1(f335(f335(f244(x80901),f84(x80901)),x80902))+~P1(f335(f335(f244(a927),x80903),x80904))+P1(f335(f335(f244(x80901),f335(f335(f252(x80901),x80902),x80903)),f335(f335(f252(x80901),x80902),x80904))) % 186.01/186.04 [8117]P1(f335(f335(f244(a927),f2(a927)),f335(x81171,x81172)))+~P1(f335(f67(x81173),x81174))+~P1(f335(f335(f337(x81173),x81172),x81174))+~P1(f335(f335(f244(a927),f2(a927)),f335(f335(f9(x81173,a927),x81171),x81174))) % 186.01/186.04 [8125]~P127(x81251)+~P1(f335(f335(f244(x81251),f2(x81251)),x81252))+~P1(f335(f335(f243(x81251),x81253),x81254))+P1(f335(f335(f243(x81251),f335(f335(f87(x81251),x81252),x81253)),f335(f335(f87(x81251),x81252),x81254))) % 186.01/186.04 [8126]~P137(x81261)+~P1(f335(f335(f243(x81261),x81263),x81264))+~P1(f335(f335(f243(x81261),f2(x81261)),x81262))+P1(f335(f335(f243(x81261),f335(f335(f87(x81261),x81262),x81263)),f335(f335(f87(x81261),x81262),x81264))) % 186.01/186.04 [8127]~P136(x81271)+~P1(f335(f335(f243(x81271),x81273),x81274))+~P1(f335(f335(f243(x81271),f2(x81271)),x81272))+P1(f335(f335(f243(x81271),f335(f335(f87(x81271),x81272),x81273)),f335(f335(f87(x81271),x81272),x81274))) % 186.01/186.04 [8128]~P137(x81281)+~P1(f335(f335(f243(x81281),x81282),x81284))+~P1(f335(f335(f243(x81281),f2(x81281)),x81283))+P1(f335(f335(f243(x81281),f335(f335(f87(x81281),x81282),x81283)),f335(f335(f87(x81281),x81284),x81283))) % 186.01/186.04 [8129]~P125(x81291)+~P1(f335(f335(f243(x81291),x81292),x81294))+~P1(f335(f335(f243(x81291),f2(x81291)),x81292))+P1(f335(f335(f243(x81291),f335(f335(f252(x81291),x81292),x81293)),f335(f335(f252(x81291),x81294),x81293))) % 186.01/186.04 [8130]~P68(x81301)+~P1(f335(f335(f243(x81301),x81302),x81304))+~P1(f335(f335(f243(x81301),f2(x81301)),x81303))+P1(f335(f335(f243(x81301),f335(f335(f299(x81301),x81302),x81303)),f335(f335(f299(x81301),x81304),x81303))) % 186.01/186.04 [8132]~P123(x81321)+~P1(f335(f335(f244(x81321),x81323),x81324))+~P1(f335(f335(f244(x81321),f2(x81321)),x81322))+P1(f335(f335(f244(x81321),f335(f335(f87(x81321),x81322),x81323)),f335(f335(f87(x81321),x81322),x81324))) % 186.01/186.04 [8133]~P131(x81331)+~P1(f335(f335(f244(x81331),x81333),x81334))+~P1(f335(f335(f244(x81331),f2(x81331)),x81332))+P1(f335(f335(f244(x81331),f335(f335(f87(x81331),x81332),x81333)),f335(f335(f87(x81331),x81332),x81334))) % 186.01/186.04 [8134]~P127(x81341)+~P1(f335(f335(f244(x81341),x81342),x81344))+~P1(f335(f335(f244(x81341),f2(x81341)),x81343))+P1(f335(f335(f244(x81341),f335(f335(f87(x81341),x81342),x81343)),f335(f335(f87(x81341),x81344),x81343))) % 186.01/186.04 [8135]~P131(x81351)+~P1(f335(f335(f244(x81351),x81352),x81354))+~P1(f335(f335(f244(x81351),f2(x81351)),x81353))+P1(f335(f335(f244(x81351),f335(f335(f87(x81351),x81352),x81353)),f335(f335(f87(x81351),x81354),x81353))) % 186.01/186.04 [8136]~P127(x81361)+~P1(f335(f335(f244(x81361),x81363),x81364))+~P1(f335(f335(f244(x81361),f2(x81361)),x81362))+P1(f335(f335(f244(x81361),f335(f335(f87(x81361),x81362),x81363)),f335(f335(f87(x81361),x81362),x81364))) % 186.01/186.04 [8137]~P69(x81371)+~P1(f335(f335(f244(x81371),x81372),x81374))+~P1(f335(f335(f244(x81371),f2(x81371)),x81373))+P1(f335(f335(f244(x81371),f335(f335(f299(x81371),x81372),x81373)),f335(f335(f299(x81371),x81374),x81373))) % 186.01/186.04 [8179]~P108(x81792)+P1(f335(f335(f244(f934(x81791,x81792)),x81794),x81793))+~P1(f335(f335(f243(f934(x81791,x81792)),x81794),x81793))+P1(f335(f335(f243(f934(x81791,x81792)),x81793),x81794)) % 186.01/186.04 [8220]P1(f335(f335(f337(x82201),x82202),x82203))+P1(f335(f335(f337(x82201),x82202),x82204))+~P1(f335(f335(f243(f934(x82201,a922)),x82204),x82203))+P1(f335(f335(f244(f934(x82201,a922)),x82204),f335(f335(f317(x82201),x82202),x82203))) % 186.01/186.04 [8376]P1(f335(f335(f337(x83761),x83762),x83763))+P1(f335(f335(f337(x83761),x83762),x83764))+~P1(f335(f335(f244(f934(x83761,a922)),x83764),f335(f335(f317(x83761),x83762),x83763)))+P1(f335(f335(f243(f934(x83761,a922)),x83764),x83763)) % 186.01/186.04 [8441]~P127(x84411)+P1(f335(f335(f244(x84411),x84413),x84412))+P1(f335(f335(f244(x84411),x84412),x84413))+~P1(f335(f335(f244(x84411),f335(f335(f87(x84411),x84414),x84412)),f335(f335(f87(x84411),x84414),x84413))) % 186.01/186.04 [8442]~P127(x84421)+P1(f335(f335(f244(x84421),x84423),x84422))+P1(f335(f335(f244(x84421),x84422),x84423))+~P1(f335(f335(f244(x84421),f335(f335(f87(x84421),x84422),x84424)),f335(f335(f87(x84421),x84423),x84424))) % 186.01/186.04 [8453]~P127(x84531)+P1(f335(f335(f244(x84531),x84534),f2(x84531)))+P1(f335(f335(f244(x84531),x84532),x84533))+~P1(f335(f335(f244(x84531),f335(f335(f87(x84531),x84532),x84534)),f335(f335(f87(x84531),x84533),x84534))) % 186.01/186.04 [8454]~P127(x84541)+P1(f335(f335(f244(x84541),x84544),f2(x84541)))+P1(f335(f335(f244(x84541),x84542),x84543))+~P1(f335(f335(f244(x84541),f335(f335(f87(x84541),x84544),x84542)),f335(f335(f87(x84541),x84544),x84543))) % 186.01/186.04 [8458]~P127(x84581)+P1(f335(f335(f244(x84581),x84582),x84583))+P1(f335(f335(f244(x84581),f2(x84581)),x84584))+~P1(f335(f335(f244(x84581),f335(f335(f87(x84581),x84584),x84583)),f335(f335(f87(x84581),x84584),x84582))) % 186.01/186.04 [8459]~P127(x84591)+P1(f335(f335(f244(x84591),x84592),x84593))+P1(f335(f335(f244(x84591),f2(x84591)),x84594))+~P1(f335(f335(f244(x84591),f335(f335(f87(x84591),x84593),x84594)),f335(f335(f87(x84591),x84592),x84594))) % 186.01/186.04 [8472]~P127(x84721)+P1(f335(f335(f244(x84721),x84722),f2(x84721)))+P1(f335(f335(f244(x84721),f2(x84721)),x84722))+~P1(f335(f335(f244(x84721),f335(f335(f87(x84721),x84723),x84722)),f335(f335(f87(x84721),x84724),x84722))) % 186.01/186.04 [8473]~P127(x84731)+P1(f335(f335(f244(x84731),x84732),f2(x84731)))+P1(f335(f335(f244(x84731),f2(x84731)),x84732))+~P1(f335(f335(f244(x84731),f335(f335(f87(x84731),x84732),x84733)),f335(f335(f87(x84731),x84732),x84734))) % 186.01/186.04 [8503]~P127(x85031)+~P1(f335(f335(f244(x85031),x85034),f2(x85031)))+P1(f335(f335(f243(x85031),x85032),x85033))+~P1(f335(f335(f243(x85031),f335(f335(f87(x85031),x85034),x85033)),f335(f335(f87(x85031),x85034),x85032))) % 186.01/186.04 [8504]~P127(x85041)+~P1(f335(f335(f244(x85041),x85044),f2(x85041)))+P1(f335(f335(f244(x85041),x85042),x85043))+~P1(f335(f335(f244(x85041),f335(f335(f87(x85041),x85044),x85043)),f335(f335(f87(x85041),x85044),x85042))) % 186.01/186.04 [8515]~P125(x85153)+~P1(f335(f335(f244(x85153),f84(x85153)),x85154))+P1(f335(f335(f243(a927),x85151),x85152))+~P1(f335(f335(f243(x85153),f335(f335(f252(x85153),x85154),x85151)),f335(f335(f252(x85153),x85154),x85152))) % 186.01/186.04 [8517]~P125(x85173)+~P1(f335(f335(f244(x85173),f84(x85173)),x85174))+P1(f335(f335(f244(a927),x85171),x85172))+~P1(f335(f335(f244(x85173),f335(f335(f252(x85173),x85174),x85171)),f335(f335(f252(x85173),x85174),x85172))) % 186.01/186.04 [8527]~P127(x85271)+P1(f335(f335(f243(x85271),x85272),x85273))+~P1(f335(f335(f244(x85271),f2(x85271)),x85274))+~P1(f335(f335(f243(x85271),f335(f335(f87(x85271),x85274),x85272)),f335(f335(f87(x85271),x85274),x85273))) % 186.01/186.04 [8528]~P131(x85281)+P1(f335(f335(f243(x85281),x85282),x85283))+~P1(f335(f335(f244(x85281),f2(x85281)),x85284))+~P1(f335(f335(f243(x85281),f335(f335(f87(x85281),x85284),x85282)),f335(f335(f87(x85281),x85284),x85283))) % 186.01/186.04 [8529]~P131(x85291)+P1(f335(f335(f243(x85291),x85292),x85293))+~P1(f335(f335(f244(x85291),f2(x85291)),x85294))+~P1(f335(f335(f243(x85291),f335(f335(f87(x85291),x85292),x85294)),f335(f335(f87(x85291),x85293),x85294))) % 186.01/186.04 [8530]~P127(x85301)+P1(f335(f335(f244(x85301),x85302),x85303))+~P1(f335(f335(f244(x85301),f2(x85301)),x85304))+~P1(f335(f335(f244(x85301),f335(f335(f87(x85301),x85304),x85302)),f335(f335(f87(x85301),x85304),x85303))) % 186.01/186.04 [8531]~P131(x85311)+P1(f335(f335(f244(x85311),x85312),x85313))+~P1(f335(f335(f243(x85311),f2(x85311)),x85314))+~P1(f335(f335(f244(x85311),f335(f335(f87(x85311),x85314),x85312)),f335(f335(f87(x85311),x85314),x85313))) % 186.01/186.04 [8532]~P132(x85321)+P1(f335(f335(f244(x85321),x85322),x85323))+~P1(f335(f335(f243(x85321),f2(x85321)),x85324))+~P1(f335(f335(f244(x85321),f335(f335(f87(x85321),x85324),x85322)),f335(f335(f87(x85321),x85324),x85323))) % 186.01/186.04 [8533]~P125(x85331)+~P1(f335(f335(f243(x85331),f2(x85331)),x85333))+P1(f335(f335(f244(x85331),x85332),x85333))+~P1(f335(f335(f244(x85331),f335(f335(f252(x85331),x85332),x85334)),f335(f335(f252(x85331),x85333),x85334))) % 186.01/186.04 [8534]~P131(x85341)+P1(f335(f335(f244(x85341),x85342),x85343))+~P1(f335(f335(f243(x85341),f2(x85341)),x85344))+~P1(f335(f335(f244(x85341),f335(f335(f87(x85341),x85342),x85344)),f335(f335(f87(x85341),x85343),x85344))) % 186.01/186.04 [8535]~P132(x85351)+P1(f335(f335(f244(x85351),x85352),x85353))+~P1(f335(f335(f243(x85351),f2(x85351)),x85354))+~P1(f335(f335(f244(x85351),f335(f335(f87(x85351),x85352),x85354)),f335(f335(f87(x85351),x85353),x85354))) % 186.01/186.04 [8578]P1(f335(f335(f337(x85781),x85782),x85783))+~P1(f335(f335(f243(f934(x85781,a922)),x85783),x85784))+~P1(f335(f335(f244(f934(x85781,a922)),x85783),x85784))+P1(f335(f335(f244(f934(x85781,a922)),x85783),f335(f335(f317(x85781),x85782),x85784))) % 186.01/186.04 [8957]E(f335(f335(f23(a1),f522(x89571,x89572,x89573,x89574)),f523(x89571,x89572,x89573,x89574)),x89574)+~P1(f335(f335(f244(a1),f2(a1)),x89573))+~P1(f335(f335(f243(a1),x89571),x89574))+P1(f335(f335(f243(a1),x89571),f335(f335(f86(a1),x89574),x89573))) % 186.01/186.04 [8958]E(f335(f335(f23(a1),f532(x89581,x89582,x89583,x89584)),f533(x89581,x89582,x89583,x89584)),x89584)+~P1(f335(f335(f244(a1),f2(a1)),x89583))+~P1(f335(f335(f244(a1),x89581),x89584))+P1(f335(f335(f244(a1),x89581),f335(f335(f86(a1),x89584),x89583))) % 186.01/186.04 [9108]~E(f335(f335(f171(x91081),x91083),f702(x91084,x91083,x91081,x91082)),f335(f335(f171(x91081),x91084),f702(x91084,x91083,x91081,x91082)))+E(f335(f335(f182(x91081),x91082),x91083),f335(f335(f182(x91081),x91082),x91084))+~P1(f335(f335(f243(a927),x91082),f335(f196(f928(x91081)),x91083)))+~P1(f335(f335(f243(a927),x91082),f335(f196(f928(x91081)),x91084))) % 186.01/186.04 [9174]~P1(f335(f335(f244(a1),f2(a1)),x91743))+~P1(f335(f335(f243(a1),x91741),x91744))+P1(f335(f335(f337(a1),f522(x91741,x91742,x91743,x91744)),x91742))+P1(f335(f335(f243(a1),x91741),f335(f335(f86(a1),x91744),x91743))) % 186.01/186.04 [9175]~P1(f335(f335(f244(a1),f2(a1)),x91753))+~P1(f335(f335(f244(a1),x91751),x91754))+P1(f335(f335(f337(a1),f532(x91751,x91752,x91753,x91754)),x91752))+P1(f335(f335(f244(a1),x91751),f335(f335(f86(a1),x91754),x91753))) % 186.01/186.04 [9215]~P97(x92151)+~P1(f335(f67(x92151),x92153))+~P1(f335(f335(f337(x92151),x92154),x92153))+P1(f335(f335(f243(x92151),f335(f335(f70(x92151,x92151,f108(x92151)),x92152),x92153)),f335(f335(f108(x92151),x92154),x92152))) % 186.01/186.04 [9216]~P109(x92161)+~P1(f335(f67(x92161),x92163))+~P1(f335(f335(f337(x92161),x92164),x92163))+P1(f335(f335(f243(x92161),f335(f335(f70(x92161,x92161,f241(x92161)),x92162),x92163)),f335(f335(f241(x92161),x92164),x92162))) % 186.01/186.04 [9260]E(f335(f335(f182(x92601),x92602),x92603),f335(f335(f182(x92601),x92602),x92604))+P1(f335(f335(f244(a927),f702(x92603,x92604,x92601,x92602)),x92602))+~P1(f335(f335(f243(a927),x92602),f335(f196(f928(x92601)),x92603)))+~P1(f335(f335(f243(a927),x92602),f335(f196(f928(x92601)),x92604))) % 186.01/186.04 [9265]~P1(f335(f335(f244(a1),f2(a1)),x92653))+~P1(f335(f335(f243(a1),x92651),x92652))+P1(f335(f335(f337(a1),f523(x92651,x92654,x92653,x92652)),f311(a1,f84(a1),x92653)))+P1(f335(f335(f243(a1),x92651),f335(f335(f86(a1),x92652),x92653))) % 186.01/186.04 [9266]~P1(f335(f335(f244(a1),f2(a1)),x92663))+~P1(f335(f335(f244(a1),x92661),x92662))+P1(f335(f335(f337(a1),f533(x92661,x92664,x92663,x92662)),f311(a1,f84(a1),x92663)))+P1(f335(f335(f244(a1),x92661),f335(f335(f86(a1),x92662),x92663))) % 186.01/186.04 [9585]~P109(x95851)+~P1(f335(f67(x95851),x95854))+P1(f335(f335(f337(x95851),f650(x95852,x95853,x95854,x95851)),x95854))+P1(f335(f335(f243(x95851),f335(f335(f70(x95851,x95851,f242(x95851)),x95852),x95854)),f335(f335(f242(x95851),x95853),x95852))) % 186.01/186.04 [9586]~P103(x95861)+~P1(f335(f67(x95861),x95864))+P1(f335(f335(f337(x95861),f661(x95862,x95863,x95864,x95861)),x95864))+P1(f335(f335(f243(x95861),f335(f335(f70(x95861,x95861,f117(x95861)),x95862),x95864)),f335(f335(f117(x95861),x95863),x95862))) % 186.01/186.04 [9711]~P103(x97111)+~P1(f335(f67(x97111),x97113))+~P1(f335(f335(f243(x97111),f661(x97112,x97114,x97113,x97111)),x97114))+P1(f335(f335(f243(x97111),f335(f335(f70(x97111,x97111,f117(x97111)),x97112),x97113)),f335(f335(f117(x97111),x97114),x97112))) % 186.01/186.04 [9712]~P109(x97121)+~P1(f335(f67(x97121),x97123))+~P1(f335(f335(f243(x97121),f650(x97122,x97124,x97123,x97121)),x97124))+P1(f335(f335(f243(x97121),f335(f335(f70(x97121,x97121,f242(x97121)),x97122),x97123)),f335(f335(f242(x97121),x97124),x97122))) % 186.01/186.04 [9714]~P1(f335(f335(f243(a1),f2(a1)),x97144))+~P1(f335(f335(f244(a1),f2(a1)),x97143))+~P1(f335(f335(f244(a1),x97144),x97141))+P1(f335(f335(f244(a1),f335(f335(f86(a1),f335(f335(f87(a1),x97141),f51(a1,x97142,x97143))),x97144)),f335(f335(f87(a1),x97141),x97143))) % 186.01/186.04 [10104]E(x101041,x101042)+P1(f335(f335(f337(f933(f928(x101043),f928(x101043))),f335(f335(f260(f928(x101043),f928(x101043)),x101042),x101041)),f154(x101043,x101044)))+P1(f335(f335(f337(f933(f928(x101043),f928(x101043))),f335(f335(f260(f928(x101043),f928(x101043)),x101041),x101042)),f154(x101043,x101044)))+~P1(f335(f335(f337(f933(x101043,x101043)),f335(f335(f260(x101043,x101043),f672(x101041,x101042,x101044,x101043)),f674(x101041,x101042,x101044,x101043))),x101044)) % 186.01/186.04 [10105]E(x101051,x101052)+P1(f335(f335(f337(f933(f928(x101053),f928(x101053))),f335(f335(f260(f928(x101053),f928(x101053)),x101052),x101051)),f154(x101053,x101054)))+P1(f335(f335(f337(f933(f928(x101053),f928(x101053))),f335(f335(f260(f928(x101053),f928(x101053)),x101051),x101052)),f154(x101053,x101054)))+~P1(f335(f335(f337(f933(x101053,x101053)),f335(f335(f260(x101053,x101053),f674(x101051,x101052,x101054,x101053)),f672(x101051,x101052,x101054,x101053))),x101054)) % 186.01/186.04 [7680]~P103(x76801)+~P1(f335(f335(f243(x76801),x76803),x76804))+~P1(f335(f335(f243(x76801),x76802),x76804))+P1(f335(f335(f243(x76801),f335(f335(f117(x76801),x76802),x76803)),x76804)) % 186.01/186.04 [7683]~P109(x76831)+~P1(f335(f335(f243(x76831),x76833),x76834))+~P1(f335(f335(f243(x76831),x76832),x76834))+P1(f335(f335(f243(x76831),f335(f335(f242(x76831),x76832),x76833)),x76834)) % 186.01/186.04 [7684]~P109(x76841)+~P1(f335(f335(f244(x76841),x76843),x76844))+~P1(f335(f335(f244(x76841),x76842),x76844))+P1(f335(f335(f244(x76841),f335(f335(f242(x76841),x76842),x76843)),x76844)) % 186.01/186.04 [7996]~E(x79961,x79963)+E(f146(a927,f335(f310(a927,x79961),x79962)),f335(f335(f158(a927),x79963),x79964))+~E(f146(a927,f335(f310(a927,f335(f335(f86(a927),x79961),f84(a927))),x79962)),x79964)+~P1(f335(f335(f244(a927),x79961),x79962)) % 186.01/186.04 [8004]~P109(x80041)+P1(f335(f335(f243(x80041),x80042),x80043))+P1(f335(f335(f243(x80041),x80044),x80043))+~P1(f335(f335(f243(x80041),f335(f335(f241(x80041),x80044),x80042)),x80043)) % 186.01/186.04 [8005]~P109(x80051)+P1(f335(f335(f244(x80051),x80052),x80053))+P1(f335(f335(f244(x80051),x80054),x80053))+~P1(f335(f335(f244(x80051),f335(f335(f241(x80051),x80054),x80052)),x80053)) % 186.01/186.04 [8278]~P68(x82781)+~P1(f335(f335(f244(x82781),f2(x82781)),x82783))+~P1(f335(f335(f243(x82781),x82782),f335(f335(f299(x82781),x82784),x82783)))+P1(f335(f335(f243(x82781),f335(f335(f87(x82781),x82782),x82783)),x82784)) % 186.01/186.04 [8279]~P69(x82791)+~P1(f335(f335(f244(x82791),f2(x82791)),x82793))+~P1(f335(f335(f243(x82791),x82792),f335(f335(f299(x82791),x82794),x82793)))+P1(f335(f335(f243(x82791),f335(f335(f87(x82791),x82792),x82793)),x82794)) % 186.01/186.04 [8280]~P68(x82801)+~P1(f335(f335(f244(x82801),f2(x82801)),x82803))+~P1(f335(f335(f243(x82801),x82802),f335(f335(f87(x82801),x82804),x82803)))+P1(f335(f335(f243(x82801),f335(f335(f299(x82801),x82802),x82803)),x82804)) % 186.01/186.04 [8282]~P69(x82821)+~P1(f335(f335(f244(x82821),f2(x82821)),x82823))+~P1(f335(f335(f243(x82821),x82822),f335(f335(f87(x82821),x82824),x82823)))+P1(f335(f335(f243(x82821),f335(f335(f299(x82821),x82822),x82823)),x82824)) % 186.01/186.04 [8283]~P68(x82831)+~P1(f335(f335(f244(x82831),f2(x82831)),x82833))+~P1(f335(f335(f244(x82831),x82832),f335(f335(f299(x82831),x82834),x82833)))+P1(f335(f335(f244(x82831),f335(f335(f87(x82831),x82832),x82833)),x82834)) % 186.01/186.04 [8284]~P69(x82841)+~P1(f335(f335(f244(x82841),f2(x82841)),x82843))+~P1(f335(f335(f244(x82841),x82842),f335(f335(f299(x82841),x82844),x82843)))+P1(f335(f335(f244(x82841),f335(f335(f87(x82841),x82842),x82843)),x82844)) % 186.01/186.04 [8285]~P68(x82851)+~P1(f335(f335(f244(x82851),f2(x82851)),x82853))+~P1(f335(f335(f244(x82851),x82852),f335(f335(f87(x82851),x82854),x82853)))+P1(f335(f335(f244(x82851),f335(f335(f299(x82851),x82852),x82853)),x82854)) % 186.01/186.04 [8287]~P69(x82871)+~P1(f335(f335(f244(x82871),f2(x82871)),x82873))+~P1(f335(f335(f244(x82871),x82872),f335(f335(f87(x82871),x82874),x82873)))+P1(f335(f335(f244(x82871),f335(f335(f299(x82871),x82872),x82873)),x82874)) % 186.01/186.04 [8411]~P68(x84111)+~P1(f335(f335(f244(x84111),f2(x84111)),x84114))+P1(f335(f335(f243(x84111),x84112),f335(f335(f87(x84111),x84113),x84114)))+~P1(f335(f335(f243(x84111),f335(f335(f299(x84111),x84112),x84114)),x84113)) % 186.01/186.04 [8412]~P68(x84121)+~P1(f335(f335(f244(x84121),f2(x84121)),x84124))+P1(f335(f335(f243(x84121),x84122),f335(f335(f299(x84121),x84123),x84124)))+~P1(f335(f335(f243(x84121),f335(f335(f87(x84121),x84122),x84124)),x84123)) % 186.01/186.04 [8414]~P69(x84141)+~P1(f335(f335(f244(x84141),f2(x84141)),x84144))+P1(f335(f335(f243(x84141),x84142),f335(f335(f87(x84141),x84143),x84144)))+~P1(f335(f335(f243(x84141),f335(f335(f299(x84141),x84142),x84144)),x84143)) % 186.01/186.04 [8415]~P69(x84151)+~P1(f335(f335(f244(x84151),f2(x84151)),x84154))+P1(f335(f335(f243(x84151),x84152),f335(f335(f299(x84151),x84153),x84154)))+~P1(f335(f335(f243(x84151),f335(f335(f87(x84151),x84152),x84154)),x84153)) % 186.01/186.04 [8416]~P68(x84161)+~P1(f335(f335(f244(x84161),f2(x84161)),x84164))+P1(f335(f335(f244(x84161),x84162),f335(f335(f87(x84161),x84163),x84164)))+~P1(f335(f335(f244(x84161),f335(f335(f299(x84161),x84162),x84164)),x84163)) % 186.01/186.04 [8417]~P68(x84171)+~P1(f335(f335(f244(x84171),f2(x84171)),x84174))+P1(f335(f335(f244(x84171),x84172),f335(f335(f299(x84171),x84173),x84174)))+~P1(f335(f335(f244(x84171),f335(f335(f87(x84171),x84172),x84174)),x84173)) % 186.01/186.04 [8419]~P69(x84191)+~P1(f335(f335(f244(x84191),f2(x84191)),x84194))+P1(f335(f335(f244(x84191),x84192),f335(f335(f87(x84191),x84193),x84194)))+~P1(f335(f335(f244(x84191),f335(f335(f299(x84191),x84192),x84194)),x84193)) % 186.01/186.04 [8420]~P69(x84201)+~P1(f335(f335(f244(x84201),f2(x84201)),x84204))+P1(f335(f335(f244(x84201),x84202),f335(f335(f299(x84201),x84203),x84204)))+~P1(f335(f335(f244(x84201),f335(f335(f87(x84201),x84202),x84204)),x84203)) % 186.01/186.04 [8581]~P69(x85811)+~P1(f335(f335(f244(x85811),x85813),f2(x85811)))+~P1(f335(f335(f243(x85811),f335(f335(f299(x85811),x85814),x85813)),x85812))+P1(f335(f335(f243(x85811),f335(f335(f87(x85811),x85812),x85813)),x85814)) % 186.01/186.04 [8582]~P69(x85821)+~P1(f335(f335(f244(x85821),x85823),f2(x85821)))+~P1(f335(f335(f243(x85821),f335(f335(f87(x85821),x85824),x85823)),x85822))+P1(f335(f335(f243(x85821),f335(f335(f299(x85821),x85822),x85823)),x85824)) % 186.01/186.04 [8583]~P69(x85831)+~P1(f335(f335(f244(x85831),x85833),f2(x85831)))+~P1(f335(f335(f244(x85831),f335(f335(f299(x85831),x85834),x85833)),x85832))+P1(f335(f335(f244(x85831),f335(f335(f87(x85831),x85832),x85833)),x85834)) % 186.01/186.04 [8584]~P69(x85841)+~P1(f335(f335(f244(x85841),x85843),f2(x85841)))+~P1(f335(f335(f244(x85841),f335(f335(f87(x85841),x85844),x85843)),x85842))+P1(f335(f335(f244(x85841),f335(f335(f299(x85841),x85842),x85843)),x85844)) % 186.01/186.04 [8596]~P1(f335(x85961,x85964))+~P1(f335(f335(f244(a927),x85962),f335(f335(f87(a927),x85963),f335(a119,x85964))))+P1(f335(x85961,f335(f335(f42(a927),x85962),x85963)))+~P1(f335(f335(f243(a927),f335(f335(f87(a927),x85963),x85964)),x85962)) % 186.01/186.04 [8805]~P103(x88051)+~P1(f335(f67(x88051),x88054))+~P1(f335(f335(f337(x88051),x88052),x88054))+P1(f335(f335(f243(x88051),f335(f335(f117(x88051),x88052),x88053)),f335(f335(f70(x88051,x88051,f117(x88051)),x88053),x88054))) % 186.01/186.04 [8806]~P109(x88061)+~P1(f335(f67(x88061),x88064))+~P1(f335(f335(f337(x88061),x88062),x88064))+P1(f335(f335(f243(x88061),f335(f335(f242(x88061),x88062),x88063)),f335(f335(f70(x88061,x88061,f242(x88061)),x88063),x88064))) % 186.01/186.04 [8959]~P1(f335(f67(x89591),x89592))+E(f335(f41(x89591),f335(f335(f23(f934(x89591,a922)),x89592),f335(f335(f317(x89591),x89593),x89594))),f335(f335(f23(a927),f335(f41(x89591),f335(f335(f23(f934(x89591,a922)),x89592),x89594))),f84(a927)))+P1(f335(f335(f337(x89591),x89593),x89594))+~P1(f335(f335(f337(x89591),x89593),x89592)) % 186.01/186.04 [9036]E(f335(f335(f86(a1),f526(x90361,x90362,x90363,x90364)),f527(x90361,x90362,x90363,x90364)),x90364)+~P1(f335(f335(f244(a1),f2(a1)),x90363))+~P1(f335(f335(f243(a1),x90364),x90361))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x90364),x90363)),x90361)) % 186.01/186.04 [9037]E(f335(f335(f86(a1),f534(x90371,x90372,x90373,x90374)),f535(x90371,x90372,x90373,x90374)),x90374)+~P1(f335(f335(f244(a1),f2(a1)),x90373))+~P1(f335(f335(f244(a1),x90374),x90371))+P1(f335(f335(f244(a1),f335(f335(f23(a1),x90374),x90373)),x90371)) % 186.01/186.04 [9245]~P1(f335(f335(f244(a1),f2(a1)),x92453))+~P1(f335(f335(f243(a1),x92454),x92451))+P1(f335(f335(f337(a1),f526(x92451,x92452,x92453,x92454)),x92452))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x92454),x92453)),x92451)) % 186.01/186.04 [9246]~P1(f335(f335(f244(a1),f2(a1)),x92463))+~P1(f335(f335(f244(a1),x92464),x92461))+P1(f335(f335(f337(a1),f534(x92461,x92462,x92463,x92464)),x92462))+P1(f335(f335(f244(a1),f335(f335(f23(a1),x92464),x92463)),x92461)) % 186.01/186.04 [9333]~P1(f335(f335(f244(a1),f2(a1)),x93332))+~P1(f335(f335(f243(a1),x93331),x93333))+P1(f335(f335(f337(a1),f527(x93333,x93334,x93332,x93331)),f311(a1,f84(a1),x93332)))+P1(f335(f335(f243(a1),f335(f335(f23(a1),x93331),x93332)),x93333)) % 186.01/186.04 [9334]~P1(f335(f335(f244(a1),f2(a1)),x93342))+~P1(f335(f335(f244(a1),x93341),x93343))+P1(f335(f335(f337(a1),f535(x93343,x93344,x93342,x93341)),f311(a1,f84(a1),x93342)))+P1(f335(f335(f244(a1),f335(f335(f23(a1),x93341),x93342)),x93343)) % 186.01/186.04 [9352]~P1(f335(f335(f243(a1),f2(a1)),x93524))+~P1(f335(f335(f244(a1),f2(a1)),x93523))+~P1(f335(f335(f244(a1),x93524),x93521))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),f335(f335(f87(a1),x93521),f51(a1,x93522,x93523))),x93524))) % 186.01/186.04 [9381]E(x93811,x93812)+~P40(x93813,x93814)+~P1(f335(f335(f337(f933(x93813,x93813)),f335(f335(f260(x93813,x93813),x93812),x93811)),x93814))+~P1(f335(f335(f337(f933(x93813,x93813)),f335(f335(f260(x93813,x93813),x93811),x93812)),x93814)) % 186.01/186.04 [9413]~P97(x94131)+~P1(f335(f67(x94131),x94134))+~P1(f335(f335(f243(x94131),x94132),f648(x94133,x94132,x94134,x94131)))+P1(f335(f335(f243(x94131),f335(f335(f108(x94131),x94132),x94133)),f335(f335(f70(x94131,x94131,f108(x94131)),x94133),x94134))) % 186.01/186.04 [9414]~P109(x94141)+~P1(f335(f67(x94141),x94144))+~P1(f335(f335(f243(x94141),x94142),f649(x94143,x94142,x94144,x94141)))+P1(f335(f335(f243(x94141),f335(f335(f241(x94141),x94142),x94143)),f335(f335(f70(x94141,x94141,f241(x94141)),x94143),x94144))) % 186.01/186.04 [9428]~P1(f335(f335(f243(a1),x94284),f2(a1)))+~P1(f335(f335(f244(a1),f2(a1)),x94282))+~P1(f335(f335(f244(a1),x94281),x94284))+P1(f335(f335(f244(a1),f335(f335(f87(a1),x94281),x94282)),f335(f335(f86(a1),f335(f335(f87(a1),x94281),f51(a1,x94283,x94282))),x94284))) % 186.01/186.04 [9453]P1(f335(f67(x94531),x94532))+~P1(f335(f67(x94531),x94533))+~P1(f335(f335(f337(f934(x94531,a922)),x94532),f335(f335(f66(x94531),x94533),x94534)))+~P1(f335(f335(f243(f934(f933(x94531,x94531),a922)),x94534),f335(f335(f262(x94531,x94531),x94533),f335(f16(f934(x94531,a922),x94531),x94533)))) % 186.01/186.04 [9477]~P109(x94771)+~P1(f335(f67(x94771),x94774))+P1(f335(f335(f337(x94771),f649(x94772,x94773,x94774,x94771)),x94774))+P1(f335(f335(f243(x94771),f335(f335(f241(x94771),x94773),x94772)),f335(f335(f70(x94771,x94771,f241(x94771)),x94772),x94774))) % 186.01/186.04 [9478]~P97(x94781)+~P1(f335(f67(x94781),x94784))+P1(f335(f335(f337(x94781),f648(x94782,x94783,x94784,x94781)),x94784))+P1(f335(f335(f243(x94781),f335(f335(f108(x94781),x94783),x94782)),f335(f335(f70(x94781,x94781,f108(x94781)),x94782),x94784))) % 186.01/186.04 [9878]~P1(f335(f67(x98782),x98784))+~P1(f335(f67(x98781),x98783))+~P1(f335(f335(f243(a927),f335(f41(x98782),x98784)),f335(f41(x98781),x98783)))+P1(f335(f335(f243(f934(x98781,a922)),f335(f318(x98782,x98781,f365(x98783,x98781,x98784,x98782)),x98784)),x98783)) % 186.01/186.04 [9526]~P1(f335(f335(f337(x95261),x95262),x95264))+P1(f335(f335(f337(x95261),x95262),x95263))+~P1(f335(f335(f244(f934(x95261,a922)),x95264),f335(f335(f317(x95261),x95262),x95263)))+P1(f335(f335(f244(f934(x95261,a922)),f335(f335(f23(f934(x95261,a922)),x95264),f335(f335(f317(x95261),x95262),f195(f934(x95261,a922))))),x95263)) % 186.01/186.04 [9692]~P1(f335(f335(f337(x96921),x96922),x96924))+P1(f335(f335(f337(x96921),x96922),x96923))+P1(f335(f335(f244(f934(x96921,a922)),x96924),f335(f335(f317(x96921),x96922),x96923)))+~P1(f335(f335(f244(f934(x96921,a922)),f335(f335(f23(f934(x96921,a922)),x96924),f335(f335(f317(x96921),x96922),f195(f934(x96921,a922))))),x96923)) % 186.01/186.04 [9717]P1(f335(f335(f337(x97171),x97172),x97173))+~P1(f335(f335(f243(f934(x97171,a922)),x97174),x97173))+P1(f335(f335(f244(f934(x97171,a922)),x97174),f335(f335(f317(x97171),x97172),x97173)))+~P1(f335(f335(f244(f934(x97171,a922)),f335(f335(f23(f934(x97171,a922)),x97174),f335(f335(f317(x97171),x97172),f195(f934(x97171,a922))))),x97173)) % 186.01/186.04 [9722]~P1(f335(f335(f337(x97221),x97223),x97222))+~P1(f335(f335(f244(f934(x97221,a922)),x97222),x97224))+P1(f335(f335(f244(f934(x97221,a922)),x97222),f335(f335(f317(x97221),x97223),x97224)))+~P1(f335(f335(f244(f934(x97221,a922)),f335(f335(f23(f934(x97221,a922)),x97222),f335(f335(f317(x97221),x97223),f195(f934(x97221,a922))))),x97224)) % 186.01/186.04 [9738]~P1(f335(f335(f243(f934(x97381,a922)),x97382),x97384))+~P1(f335(f335(f244(f934(x97381,a922)),x97382),x97384))+P1(f335(f335(f244(f934(x97381,a922)),x97382),f335(f335(f317(x97381),x97383),x97384)))+~P1(f335(f335(f244(f934(x97381,a922)),f335(f335(f23(f934(x97381,a922)),x97382),f335(f335(f317(x97381),x97383),f195(f934(x97381,a922))))),x97384)) % 186.01/186.04 [9783]~P110(x97832)+~P65(x97831)+~P1(f335(f335(f243(f934(x97831,x97832)),x97833),x97834))+P1(f335(f63(x97831),f335(f335(f18(x97831,x97832,a922),f335(f335(f8(x97832,f934(x97832,a922),x97831),f243(x97832)),x97833)),x97834))) % 186.01/186.04 [9927]~P110(x99272)+~P65(x99271)+P1(f335(f335(f243(f934(x99271,x99272)),x99273),x99274))+~P1(f335(f63(x99271),f335(f335(f18(x99271,x99272,a922),f335(f335(f8(x99272,f934(x99272,a922),x99271),f243(x99272)),x99273)),x99274))) % 186.01/186.04 [10095]E(f335(f335(f171(x100951),f335(f335(f171(f928(x100951)),f186(x100951,x100952)),x100953)),x100954),f335(f335(f171(x100951),f335(f335(f171(f928(x100951)),x100952),x100954)),x100953))+~P1(f335(f335(f244(a927),x100953),f335(f196(f928(f928(x100951))),f186(x100951,x100952))))+~P14(a927,f335(f175(a927),f335(f335(f161(f928(x100951),a927),f196(f928(x100951))),x100952)))+~P1(f335(f335(f244(a927),x100954),f335(f196(f928(f928(x100951))),f335(f143(f928(x100951),f335(f335(f8(a927,a922,f928(x100951)),f335(f244(a927),x100953)),f196(f928(x100951)))),x100952)))) % 186.01/186.04 [10117]~P1(f335(f335(f337(f933(a927,a927)),x101174),x101171))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x101174),x101172)),a38))+~P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101171),x101173)),a39))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101171),f335(f335(f317(f933(a927,a927)),x101172),x101173))),a39)) % 186.01/186.04 [10118]~P1(f335(f335(f337(f933(a927,a927)),x101184),x101181))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x101184),x101182)),a76))+~P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101181),x101183)),a77))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101181),f335(f335(f317(f933(a927,a927)),x101182),x101183))),a77)) % 186.01/186.04 [10006]~P110(x100062)+~P65(x100061)+~P1(f335(f335(f244(f934(x100061,x100062)),x100063),x100064))+P1(f335(f62(x100061),f335(f335(f8(a922,a922,x100061),a330),f335(f335(f18(x100061,x100062,a922),f335(f335(f8(x100062,f934(x100062,a922),x100061),a332),x100063)),x100064)))) % 186.01/186.04 [10129]~P1(f335(f335(f337(f933(a927,a927)),x101294),x101293))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x101291),x101294)),a38))+~P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101292),x101293)),a40))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f335(f335(f317(f933(a927,a927)),x101291),x101292)),x101293)),a40)) % 186.01/186.04 [10130]~P1(f335(f335(f337(f933(a927,a927)),x101304),x101303))+~P1(f335(f335(f337(f933(f933(a927,a927),f933(a927,a927))),f335(f335(f260(f933(a927,a927),f933(a927,a927)),x101301),x101304)),a76))+~P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),x101302),x101303)),a75))+P1(f335(f335(f337(f933(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922))),f335(f335(f260(f934(f933(a927,a927),a922),f934(f933(a927,a927),a922)),f335(f335(f317(f933(a927,a927)),x101301),x101302)),x101303)),a75)) % 186.01/186.04 [6278]~P8(x62784,x62781)+~P1(f335(f335(x62781,x62782),x62785))+P1(f335(f335(x62781,x62782),x62783))+~P1(f335(f335(x62781,x62785),x62783)) % 186.01/186.04 [6279]~P51(x62794,x62791)+~P1(f335(f335(x62791,x62792),x62795))+P1(f335(f335(x62791,x62792),x62793))+~P1(f335(f335(x62791,x62795),x62793)) % 186.01/186.04 [6280]~P16(x62804,x62801)+~P1(f335(f335(x62801,x62802),x62805))+P1(f335(f335(x62801,x62802),x62803))+~P1(f335(f335(x62801,x62805),x62803)) % 186.01/186.04 [8944]~P8(x89444,x89443)+~P1(f335(x89441,x89445))+P1(f335(x89442,f850(x89442,x89441,x89443,x89444)))+P1(f335(x89441,f849(x89442,x89441,x89443,x89444))) % 186.01/186.04 [9182]~P8(x91824,x91823)+~P1(f335(x91822,x91825))+~P1(f335(x91821,f849(x91821,x91822,x91823,x91824)))+P1(f335(x91821,f850(x91821,x91822,x91823,x91824))) % 186.01/186.04 [9365]~P8(x93654,x93653)+~P1(f335(x93651,x93655))+P1(f335(f335(f337(x93654),f850(x93652,x93651,x93653,x93654)),f278(x93654,x93653)))+P1(f335(x93651,f849(x93652,x93651,x93653,x93654))) % 186.01/186.04 [9484]~P8(x94841,x94844)+~P1(f335(x94843,x94845))+~P1(f335(x94842,f849(x94842,x94843,x94844,x94841)))+P1(f335(f335(f337(x94841),f850(x94842,x94843,x94844,x94841)),f278(x94841,x94844))) % 186.01/186.04 [9772]~P39(x97721,x97724)+P1(f335(f335(f337(f933(f928(x97721),f928(x97721))),f335(f335(f260(f928(x97721),f928(x97721)),x97722),x97723)),f154(x97721,x97724)))+~P1(f335(f335(f337(f933(f928(x97721),f928(x97721))),f335(f335(f260(f928(x97721),f928(x97721)),x97722),x97725)),f154(x97721,x97724)))+~P1(f335(f335(f337(f933(f928(x97721),f928(x97721))),f335(f335(f260(f928(x97721),f928(x97721)),x97725),x97723)),f154(x97721,x97724))) % 186.01/186.04 [5527]~P5(x55275)+E(x55271,x55272)+~E(x55273,x55274)+~E(f335(f335(f23(x55275),x55273),x55274),f335(f335(f23(x55275),x55271),x55272)) % 186.01/186.04 [6392]~P18(x63925,x63921,x63923)+E(f335(f335(x63921,x63922),f335(x63923,x63924)),f335(x63923,x63924))+~P1(f335(f67(x63925),x63924))+~P1(f335(f335(f337(x63925),x63922),x63924)) % 186.01/186.04 [6578]~P79(x65781)+~E(f335(f335(f23(x65781),x65784),x65785),f335(f335(f23(x65781),x65782),x65783))+~P1(f335(f335(f243(x65781),x65784),x65785))+P1(f335(f335(f243(x65781),x65782),x65783)) % 186.01/186.04 [6580]~P79(x65801)+~E(f335(f335(f23(x65801),x65804),x65805),f335(f335(f23(x65801),x65802),x65803))+~P1(f335(f335(f244(x65801),x65804),x65805))+P1(f335(f335(f244(x65801),x65802),x65803)) % 186.01/186.04 [7548]~E(x75482,f335(f335(f158(x75481),x75484),x75485))+P1(f335(f335(f337(f928(x75481)),x75482),f168(x75481,x75483)))+~P1(f335(f335(f337(f928(x75481)),x75485),f168(x75481,x75483)))+~P1(f335(f335(f337(x75481),x75484),x75483)) % 186.01/186.04 [7945]~E(f335(f196(f928(x79451)),x79453),f335(f196(f928(x79452)),x79454))+~E(f335(f335(f161(f933(x79451,x79452),x79452),f264(x79451,x79452)),x79455),x79454)+~E(f335(f335(f161(f933(x79451,x79452),x79451),f259(x79451,x79452)),x79455),x79453)+E(f335(f335(f188(x79451,x79452),x79453),x79454),x79455) % 186.01/186.04 [8274]~P110(x82741)+P1(f335(f335(f244(f934(x82741,a922)),f311(x82741,x82742,x82743)),f311(x82741,x82744,x82745)))+~P1(f335(f335(f243(x82741),x82744),x82745))+P1(f335(f335(f243(x82741),x82742),x82743)) % 186.01/186.04 [8369]~P110(x83691)+P1(f335(f335(f243(f934(x83691,a922)),f311(x83691,x83692,x83693)),f311(x83691,x83694,x83695)))+~P1(f335(f335(f243(x83691),x83693),x83695))+~P1(f335(f335(f243(x83691),x83694),x83692)) % 186.01/186.04 [8488]~P109(x84881)+P1(f335(f335(f243(x84881),x84882),x84883))+P1(f335(f335(f243(x84881),x84884),x84883))+~P1(f335(f335(f243(f934(x84881,a922)),f335(f310(x84881,x84883),x84882)),f335(f310(x84881,x84884),x84885))) % 186.01/186.04 [8489]~P109(x84891)+P1(f335(f335(f243(x84891),x84892),x84893))+P1(f335(f335(f243(x84891),x84892),x84894))+~P1(f335(f335(f243(f934(x84891,a922)),f335(f310(x84891,x84893),x84892)),f335(f310(x84891,x84895),x84894))) % 186.01/186.04 [8722]~P110(x87221)+~P1(f335(f335(f243(f934(x87221,a922)),f311(x87221,x87224,x87222)),f311(x87221,x87225,x87223)))+P1(f335(f335(f243(x87221),x87222),x87223))+~P1(f335(f335(f243(x87221),x87224),x87222)) % 186.01/186.04 [8723]~P110(x87231)+~P1(f335(f335(f244(f934(x87231,a922)),f311(x87231,x87234,x87232)),f311(x87231,x87235,x87233)))+P1(f335(f335(f243(x87231),x87232),x87233))+~P1(f335(f335(f243(x87231),x87234),x87232)) % 186.01/186.04 [8724]~P110(x87241)+~P1(f335(f335(f243(f934(x87241,a922)),f311(x87241,x87243,x87244)),f311(x87241,x87242,x87245)))+P1(f335(f335(f243(x87241),x87242),x87243))+~P1(f335(f335(f243(x87241),x87243),x87244)) % 186.01/186.04 [8725]~P110(x87251)+~P1(f335(f335(f244(f934(x87251,a922)),f311(x87251,x87253,x87254)),f311(x87251,x87252,x87255)))+P1(f335(f335(f243(x87251),x87252),x87253))+~P1(f335(f335(f243(x87251),x87253),x87254)) % 186.01/186.04 [6277]~P18(x62772,x62775,x62773)+E(x62771,f195(f934(x62772,a922)))+~P1(f335(f67(x62772),x62771))+E(f335(x62773,f335(f335(f317(x62772),x62774),x62771)),f335(f335(x62775,x62774),f335(x62773,x62771))) % 186.01/186.04 [7045]~E(x70451,x70452)+~E(f335(f335(f108(f934(x70453,a922)),x70454),x70455),f195(f934(x70453,a922)))+~P1(f335(f335(f337(x70453),x70452),x70455))+~P1(f335(f335(f337(x70453),x70451),x70454)) % 186.01/186.04 [7123]~P19(x71232,x71235,x71231)+~P1(f335(f67(x71232),x71234))+E(f335(x71231,f335(f335(f317(x71232),x71233),x71234)),f335(f335(f70(x71232,x71232,x71235),x71233),x71234))+P1(f335(f335(f337(x71232),x71233),x71234)) % 186.01/186.04 [7188]~P76(x71882)+~P1(f335(f67(x71881),x71885))+E(f335(f335(f6(x71881,x71882),x71883),f335(f335(f317(x71881),x71884),x71885)),f335(f335(f86(x71882),f335(x71883,x71884)),f335(f335(f6(x71881,x71882),x71883),x71885)))+P1(f335(f335(f337(x71881),x71884),x71885)) % 186.01/186.04 [7190]~P72(x71902)+~P1(f335(f67(x71901),x71905))+E(f335(f335(f9(x71901,x71902),x71903),f335(f335(f317(x71901),x71904),x71905)),f335(f335(f87(x71902),f335(x71903,x71904)),f335(f335(f9(x71901,x71902),x71903),x71905)))+P1(f335(f335(f337(x71901),x71904),x71905)) % 186.01/186.04 [7693]~P19(x76932,x76935,x76931)+~P1(f335(f67(x76932),x76934))+E(f335(x76931,f335(f335(f317(x76932),x76933),x76934)),x76933)+~E(f335(f335(f23(f934(x76932,a922)),x76934),f335(f335(f317(x76932),x76933),f195(f934(x76932,a922)))),f195(f934(x76932,a922))) % 186.01/186.04 [8047]~P97(x80471)+~P1(f335(f335(f243(x80471),x80473),x80475))+~P1(f335(f335(f243(x80471),x80472),x80474))+P1(f335(f335(f243(x80471),f335(f335(f108(x80471),x80472),x80473)),f335(f335(f108(x80471),x80474),x80475))) % 186.01/186.04 [8048]~P103(x80481)+~P1(f335(f335(f243(x80481),x80483),x80485))+~P1(f335(f335(f243(x80481),x80482),x80484))+P1(f335(f335(f243(x80481),f335(f335(f117(x80481),x80482),x80483)),f335(f335(f117(x80481),x80484),x80485))) % 186.01/186.04 [8049]~P86(x80491)+~P1(f335(f335(f243(x80491),x80493),x80495))+~P1(f335(f335(f243(x80491),x80492),x80494))+P1(f335(f335(f243(x80491),f335(f335(f86(x80491),x80492),x80493)),f335(f335(f86(x80491),x80494),x80495))) % 186.01/186.04 [8050]~P109(x80501)+~P1(f335(f335(f243(x80501),x80503),x80505))+~P1(f335(f335(f243(x80501),x80502),x80504))+P1(f335(f335(f243(x80501),f335(f335(f241(x80501),x80502),x80503)),f335(f335(f241(x80501),x80504),x80505))) % 186.01/186.04 [8051]~P109(x80511)+~P1(f335(f335(f243(x80511),x80513),x80515))+~P1(f335(f335(f243(x80511),x80512),x80514))+P1(f335(f335(f243(x80511),f335(f335(f242(x80511),x80512),x80513)),f335(f335(f242(x80511),x80514),x80515))) % 186.01/186.04 [8052]~P88(x80521)+~P1(f335(f335(f243(x80521),x80523),x80525))+~P1(f335(f335(f244(x80521),x80522),x80524))+P1(f335(f335(f244(x80521),f335(f335(f86(x80521),x80522),x80523)),f335(f335(f86(x80521),x80524),x80525))) % 186.01/186.04 [8053]~P88(x80531)+~P1(f335(f335(f243(x80531),x80532),x80534))+~P1(f335(f335(f244(x80531),x80533),x80535))+P1(f335(f335(f244(x80531),f335(f335(f86(x80531),x80532),x80533)),f335(f335(f86(x80531),x80534),x80535))) % 186.01/186.04 [8054]~P88(x80541)+~P1(f335(f335(f244(x80541),x80543),x80545))+~P1(f335(f335(f244(x80541),x80542),x80544))+P1(f335(f335(f244(x80541),f335(f335(f86(x80541),x80542),x80543)),f335(f335(f86(x80541),x80544),x80545))) % 186.01/186.04 [8190]~P143(x81905)+E(x81901,x81902)+E(x81903,x81904)+~E(f335(f335(f86(x81905),f335(f335(f87(x81905),x81903),x81901)),f335(f335(f87(x81905),x81904),x81902)),f335(f335(f86(x81905),f335(f335(f87(x81905),x81903),x81902)),f335(f335(f87(x81905),x81904),x81901))) % 186.01/186.04 [8389]~P109(x83894)+~P1(f335(f144(x83891),x83893))+P1(f335(f335(f337(x83891),x83892),f335(f179(x83891),x83893)))+P1(f335(f144(x83891),f335(f335(f155(x83891,x83894,x83895),x83892),x83893))) % 186.01/186.04 [8536]~P5(x85361)+E(f335(f335(f23(x85361),f335(f335(f6(a927,x85361),x85362),f335(f310(a927,x85363),x85364))),f335(f335(f6(a927,x85361),x85362),f335(f310(a927,x85363),x85365))),f335(f335(f6(a927,x85361),x85362),f335(f310(a927,x85365),x85364)))+~P1(f335(f335(f243(a927),x85365),x85364))+~P1(f335(f335(f243(a927),x85363),x85365)) % 186.01/186.04 [8537]~P76(x85371)+E(f335(f335(f86(x85371),f335(f335(f6(a927,x85371),x85372),f335(f310(a927,x85373),x85374))),f335(f335(f6(a927,x85371),x85372),f335(f310(a927,x85374),x85375))),f335(f335(f6(a927,x85371),x85372),f335(f310(a927,x85373),x85375)))+~P1(f335(f335(f243(a927),x85374),x85375))+~P1(f335(f335(f243(a927),x85373),x85374)) % 186.01/186.04 [8865]~P67(x88652)+E(x88651,f2(x88652))+E(x88653,f2(x88652))+E(f335(f335(f299(x88652),f335(f335(f23(x88652),f335(f335(f87(x88652),x88654),x88651)),f335(f335(f87(x88652),x88655),x88653))),f335(f335(f87(x88652),x88653),x88651)),f335(f335(f23(x88652),f335(f335(f299(x88652),x88654),x88653)),f335(f335(f299(x88652),x88655),x88651))) % 186.01/186.04 [8866]~P67(x88662)+E(x88661,f2(x88662))+E(x88663,f2(x88662))+E(f335(f335(f299(x88662),f335(f335(f86(x88662),f335(f335(f87(x88662),x88664),x88661)),f335(f335(f87(x88662),x88665),x88663))),f335(f335(f87(x88662),x88663),x88661)),f335(f335(f86(x88662),f335(f335(f299(x88662),x88664),x88663)),f335(f335(f299(x88662),x88665),x88661))) % 186.01/186.04 [8875]~E(x88752,f335(x88753,x88751))+E(x88751,f462(x88752,x88753,x88754,x88755))+~P26(x88755,x88754,x88753,f250(f934(x88755,a922)))+~P1(f335(f335(f337(x88754),x88752),f335(f318(x88755,x88754,x88753),f250(f934(x88755,a922))))) % 186.01/186.04 [9092]~P113(x90921)+~P1(f335(f335(f244(x90921),f335(f81(x90921),x90922)),x90924))+P1(f335(f335(f244(x90921),f335(f335(f87(x90921),f335(f81(x90921),x90922)),f335(f81(x90921),x90923))),f335(f335(f87(x90921),x90924),x90925)))+~P1(f335(f335(f244(x90921),f335(f81(x90921),x90923)),x90925)) % 186.01/186.04 [9207]~P26(x92071,x92073,x92075,x92072)+~P1(f335(f67(x92073),x92074))+P1(f335(f335(f243(a927),f335(f41(x92071),x92072)),f335(f41(x92073),x92074)))+~P1(f335(f335(f243(f934(x92073,a922)),f335(f318(x92071,x92073,x92075),x92072)),x92074)) % 186.01/186.04 [9274]~P76(x92742)+~P26(x92741,x92741,x92744,x92745)+~P1(f335(f67(x92741),x92745))+E(f335(f335(f6(x92741,x92742),f335(f78(x92741,x92742,x92741,x92743),x92744)),x92745),f335(f335(f6(x92741,x92742),x92743),f335(f318(x92741,x92741,x92744),x92745))) % 186.01/186.04 [9275]~P72(x92752)+~P26(x92751,x92751,x92754,x92755)+~P1(f335(f67(x92751),x92755))+E(f335(f335(f9(x92751,x92752),f335(f78(x92751,x92752,x92751,x92753),x92754)),x92755),f335(f335(f9(x92751,x92752),x92753),f335(f318(x92751,x92751,x92754),x92755))) % 186.01/186.04 [9393]~P38(x93931,x93932)+~P1(f335(f335(f337(x93931),x93933),x93934))+~P1(f335(f335(f337(x93931),x93935),x93934))+~P1(f335(f335(f337(f933(x93931,x93931)),f335(f335(f260(x93931,x93931),x93935),f914(x93932,x93931,x93934))),x93932)) % 186.01/186.04 [9427]~P26(x94272,x94273,x94275,x94271)+E(x94271,f195(f934(x94272,a922)))+E(f335(f318(x94273,x94272,f496(x94274,x94273,x94272,x94271)),x94274),x94271)+~P1(f335(f335(f243(f934(x94273,a922)),f335(f318(x94272,x94273,x94275),x94271)),x94274)) % 186.01/186.04 [9908]~P109(x99085)+~P6(x99085)+P1(f335(f335(f337(x99081),f675(x99082,x99083,x99081,x99084,x99085)),x99083))+~P1(f335(f335(f244(x99085),x99084),f335(f335(f45(x99081,x99085),x99083),x99082))) % 186.01/186.04 [9913]~P109(x99131)+~P6(x99131)+P1(f335(f335(f244(x99131),x99132),f335(x99133,f675(x99133,x99134,x99135,x99132,x99131))))+~P1(f335(f335(f244(x99131),x99132),f335(f335(f45(x99135,x99131),x99134),x99133))) % 186.01/186.04 [9993]~P70(x99931)+~P1(f335(f72(x99931,x99931,f87(x99931),x99932,x99933),x99935))+P1(f335(f335(f337(x99931),x99932),x99933))+P1(f335(f72(x99931,x99931,f87(x99931),x99934,f335(f335(f317(x99931),x99932),x99933)),f335(f335(f87(x99931),x99934),x99935))) % 186.01/186.04 [10210]~P76(x102102)+~P1(f335(f67(x102101),x102105))+E(f335(f335(f6(x102101,x102102),f335(f335(f7(x102101,x102102,x102102),f335(f335(f18(x102101,x102102,f934(x102102,x102102)),f335(f335(f8(a922,f934(x102102,f934(x102102,x102102)),x102101),f103(x102102)),f335(a332,x102103))),x102104)),f2(x102102))),x102105),f2(x102102))+P1(f335(f335(f337(x102101),x102103),x102105)) % 186.01/186.04 [10211]~P72(x102112)+~P1(f335(f67(x102111),x102115))+E(f335(f335(f9(x102111,x102112),f335(f335(f7(x102111,x102112,x102112),f335(f335(f18(x102111,x102112,f934(x102112,x102112)),f335(f335(f8(a922,f934(x102112,f934(x102112,x102112)),x102111),f103(x102112)),f335(a332,x102113))),x102114)),f84(x102112))),x102115),f84(x102112))+P1(f335(f335(f337(x102111),x102113),x102115)) % 186.01/186.04 [10212]~P76(x102122)+~P1(f335(f67(x102121),x102125))+E(f335(f335(f6(x102121,x102122),f335(f335(f7(x102121,x102122,x102122),f335(f335(f18(x102121,x102122,f934(x102122,x102122)),f335(f335(f8(a922,f934(x102122,f934(x102122,x102122)),x102121),f103(x102122)),f335(a332,x102123))),x102124)),f2(x102122))),x102125),f335(x102124,x102123))+~P1(f335(f335(f337(x102121),x102123),x102125)) % 186.01/186.04 [10213]~P72(x102132)+~P1(f335(f67(x102131),x102135))+E(f335(f335(f9(x102131,x102132),f335(f335(f7(x102131,x102132,x102132),f335(f335(f18(x102131,x102132,f934(x102132,x102132)),f335(f335(f8(a922,f934(x102132,f934(x102132,x102132)),x102131),f103(x102132)),f335(a332,x102133))),x102134)),f84(x102132))),x102135),f335(x102134,x102133))+~P1(f335(f335(f337(x102131),x102133),x102135)) % 186.01/186.04 [10270]~P76(x102702)+~P1(f335(f67(x102701),x102705))+E(f335(f335(f6(x102701,x102702),f335(f335(f7(x102701,x102702,x102702),f335(f335(f18(x102701,x102702,f934(x102702,x102702)),f335(f335(f8(a922,f934(x102702,f934(x102702,x102702)),x102701),f103(x102702)),f335(f335(f7(x102701,x102701,a922),a332),x102703))),x102704)),f2(x102702))),x102705),f2(x102702))+P1(f335(f335(f337(x102701),x102703),x102705)) % 186.01/186.04 [10271]~P72(x102712)+~P1(f335(f67(x102711),x102715))+E(f335(f335(f9(x102711,x102712),f335(f335(f7(x102711,x102712,x102712),f335(f335(f18(x102711,x102712,f934(x102712,x102712)),f335(f335(f8(a922,f934(x102712,f934(x102712,x102712)),x102711),f103(x102712)),f335(f335(f7(x102711,x102711,a922),a332),x102713))),x102714)),f84(x102712))),x102715),f84(x102712))+P1(f335(f335(f337(x102711),x102713),x102715)) % 186.01/186.04 [10273]~P76(x102732)+~P1(f335(f67(x102731),x102735))+E(f335(f335(f6(x102731,x102732),f335(f335(f7(x102731,x102732,x102732),f335(f335(f18(x102731,x102732,f934(x102732,x102732)),f335(f335(f8(a922,f934(x102732,f934(x102732,x102732)),x102731),f103(x102732)),f335(f335(f7(x102731,x102731,a922),a332),x102733))),x102734)),f2(x102732))),x102735),f335(x102734,x102733))+~P1(f335(f335(f337(x102731),x102733),x102735)) % 186.01/186.04 [10274]~P72(x102742)+~P1(f335(f67(x102741),x102745))+E(f335(f335(f9(x102741,x102742),f335(f335(f7(x102741,x102742,x102742),f335(f335(f18(x102741,x102742,f934(x102742,x102742)),f335(f335(f8(a922,f934(x102742,f934(x102742,x102742)),x102741),f103(x102742)),f335(f335(f7(x102741,x102741,a922),a332),x102743))),x102744)),f84(x102742))),x102745),f335(x102744,x102743))+~P1(f335(f335(f337(x102741),x102743),x102745)) % 186.01/186.04 [8046]~P5(x80462)+~P1(f335(f67(x80461),x80464))+E(f335(f335(f6(x80461,x80462),x80463),f335(f335(f23(f934(x80461,a922)),x80464),f335(f335(f317(x80461),x80465),f195(f934(x80461,a922))))),f335(f335(f6(x80461,x80462),x80463),x80464))+P1(f335(f335(f337(x80461),x80465),x80464)) % 186.01/186.04 [8544]~P112(x85442)+~P1(f335(f67(x85441),x85444))+E(f335(f335(f6(x85441,x85442),x85443),f335(f335(f23(f934(x85441,a922)),x85444),f335(f335(f317(x85441),x85445),f195(f934(x85441,a922))))),f335(f335(f23(x85442),f335(f335(f6(x85441,x85442),x85443),x85444)),f335(x85443,x85445)))+~P1(f335(f335(f337(x85441),x85445),x85444)) % 186.01/186.04 [8545]~P5(x85452)+~P1(f335(f67(x85451),x85454))+E(f335(f335(f6(x85451,x85452),x85453),f335(f335(f23(f934(x85451,a922)),x85454),f335(f335(f317(x85451),x85455),f195(f934(x85451,a922))))),f335(f335(f23(x85452),f335(f335(f6(x85451,x85452),x85453),x85454)),f335(x85453,x85455)))+~P1(f335(f335(f337(x85451),x85455),x85454)) % 186.01/186.04 [8574]~P5(x85741)+~P1(f335(f67(x85742),x85744))+E(f335(f335(f23(x85741),f335(f335(f6(x85742,x85741),x85743),x85744)),f335(f335(f6(x85742,x85741),x85743),x85745)),f335(f335(f6(x85742,x85741),x85743),f335(f335(f23(f934(x85742,a922)),x85744),x85745)))+~P1(f335(f335(f243(f934(x85742,a922)),x85745),x85744)) % 186.01/186.04 [8593]P1(f335(f67(x85931),f335(x85932,x85933)))+~P1(f335(f67(x85934),x85935))+~P1(f335(f335(f337(x85934),x85933),x85935))+~P1(f335(f67(x85931),f335(f335(f45(x85934,f934(x85931,a922)),x85935),x85932))) % 186.01/186.04 [9048]~P9(x90481,x90485,x90484)+~E(f335(f293(x90481,x90481,x90484),f335(f335(f317(x90481),x90482),f195(f934(x90481,a922)))),f335(f293(x90481,x90481,x90484),f335(f335(f317(x90481),x90483),f195(f934(x90481,a922)))))+~P1(f335(f335(f337(x90481),x90483),x90485))+P1(f335(f335(f337(f933(x90481,x90481)),f335(f335(f260(x90481,x90481),x90482),x90483)),x90484)) % 186.01/186.04 [9350]~P1(f335(x93501,x93505))+P1(f335(x93501,f887(x93501,x93502,x93503,x93504)))+P1(f335(x93501,f884(x93501,x93502,x93503,x93504)))+~P1(f335(f335(f337(x93504),x93505),f335(f335(f117(f934(x93504,a922)),x93503),x93502))) % 186.01/186.04 [9531]~P1(f335(x95311,x95315))+P1(f335(x95311,f884(x95311,x95312,x95313,x95314)))+P1(f335(f335(f337(x95314),f887(x95311,x95312,x95313,x95314)),x95312))+~P1(f335(f335(f337(x95314),x95315),f335(f335(f117(f934(x95314,a922)),x95313),x95312))) % 186.01/186.04 [9532]~P1(f335(x95321,x95325))+P1(f335(x95321,f887(x95321,x95322,x95323,x95324)))+P1(f335(f335(f337(x95324),f884(x95321,x95322,x95323,x95324)),x95323))+~P1(f335(f335(f337(x95324),x95325),f335(f335(f117(f934(x95324,a922)),x95323),x95322))) % 186.01/186.04 [9536]P1(f335(x95361,x95362))+~P1(f335(x95361,f886(x95361,x95363,x95364,x95365)))+~P1(f335(x95361,f885(x95361,x95363,x95364,x95365)))+~P1(f335(f335(f337(x95365),x95362),f335(f335(f117(f934(x95365,a922)),x95364),x95363))) % 186.01/186.04 [9541]~P39(x95411,x95414)+~P1(f335(f335(f337(f933(x95411,x95411)),f335(f335(f260(x95411,x95411),x95412),x95415)),x95414))+P1(f335(f335(f337(f933(x95411,x95411)),f335(f335(f260(x95411,x95411),x95412),x95413)),x95414))+~P1(f335(f335(f337(f933(x95411,x95411)),f335(f335(f260(x95411,x95411),x95415),x95413)),x95414)) % 186.01/186.04 [9580]E(x95801,x95802)+~P1(f335(f335(f337(f933(x95803,x95803)),f335(f335(f260(x95803,x95803),x95801),x95802)),f315(x95803,x95805)))+P1(f335(f335(f337(x95803),x95801),x95804))+~P1(f335(f335(f243(f934(f933(x95803,x95803),a922)),x95805),f335(f335(f262(x95803,x95803),x95804),f335(f16(f934(x95803,a922),x95803),x95804)))) % 186.01/186.04 [9598]P1(f335(x95981,x95982))+~P1(f335(x95981,f885(x95981,x95984,x95985,x95983)))+P1(f335(f335(f337(x95983),f886(x95981,x95984,x95985,x95983)),x95984))+~P1(f335(f335(f337(x95983),x95982),f335(f335(f117(f934(x95983,a922)),x95985),x95984))) % 186.01/186.04 [9599]P1(f335(x95991,x95992))+~P1(f335(x95991,f886(x95991,x95994,x95995,x95993)))+P1(f335(f335(f337(x95993),f885(x95991,x95994,x95995,x95993)),x95995))+~P1(f335(f335(f337(x95993),x95992),f335(f335(f117(f934(x95993,a922)),x95995),x95994))) % 186.01/186.04 [9664]P1(f335(x96641,x96642))+P1(f335(f335(f337(x96643),f886(x96641,x96644,x96645,x96643)),x96644))+P1(f335(f335(f337(x96643),f885(x96641,x96644,x96645,x96643)),x96645))+~P1(f335(f335(f337(x96643),x96642),f335(f335(f117(f934(x96643,a922)),x96645),x96644))) % 186.01/186.04 [9666]~P1(f335(x96662,x96665))+P1(f335(f335(f337(x96661),f887(x96662,x96663,x96664,x96661)),x96663))+P1(f335(f335(f337(x96661),f884(x96662,x96663,x96664,x96661)),x96664))+~P1(f335(f335(f337(x96661),x96665),f335(f335(f117(f934(x96661,a922)),x96664),x96663))) % 186.01/186.04 [9814]~P9(x98141,x98145,x98144)+~P1(f335(f335(f337(x98141),x98143),x98145))+P1(f335(f335(f337(f933(x98141,x98141)),f335(f335(f260(x98141,x98141),x98142),x98143)),x98144))+~P1(f335(f335(f243(f934(x98141,a922)),f335(f293(x98141,x98141,x98144),f335(f335(f317(x98141),x98143),f195(f934(x98141,a922))))),f335(f293(x98141,x98141,x98144),f335(f335(f317(x98141),x98142),f195(f934(x98141,a922)))))) % 186.01/186.04 [9943]~P109(x99435)+~P6(x99435)+P1(f335(f335(f337(x99431),f655(x99432,x99433,x99434,x99431,x99435)),x99434))+~P1(f335(f335(f244(x99435),f335(f335(f46(x99431,x99435),x99434),x99433)),x99432)) % 186.01/186.04 [9976]~P86(x99765)+~P82(x99765)+P1(f335(f335(f337(x99761),f719(x99762,x99763,x99764,x99761,x99765)),f335(f179(x99761),x99764)))+P1(f335(f335(f243(x99765),f335(f172(x99765),f335(f335(f161(x99761,x99765),x99763),x99764))),f335(f172(x99765),f335(f335(f161(x99761,x99765),x99762),x99764)))) % 186.01/186.04 [10085]~P109(x100851)+~P6(x100851)+P1(f335(f335(f244(x100851),f335(x100852,f655(x100853,x100852,x100854,x100855,x100851))),x100853))+~P1(f335(f335(f244(x100851),f335(f335(f46(x100855,x100851),x100854),x100852)),x100853)) % 186.01/186.04 [10228]~P86(x102281)+~P82(x102281)+~P1(f335(f335(f243(x102281),f335(x102283,f719(x102285,x102283,x102284,x102282,x102281))),f335(x102285,f719(x102285,x102283,x102284,x102282,x102281))))+P1(f335(f335(f243(x102281),f335(f172(x102281),f335(f335(f161(x102282,x102281),x102283),x102284))),f335(f172(x102281),f335(f335(f161(x102282,x102281),x102285),x102284)))) % 186.01/186.04 [8888]~P76(x88881)+~P1(f335(f67(x88884),x88885))+~P1(f335(f335(f337(x88884),x88883),x88885))+E(f335(f335(f86(x88881),f335(x88882,x88883)),f335(f335(f6(x88884,x88881),x88882),f335(f335(f23(f934(x88884,a922)),x88885),f335(f335(f317(x88884),x88883),f195(f934(x88884,a922)))))),f335(f335(f6(x88884,x88881),x88882),x88885)) % 186.01/186.04 [8889]~P72(x88891)+~P1(f335(f67(x88894),x88895))+~P1(f335(f335(f337(x88894),x88893),x88895))+E(f335(f335(f87(x88891),f335(x88892,x88893)),f335(f335(f9(x88894,x88891),x88892),f335(f335(f23(f934(x88894,a922)),x88895),f335(f335(f317(x88894),x88893),f195(f934(x88894,a922)))))),f335(f335(f9(x88894,x88891),x88892),x88895)) % 186.01/186.04 [8949]~P19(x89491,x89494,x89495)+~P1(f335(f67(x89491),x89492))+E(f335(f335(f23(f934(x89491,a922)),x89492),f335(f335(f317(x89491),x89493),f195(f934(x89491,a922)))),f195(f934(x89491,a922)))+E(f335(f335(x89494,x89493),f335(x89495,f335(f335(f23(f934(x89491,a922)),x89492),f335(f335(f317(x89491),x89493),f195(f934(x89491,a922)))))),f335(x89495,f335(f335(f317(x89491),x89493),x89492))) % 186.01/186.04 [9329]~P72(x93291)+~P1(f335(f67(x93292),x93295))+~P1(f335(f67(x93292),x93294))+E(f335(f335(f87(x93291),f335(f335(f9(x93292,x93291),x93293),f335(f335(f117(f934(x93292,a922)),x93294),x93295))),f335(f335(f9(x93292,x93291),x93293),f335(f335(f108(f934(x93292,a922)),x93294),x93295))),f335(f335(f87(x93291),f335(f335(f9(x93292,x93291),x93293),x93294)),f335(f335(f9(x93292,x93291),x93293),x93295))) % 186.01/186.04 [9330]~P76(x93301)+~P1(f335(f67(x93302),x93305))+~P1(f335(f67(x93302),x93304))+E(f335(f335(f86(x93301),f335(f335(f6(x93302,x93301),x93303),f335(f335(f117(f934(x93302,a922)),x93304),x93305))),f335(f335(f6(x93302,x93301),x93303),f335(f335(f108(f934(x93302,a922)),x93304),x93305))),f335(f335(f86(x93301),f335(f335(f6(x93302,x93301),x93303),x93304)),f335(f335(f6(x93302,x93301),x93303),x93305))) % 186.01/186.04 [9466]~P5(x94661)+~P1(f335(f67(x94662),x94665))+~P1(f335(f67(x94662),x94664))+E(f335(f335(f23(x94661),f335(f335(f86(x94661),f335(f335(f6(x94662,x94661),x94663),x94664)),f335(f335(f6(x94662,x94661),x94663),x94665))),f335(f335(f6(x94662,x94661),x94663),f335(f335(f108(f934(x94662,a922)),x94664),x94665))),f335(f335(f6(x94662,x94661),x94663),f335(f335(f117(f934(x94662,a922)),x94664),x94665))) % 186.01/186.04 [9676]~P26(x96761,x96762,x96763,x96765)+~P26(x96761,x96762,x96763,x96764)+P26(x96761,x96762,x96763,f335(f335(f117(f934(x96761,a922)),x96764),x96765))+~E(f335(f335(f108(f934(x96762,a922)),f335(f318(x96761,x96762,x96763),f335(f335(f23(f934(x96761,a922)),x96764),x96765))),f335(f318(x96761,x96762,x96763),f335(f335(f23(f934(x96761,a922)),x96765),x96764))),f195(f934(x96762,a922))) % 186.01/186.04 [9789]E(x97891,f2(a1))+~P1(f335(f335(f244(a1),f2(a1)),x97893))+~P1(f335(f55(x97892,x97891),f335(f335(f260(a1,a1),x97894),x97895)))+P1(f335(f55(x97892,f335(f335(f87(a1),x97891),x97893)),f335(f335(f260(a1,a1),f335(f335(f42(a1),x97894),x97893)),f335(f335(f86(a1),f335(f335(f87(a1),x97891),f51(a1,x97894,x97893))),x97895)))) % 186.01/186.04 [9797]~P1(f335(f335(f244(a927),f2(a927)),x97973))+~P1(f335(f335(f244(a927),f2(a927)),x97972))+~P1(f335(f54(x97971,x97972),f335(f335(f260(a927,a927),x97974),x97975)))+P1(f335(f54(x97971,f335(f335(f87(a927),x97972),x97973)),f335(f335(f260(a927,a927),f335(f335(f42(a927),x97974),x97973)),f335(f335(f86(a927),f335(f335(f87(a927),x97972),f51(a927,x97974,x97973))),x97975)))) % 186.01/186.04 [9846]~P72(x98461)+~P1(f335(f67(x98462),x98465))+~P1(f335(f67(x98462),x98464))+E(f335(f335(f87(x98461),f335(f335(f335(f71(x98461,x98462,f87(x98461)),x98463),f84(x98461)),f335(f335(f117(f934(x98462,a922)),x98464),x98465))),f335(f335(f335(f71(x98461,x98462,f87(x98461)),x98463),f84(x98461)),f335(f335(f108(f934(x98462,a922)),x98464),x98465))),f335(f335(f87(x98461),f335(f335(f335(f71(x98461,x98462,f87(x98461)),x98463),f84(x98461)),x98464)),f335(f335(f335(f71(x98461,x98462,f87(x98461)),x98463),f84(x98461)),x98465))) % 186.01/186.04 [9848]~E(f335(f335(f182(x98481),x98485),x98482),f335(f335(f182(x98481),x98485),x98483))+P1(f335(f335(f337(f933(f928(x98481),f928(x98481))),f335(f335(f260(f928(x98481),f928(x98481)),x98482),x98483)),f154(x98481,x98484)))+~P1(f335(f335(f244(a927),x98485),f335(f335(f241(a927),f335(f196(f928(x98481)),x98482)),f335(f196(f928(x98481)),x98483))))+~P1(f335(f335(f337(f933(x98481,x98481)),f335(f335(f260(x98481,x98481),f335(f335(f171(x98481),x98482),x98485)),f335(f335(f171(x98481),x98483),x98485))),x98484)) % 186.01/186.04 [9965]~P86(x99655)+~P146(x99655)+P1(f335(f335(f337(x99651),f439(x99652,x99653,x99654,x99651,x99655)),x99654))+P1(f335(f335(f243(x99655),f335(f335(f6(x99651,x99655),x99653),x99654)),f335(f335(f87(x99655),f335(f107(x99655),f335(f41(x99651),x99654))),x99652))) % 186.01/186.04 [10144]~P86(x101441)+~P146(x101441)+~P1(f335(f335(f243(x101441),f335(x101443,f439(x101445,x101443,x101444,x101442,x101441))),x101445))+P1(f335(f335(f243(x101441),f335(f335(f6(x101442,x101441),x101443),x101444)),f335(f335(f87(x101441),f335(f107(x101441),f335(f41(x101442),x101444))),x101445))) % 186.01/186.04 [8917]E(f335(f335(f141(x89171),x89172),x89173),f335(f335(f141(x89171),x89174),x89175))+~E(f335(f335(f182(x89171),f335(f196(f928(x89171)),x89172)),x89174),x89172)+~E(f335(f335(f141(x89171),f335(f335(f145(x89171),f335(f196(f928(x89171)),x89172)),x89174)),x89175),x89173)+P1(f335(f335(f243(a927),f335(f196(f928(x89171)),x89174)),f335(f196(f928(x89171)),x89172))) % 186.01/186.04 [9047]E(f335(f335(f141(x90471),x90472),x90473),f335(f335(f141(x90471),x90474),x90475))+~E(f335(f335(f182(x90471),f335(f196(f928(x90471)),x90472)),x90474),x90472)+~E(x90473,f335(f335(f141(x90471),f335(f335(f145(x90471),f335(f196(f928(x90471)),x90472)),x90474)),x90475))+~P1(f335(f335(f243(a927),f335(f196(f928(x90471)),x90472)),f335(f196(f928(x90471)),x90474))) % 186.01/186.04 [10293]~P1(f335(x102935,x102934))+~P1(f335(f67(x102932),f335(f270(x102932),x102935)))+P1(f335(f67(x102931),f335(f270(x102931),f335(f335(f7(x102931,x102932,a922),x102933),x102934))))+~P1(f335(f67(x102931),f335(f270(x102931),f335(f335(f8(f934(x102932,a922),a922,x102931),f93(x102932)),f335(f335(f8(f934(x102932,a922),f934(x102932,a922),x102931),f335(f18(x102932,a922,a922),f335(f335(f8(a922,f934(a922,a922),x102932),a333),x102935))),x102933))))) % 186.01/186.04 [10365]~P1(f335(f67(x103652),x103655))+~P1(f335(f335(f337(x103652),x103654),x103655))+P1(f335(f67(x103651),f335(f270(x103651),f335(f335(f7(x103651,x103652,a922),x103653),x103654))))+~P1(f335(f67(x103651),f335(f270(x103651),f335(f335(f8(f934(x103652,a922),a922,x103651),f93(x103652)),f335(f335(f8(f934(x103652,a922),f934(x103652,a922),x103651),f335(f18(x103652,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103652),a333),f335(f335(f7(x103652,f934(x103652,a922),a922),f337(x103652)),x103655)))),x103653))))) % 186.01/186.04 [8703]~P20(x87035,x87031,x87036,x87032)+E(f335(f78(x87031,x87031,x87031,f335(x87032,x87033)),f335(x87032,x87034)),f335(f78(x87031,x87031,x87031,f335(x87032,x87034)),f335(x87032,x87033)))+~P1(f335(f67(x87035),x87034))+~P1(f335(f67(x87035),x87033)) % 186.01/186.04 [8101]~P26(x81011,x81012,x81014,x81013)+~E(f335(x81014,x81016),x81015)+E(f335(f83(x81011,x81012,x81013,x81014),x81015),x81016)+~P1(f335(f335(f337(x81011),x81016),x81013)) % 186.01/186.04 [8102]~P26(x81021,x81022,x81024,x81023)+~E(f335(x81024,x81026),x81025)+E(f335(f97(x81021,x81022,x81023,x81024),x81025),x81026)+~P1(f335(f335(f337(x81021),x81026),x81023)) % 186.01/186.04 [8295]~P21(x82956,x82951,x82954,x82952)+E(f335(f78(x82951,x82951,x82951,f335(x82952,x82953)),f335(x82954,x82955)),f335(x82952,x82953))+~P1(f335(f67(x82956),x82953))+~P1(f335(f335(f337(x82956),x82955),x82953)) % 186.01/186.04 [9419]E(x94191,x94192)+~E(f335(f97(x94193,x94194,x94195,x94196),x94191),f335(f97(x94193,x94194,x94195,x94196),x94192))+~P1(f335(f335(f337(x94194),x94192),f335(f318(x94193,x94194,x94196),x94195)))+~P1(f335(f335(f337(x94194),x94191),f335(f318(x94193,x94194,x94196),x94195))) % 186.01/186.04 [9515]~P20(x95153,x95151,x95156,x95152)+E(f335(f78(x95151,x95151,x95151,f335(x95152,f335(f335(f23(f934(x95153,a922)),x95154),f335(f335(f317(x95153),x95155),f195(f934(x95153,a922)))))),f335(x95156,x95155)),f335(x95152,x95154))+~P1(f335(f67(x95153),x95154))+~P1(f335(f335(f337(x95153),x95155),x95154)) % 186.01/186.04 [7195]~P64(x71951)+~E(f51(x71951,x71953,x71954),f51(x71951,x71956,x71954))+~E(f51(x71951,x71952,x71954),f51(x71951,x71955,x71954))+E(f51(x71951,f335(f335(f23(x71951),x71952),x71953),x71954),f51(x71951,f335(f335(f23(x71951),x71955),x71956),x71954)) % 186.01/186.04 [7196]~P63(x71961)+~E(f51(x71961,x71963,x71964),f51(x71961,x71966,x71964))+~E(f51(x71961,x71962,x71964),f51(x71961,x71965,x71964))+E(f51(x71961,f335(f335(f87(x71961),x71962),x71963),x71964),f51(x71961,f335(f335(f87(x71961),x71965),x71966),x71964)) % 186.01/186.04 [7197]~P63(x71971)+~E(f51(x71971,x71973,x71974),f51(x71971,x71976,x71974))+~E(f51(x71971,x71972,x71974),f51(x71971,x71975,x71974))+E(f51(x71971,f335(f335(f86(x71971),x71972),x71973),x71974),f51(x71971,f335(f335(f86(x71971),x71975),x71976),x71974)) % 186.01/186.04 [7999]~P17(x79991,x79992,x79993)+~P1(f335(f67(x79991),x79996))+E(f335(f335(f70(x79991,x79992,x79993),x79994),f335(f335(f317(x79991),x79995),x79996)),f335(f335(f70(x79991,x79992,x79993),f335(f335(x79993,x79995),x79994)),x79996))+P1(f335(f335(f337(x79991),x79995),x79996)) % 186.01/186.04 [8060]~P6(x80601)+P1(f335(f335(f243(x80601),x80602),f335(x80603,x80604)))+~P1(f335(f335(f337(x80605),x80604),x80606))+~P1(f335(f335(f243(x80601),x80602),f335(f335(f46(x80605,x80601),x80606),x80603))) % 186.01/186.04 [8217]~P17(x82171,x82172,x82173)+~P1(f335(f67(x82171),x82176))+E(f335(f335(f70(x82171,x82172,x82173),x82174),f335(f335(f317(x82171),x82175),x82176)),f335(f335(x82173,x82175),f335(f335(f70(x82171,x82172,x82173),x82174),x82176)))+P1(f335(f335(f337(x82171),x82175),x82176)) % 186.01/186.04 [8313]~P109(x83133)+~P1(f335(x83132,x83135))+~P14(x83133,f335(f335(f161(x83131,x83133),x83134),x83136))+E(f335(f143(x83131,x83132),f335(f335(f155(x83131,x83133,x83134),x83135),x83136)),f335(f335(f155(x83131,x83133,x83134),x83135),f335(f143(x83131,x83132),x83136))) % 186.01/186.04 [8333]E(x83331,x83332)+E(x83333,f2(a1))+~P1(f335(f55(x83334,x83333),f335(f335(f260(a1,a1),x83335),x83332)))+~P1(f335(f55(x83334,x83333),f335(f335(f260(a1,a1),x83336),x83331))) % 186.01/186.04 [8334]E(x83341,x83342)+E(x83343,f2(a1))+~P1(f335(f55(x83344,x83343),f335(f335(f260(a1,a1),x83342),x83345)))+~P1(f335(f55(x83344,x83343),f335(f335(f260(a1,a1),x83341),x83346))) % 186.01/186.04 [8355]~P20(x83552,x83555,x83556,x83551)+~P1(f335(f67(x83552),x83554))+E(f335(x83551,f335(f335(f317(x83552),x83553),x83554)),f335(f78(x83555,x83555,x83555,f335(x83551,x83554)),f335(x83556,x83553)))+P1(f335(f335(f337(x83552),x83553),x83554)) % 186.01/186.04 [8577]~P21(x85775,x85771,x85776,x85772)+E(f335(f78(x85771,x85771,x85771,f335(x85772,x85773)),f335(x85772,x85774)),f335(x85772,x85773))+~P1(f335(f67(x85775),x85773))+~P1(f335(f335(f243(f934(x85775,a922)),x85774),x85773)) % 186.01/186.04 [9719]~P26(x97191,x97192,x97194,x97193)+~P1(f335(f335(f337(x97192),x97195),f335(f318(x97191,x97192,x97194),x97193)))+P1(f335(f335(f337(x97191),f335(f83(x97191,x97192,x97193,x97194),x97195)),x97196))+~P1(f335(f335(f243(f934(x97191,a922)),x97193),x97196)) % 186.01/186.04 [10096]~P76(x100962)+~E(f430(x100961,x100963,x100965,x100966,x100964,x100962),f431(x100961,x100963,x100965,x100966,x100964,x100962))+~P1(f335(f67(x100964),x100966))+E(f335(f335(f6(x100961,x100962),x100963),f335(f318(x100964,x100961,x100965),x100966)),f335(f335(f6(x100964,x100962),f335(f78(x100961,x100962,x100964,x100963),x100965)),x100966)) % 186.01/186.04 [10125]~P76(x101256)+E(f335(x101251,f430(x101252,x101253,x101251,x101254,x101255,x101256)),f335(x101251,f431(x101252,x101253,x101251,x101254,x101255,x101256)))+E(f335(f335(f6(x101252,x101256),x101253),f335(f318(x101255,x101252,x101251),x101254)),f335(f335(f6(x101255,x101256),f335(f78(x101252,x101256,x101255,x101253),x101251)),x101254))+~P1(f335(f67(x101255),x101254)) % 186.01/186.04 [10178]~P76(x101782)+~E(f335(x101783,f335(x101785,f431(x101781,x101783,x101785,x101786,x101784,x101782))),f2(x101782))+~P1(f335(f67(x101784),x101786))+E(f335(f335(f6(x101781,x101782),x101783),f335(f318(x101784,x101781,x101785),x101786)),f335(f335(f6(x101784,x101782),f335(f78(x101781,x101782,x101784,x101783),x101785)),x101786)) % 186.01/186.04 [10236]~P76(x102362)+~P1(f335(f67(x102364),x102366))+E(f335(f335(f6(x102361,x102362),x102363),f335(f318(x102364,x102361,x102365),x102366)),f335(f335(f6(x102364,x102362),f335(f78(x102361,x102362,x102364,x102363),x102365)),x102366))+P1(f335(f335(f337(x102364),f431(x102361,x102363,x102365,x102366,x102364,x102362)),x102366)) % 186.01/186.04 [10237]~P76(x102372)+~P1(f335(f67(x102374),x102376))+E(f335(f335(f6(x102371,x102372),x102373),f335(f318(x102374,x102371,x102375),x102376)),f335(f335(f6(x102374,x102372),f335(f78(x102371,x102372,x102374,x102373),x102375)),x102376))+P1(f335(f335(f337(x102374),f430(x102371,x102373,x102375,x102376,x102374,x102372)),x102376)) % 186.01/186.04 [10364]~P72(x103641)+~P1(f335(f67(x103642),x103646))+E(f335(f335(f335(f71(x103641,x103642,f87(x103641)),f335(f335(f18(x103642,f934(x103643,a922),x103641),f335(f335(f7(x103642,x103641,f934(f934(x103643,a922),x103641)),f335(f335(f8(f934(x103643,x103641),f934(x103641,f934(f934(x103643,a922),x103641)),x103642),f71(x103641,x103643,f87(x103641))),x103644)),f84(x103641))),x103645)),f84(x103641)),x103646),f335(f335(f335(f71(x103641,f933(x103642,x103643),f87(x103641)),f335(f265(x103642,x103643,x103641),x103644)),f84(x103641)),f335(f335(f262(x103642,x103643),x103646),x103645)))+P1(f335(f335(f337(x103642),f403(x103644,x103645,x103643,x103646,x103642,x103641)),x103646)) % 186.01/186.04 [10386]~P72(x103861)+~P1(f335(f67(x103862),x103866))+E(f335(f335(f335(f71(x103861,x103862,f87(x103861)),f335(f335(f18(x103862,f934(x103863,a922),x103861),f335(f335(f7(x103862,x103861,f934(f934(x103863,a922),x103861)),f335(f335(f8(f934(x103863,x103861),f934(x103861,f934(f934(x103863,a922),x103861)),x103862),f71(x103861,x103863,f87(x103861))),x103864)),f84(x103861))),x103865)),f84(x103861)),x103866),f335(f335(f335(f71(x103861,f933(x103862,x103863),f87(x103861)),f335(f265(x103862,x103863,x103861),x103864)),f84(x103861)),f335(f335(f262(x103862,x103863),x103866),x103865)))+~P1(f335(f67(x103863),f335(x103865,f403(x103864,x103865,x103863,x103866,x103862,x103861)))) % 186.01/186.04 [8487]~P21(x84872,x84875,x84876,x84871)+~P1(f335(f67(x84872),x84874))+~P1(f335(f67(x84872),x84873))+E(f335(x84871,f335(f335(f117(f934(x84872,a922)),x84873),x84874)),f335(f78(x84875,x84875,x84875,f335(x84871,x84873)),f335(x84871,x84874))) % 186.01/186.04 [8704]~P6(x87041)+P1(f335(f335(f243(x87041),f335(x87042,x87043)),x87044))+~P1(f335(f335(f337(x87045),x87043),x87046))+~P1(f335(f335(f243(x87041),f335(f335(f45(x87045,x87041),x87046),x87042)),x87044)) % 186.01/186.04 [9135]~P26(x91352,x91351,x91353,x91356)+E(f335(f335(f23(f934(x91351,a922)),f335(f318(x91352,x91351,x91353),x91354)),f335(f318(x91352,x91351,x91353),x91355)),f335(f318(x91352,x91351,x91353),f335(f335(f23(f934(x91352,a922)),x91354),x91355)))+~P1(f335(f335(f243(f934(x91352,a922)),x91355),x91356))+~P1(f335(f335(f243(f934(x91352,a922)),x91354),x91356)) % 186.01/186.04 [9136]~P26(x91362,x91361,x91363,x91366)+E(f335(f335(f108(f934(x91361,a922)),f335(f318(x91362,x91361,x91363),x91364)),f335(f318(x91362,x91361,x91363),x91365)),f335(f318(x91362,x91361,x91363),f335(f335(f108(f934(x91362,a922)),x91364),x91365)))+~P1(f335(f335(f243(f934(x91362,a922)),x91365),x91366))+~P1(f335(f335(f243(f934(x91362,a922)),x91364),x91366)) % 186.01/186.04 [9395]E(x93951,x93952)+~P56(x93953,x93954,x93955)+~P1(f335(f335(f337(f933(x93953,x93954)),f335(f335(f260(x93953,x93954),x93956),x93952)),x93955))+~P1(f335(f335(f337(f933(x93953,x93954)),f335(f335(f260(x93953,x93954),x93956),x93951)),x93955)) % 186.01/186.04 [10174]~P70(x101741)+~E(f335(x101743,f613(x101744,x101746,x101743,x101745,x101742,x101741)),f335(x101746,f613(x101744,x101746,x101743,x101745,x101742,x101741)))+~P1(f335(f67(x101742),x101745))+E(f335(f335(f335(f71(x101741,x101742,f87(x101741)),x101743),x101744),x101745),f335(f335(f335(f71(x101741,x101742,f87(x101741)),x101746),x101744),x101745)) % 186.01/186.04 [10234]~P70(x102341)+~P1(f335(f67(x102342),x102345))+E(f335(f335(f335(f71(x102341,x102342,f87(x102341)),x102343),x102344),x102345),f335(f335(f335(f71(x102341,x102342,f87(x102341)),x102346),x102344),x102345))+P1(f335(f335(f337(x102342),f613(x102344,x102343,x102346,x102345,x102342,x102341)),x102345)) % 186.01/186.04 [8931]~P70(x89311)+~P1(f335(f67(x89312),x89316))+P1(f335(f335(f337(x89312),x89315),x89316))+E(f335(f335(f335(f71(x89311,x89312,f87(x89311)),x89313),x89314),f335(f335(f317(x89312),x89315),x89316)),f335(f335(f87(x89311),f335(x89313,x89315)),f335(f335(f335(f71(x89311,x89312,f87(x89311)),x89313),x89314),x89316))) % 186.01/186.04 [8984]~P9(x89841,x89846,x89843)+~P12(x89841,f934(x89842,a922),x89843,x89845)+~P1(f335(f335(f337(x89841),x89844),x89846))+E(f335(f335(f45(x89841,f934(x89842,a922)),f335(f293(x89841,x89841,x89843),f335(f335(f317(x89841),x89844),f195(f934(x89841,a922))))),x89845),f335(x89845,x89844)) % 186.01/186.04 [9110]~P17(x91103,x91104,x91101)+~P1(f335(f67(x91103),x91106))+~P1(f335(f335(f337(x91103),x91102),x91106))+E(f335(f335(x91101,x91102),f335(f335(f70(x91103,x91104,x91101),x91105),f335(f335(f23(f934(x91103,a922)),x91106),f335(f335(f317(x91103),x91102),f195(f934(x91103,a922)))))),f335(f335(f70(x91103,x91104,x91101),x91105),x91106)) % 186.01/186.04 [9405]~P20(x94053,x94051,x94056,x94052)+~P1(f335(f67(x94053),x94055))+~P1(f335(f67(x94053),x94054))+E(f335(f78(x94051,x94051,x94051,f335(x94052,f335(f335(f117(f934(x94053,a922)),x94054),x94055))),f335(x94052,f335(f335(f108(f934(x94053,a922)),x94054),x94055))),f335(f78(x94051,x94051,x94051,f335(x94052,x94054)),f335(x94052,x94055))) % 186.01/186.04 [9742]~E(x97423,f335(f335(f166(x97421,x97422),x97425),x97426))+P1(f335(f335(f337(f933(f928(x97421),f928(x97421))),f335(f335(f260(f928(x97421),f928(x97421)),x97422),x97423)),f164(x97421,x97424)))+~P1(f335(f335(f244(a927),x97425),f335(f196(f928(x97421)),x97422)))+~P1(f335(f335(f337(f933(x97421,x97421)),f335(f335(f260(x97421,x97421),f335(f335(f171(x97421),x97422),x97425)),x97426)),x97424)) % 186.01/186.04 [10250]~P76(x102502)+~P1(f335(f67(x102501),x102506))+P1(f335(f335(f337(x102501),f414(x102504,x102505,x102503,x102506,x102501,x102502)),x102506))+E(f335(f335(f6(x102501,x102502),f335(f335(f18(x102501,f934(x102503,a922),x102502),f335(f335(f8(f934(x102503,x102502),f934(f934(x102503,a922),x102502),x102501),f6(x102503,x102502)),x102504)),x102505)),x102506),f335(f335(f6(f933(x102501,x102503),x102502),f335(f265(x102501,x102503,x102502),x102504)),f335(f335(f262(x102501,x102503),x102506),x102505))) % 186.01/186.04 [10251]~P72(x102512)+~P1(f335(f67(x102511),x102516))+P1(f335(f335(f337(x102511),f486(x102514,x102515,x102513,x102516,x102511,x102512)),x102516))+E(f335(f335(f9(x102511,x102512),f335(f335(f18(x102511,f934(x102513,a922),x102512),f335(f335(f8(f934(x102513,x102512),f934(f934(x102513,a922),x102512),x102511),f9(x102513,x102512)),x102514)),x102515)),x102516),f335(f335(f9(f933(x102511,x102513),x102512),f335(f265(x102511,x102513,x102512),x102514)),f335(f335(f262(x102511,x102513),x102516),x102515))) % 186.01/186.04 [10291]~P76(x102912)+~P1(f335(f67(x102911),x102916))+~P1(f335(f67(x102913),f335(x102915,f414(x102914,x102915,x102913,x102916,x102911,x102912))))+E(f335(f335(f6(x102911,x102912),f335(f335(f18(x102911,f934(x102913,a922),x102912),f335(f335(f8(f934(x102913,x102912),f934(f934(x102913,a922),x102912),x102911),f6(x102913,x102912)),x102914)),x102915)),x102916),f335(f335(f6(f933(x102911,x102913),x102912),f335(f265(x102911,x102913,x102912),x102914)),f335(f335(f262(x102911,x102913),x102916),x102915))) % 186.01/186.04 [10292]~P72(x102922)+~P1(f335(f67(x102921),x102926))+~P1(f335(f67(x102923),f335(x102925,f486(x102924,x102925,x102923,x102926,x102921,x102922))))+E(f335(f335(f9(x102921,x102922),f335(f335(f18(x102921,f934(x102923,a922),x102922),f335(f335(f8(f934(x102923,x102922),f934(f934(x102923,a922),x102922),x102921),f9(x102923,x102922)),x102924)),x102925)),x102926),f335(f335(f9(f933(x102921,x102923),x102922),f335(f265(x102921,x102923,x102922),x102924)),f335(f335(f262(x102921,x102923),x102926),x102925))) % 186.01/186.04 [10272]~P72(x102722)+~P1(f335(f67(x102721),x102726))+P1(f335(f335(f337(x102721),x102723),x102726))+E(f335(f335(f9(x102721,x102722),f335(f335(f7(x102721,x102722,x102722),f335(f335(f18(x102721,x102722,f934(x102722,x102722)),f335(f335(f8(a922,f934(x102722,f934(x102722,x102722)),x102721),f103(x102722)),f335(f335(f7(x102721,x102721,a922),a332),x102723))),x102724)),x102725)),x102726),f335(f335(f252(x102722),x102725),f335(f41(x102721),x102726))) % 186.01/186.04 [10275]~P72(x102752)+~P1(f335(f67(x102751),x102756))+~P1(f335(f335(f337(x102751),x102753),x102756))+E(f335(f335(f9(x102751,x102752),f335(f335(f7(x102751,x102752,x102752),f335(f335(f18(x102751,x102752,f934(x102752,x102752)),f335(f335(f8(a922,f934(x102752,f934(x102752,x102752)),x102751),f103(x102752)),f335(f335(f7(x102751,x102751,a922),a332),x102753))),x102754)),x102755)),x102756),f335(f335(f87(x102752),f335(x102754,x102753)),f335(f335(f252(x102752),x102755),f335(f335(f23(a927),f335(f41(x102751),x102756)),f84(a927))))) % 186.01/186.04 [10355]~P1(f335(f67(x103551),x103555))+~P1(f335(f67(x103552),x103553))+P1(f335(f335(f337(x103552),f415(x103556,x103554,x103553,x103552,x103555,x103551)),x103553))+E(f335(f335(f6(x103551,a927),f335(f335(f8(f934(x103552,a922),a927,x103551),f41(x103552)),f335(f335(f8(f934(x103552,a922),f934(x103552,a922),x103551),f270(x103552)),f335(f335(f8(f934(x103552,a922),f934(x103552,a922),x103551),f335(f18(x103552,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103552),a333),f335(f335(f7(x103552,f934(x103552,a922),a922),f337(x103552)),x103553)))),x103554)))),x103555),f335(f335(f87(a927),x103556),f335(f41(x103552),x103553))) % 186.01/186.04 [10356]~P1(f335(f67(x103561),x103565))+~P1(f335(f67(x103562),x103563))+P1(f335(f335(f337(x103562),f459(x103566,x103564,x103563,x103562,x103565,x103561)),x103563))+E(f335(f335(f6(x103561,a927),f335(f335(f8(f934(x103562,a922),a927,x103561),f41(x103562)),f335(f335(f8(f934(x103562,a922),f934(x103562,a922),x103561),f270(x103562)),f335(f335(f8(f934(x103562,a922),f934(x103562,a922),x103561),f335(f18(x103562,a922,a922),f335(f335(f8(a922,f934(a922,a922),x103562),a333),f335(f335(f7(x103562,f934(x103562,a922),a922),f337(x103562)),x103563)))),x103564)))),x103565),f335(f335(f6(x103562,a927),x103566),x103563)) % 186.01/186.04 [10401]~P1(f335(f67(x104012),x104013))+~P1(f335(f67(x104011),x104015))+~E(f335(f41(x104011),f335(f270(x104011),f335(f335(f18(x104011,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104011),a333),f335(f335(f7(x104011,f934(x104011,a922),a922),f337(x104011)),x104015))),f335(f335(f7(x104011,x104012,a922),x104014),f415(x104016,x104014,x104013,x104012,x104015,x104011))))),x104016)+E(f335(f335(f6(x104011,a927),f335(f335(f8(f934(x104012,a922),a927,x104011),f41(x104012)),f335(f335(f8(f934(x104012,a922),f934(x104012,a922),x104011),f270(x104012)),f335(f335(f8(f934(x104012,a922),f934(x104012,a922),x104011),f335(f18(x104012,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104012),a333),f335(f335(f7(x104012,f934(x104012,a922),a922),f337(x104012)),x104013)))),x104014)))),x104015),f335(f335(f87(a927),x104016),f335(f41(x104012),x104013))) % 186.01/186.04 [10403]~P1(f335(f67(x104032),x104033))+~P1(f335(f67(x104031),x104035))+~E(f335(f41(x104031),f335(f270(x104031),f335(f335(f18(x104031,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104031),a333),f335(f335(f7(x104031,f934(x104031,a922),a922),f337(x104031)),x104035))),f335(f335(f7(x104031,x104032,a922),x104034),f459(x104036,x104034,x104033,x104032,x104035,x104031))))),f335(x104036,f459(x104036,x104034,x104033,x104032,x104035,x104031)))+E(f335(f335(f6(x104031,a927),f335(f335(f8(f934(x104032,a922),a927,x104031),f41(x104032)),f335(f335(f8(f934(x104032,a922),f934(x104032,a922),x104031),f270(x104032)),f335(f335(f8(f934(x104032,a922),f934(x104032,a922),x104031),f335(f18(x104032,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104032),a333),f335(f335(f7(x104032,f934(x104032,a922),a922),f337(x104032)),x104033)))),x104034)))),x104035),f335(f335(f6(x104032,a927),x104036),x104033)) % 186.01/186.04 [10021]E(x100211,x100212)+~P17(x100213,x100214,x100215)+~P1(f335(f72(x100213,x100214,x100215,x100216,x100217),x100212))+~P1(f335(f72(x100213,x100214,x100215,x100216,x100217),x100211)) % 186.01/186.04 [9818]P1(f335(x98181,x98182))+~P1(f335(f335(f337(x98187),x98182),f335(x98186,x98184)))+~P1(f335(x98181,f628(x98181,x98186,x98185,x98183,x98187)))+~P1(f335(f335(f337(x98183),x98184),x98185)) % 186.01/186.04 [10264]~P17(x102647,x102646,x102641)+E(f335(f335(x102641,x102642),f647(x102642,x102643,x102644,x102645,x102641,x102646,x102647)),x102643)+~P1(f335(f72(x102647,x102646,x102641,x102645,x102644),x102643))+~P1(f335(f335(f337(x102647),x102642),x102644)) % 186.01/186.04 [10333]~P17(x103331,x103332,x103333)+~P1(f335(f72(x103331,x103332,x103333,x103334,x103335),x103337))+P1(f335(f72(x103331,x103332,x103333,x103334,f335(f335(f23(f934(x103331,a922)),x103335),f335(f335(f317(x103331),x103336),f195(f934(x103331,a922))))),f647(x103336,x103337,x103335,x103334,x103333,x103332,x103331)))+~P1(f335(f335(f337(x103331),x103336),x103335)) % 186.01/186.04 [9473]P27(x94731,x94732,x94733,x94734,x94735)+~P27(x94731,x94732,x94733,x94736,x94737)+~E(f335(f318(x94731,x94732,x94733),x94734),x94735)+~P1(f335(f335(f243(f934(x94731,a922)),x94734),x94736)) % 186.01/186.04 [9710]~P27(x97101,x97102,x97103,x97105,x97107)+~P27(x97101,x97102,x97103,x97104,x97106)+P27(x97101,x97102,x97103,f335(f335(f117(f934(x97101,a922)),x97104),x97105),f335(f335(f117(f934(x97102,a922)),x97106),x97107))+~E(f335(f335(f108(f934(x97102,a922)),x97106),x97107),f195(f934(x97102,a922))) % 186.01/186.04 [9715]~P70(x97151)+~P26(x97155,x97152,x97156,x97157)+~P1(f335(f67(x97155),x97157))+E(f335(f335(f335(f71(x97151,x97152,f87(x97151)),x97153),x97154),f335(f318(x97155,x97152,x97156),x97157)),f335(f335(f335(f71(x97151,x97155,f87(x97151)),f335(f78(x97152,x97151,x97155,x97153),x97156)),x97154),x97157)) % 186.01/186.04 [9841]~E(f335(f335(f317(x98411),x98415),x98416),f335(f335(f317(x98411),x98412),x98413))+~P1(f335(f72(x98411,x98411,x98414,x98412,x98413),x98417))+P1(f335(f335(f337(x98411),x98412),x98413))+P1(f335(f68(x98411,x98414,f335(f335(f317(x98411),x98415),x98416)),x98417)) % 186.01/186.04 [9926]P1(f335(x99261,x99262))+~P1(f335(f335(f337(x99263),x99262),f335(x99264,x99267)))+~P1(f335(f335(f337(x99266),x99267),x99265))+P1(f335(f335(f337(x99263),f628(x99261,x99264,x99265,x99266,x99263)),f335(f335(f45(x99266,f934(x99263,a922)),x99265),x99264))) % 186.01/186.04 [9944]~P26(x99442,x99441,x99445,x99444)+~P26(x99441,x99443,x99446,f335(f318(x99442,x99441,x99445),x99444))+E(f335(f335(f78(x99441,x99442,x99443,f83(x99442,x99441,x99444,x99445)),f83(x99441,x99443,f335(f318(x99442,x99441,x99445),x99444),x99446)),x99447),f335(f83(x99442,x99443,x99444,f335(f78(x99441,x99443,x99442,x99446),x99445)),x99447))+~P1(f335(f335(f337(x99443),x99447),f335(f318(x99441,x99443,x99446),f335(f318(x99442,x99441,x99445),x99444)))) % 186.01/186.04 [9945]~P26(x99452,x99451,x99455,x99454)+~P26(x99451,x99453,x99456,f335(f318(x99452,x99451,x99455),x99454))+E(f335(f335(f78(x99451,x99452,x99453,f97(x99452,x99451,x99454,x99455)),f97(x99451,x99453,f335(f318(x99452,x99451,x99455),x99454),x99456)),x99457),f335(f97(x99452,x99453,x99454,f335(f78(x99451,x99453,x99452,x99456),x99455)),x99457))+~P1(f335(f335(f337(x99453),x99457),f335(f318(x99451,x99453,x99456),f335(f318(x99452,x99451,x99455),x99454)))) % 186.01/186.04 [10265]~P17(x102657,x102656,x102651)+E(f335(f335(x102651,x102652),f657(x102653,x102654,x102652,x102655,x102651,x102656,x102657)),x102653)+P1(f335(f335(f337(x102657),x102652),x102654))+~P1(f335(f72(x102657,x102656,x102651,x102655,f335(f335(f317(x102657),x102652),x102654)),x102653)) % 186.01/186.04 [10332]~P17(x103321,x103324,x103325)+P1(f335(f72(x103321,x103324,x103325,x103326,x103323),f657(x103327,x103323,x103322,x103326,x103325,x103324,x103321)))+P1(f335(f335(f337(x103321),x103322),x103323))+~P1(f335(f72(x103321,x103324,x103325,x103326,f335(f335(f317(x103321),x103322),x103323)),x103327)) % 186.01/186.04 [10003]E(x100031,f2(a1))+~P1(f335(f55(x100033,x100031),f335(f335(f260(a1,a1),x100035),x100037)))+~P1(f335(f55(x100032,x100031),f335(f335(f260(a1,a1),x100034),x100036)))+P1(f335(f55(f335(f335(f86(a1),x100032),x100033),x100031),f335(f335(f260(a1,a1),f335(f335(f86(a1),f335(f335(f86(a1),x100034),x100035)),f335(f335(f42(a1),f335(f335(f86(a1),x100036),x100037)),x100031))),f51(a1,f335(f335(f86(a1),x100036),x100037),x100031)))) % 186.01/186.04 [10005]~P1(f335(f335(f244(a927),f2(a927)),x100053))+~P1(f335(f54(x100052,x100053),f335(f335(f260(a927,a927),x100055),x100057)))+~P1(f335(f54(x100051,x100053),f335(f335(f260(a927,a927),x100054),x100056)))+P1(f335(f54(f335(f335(f86(a927),x100051),x100052),x100053),f335(f335(f260(a927,a927),f335(f335(f86(a927),f335(f335(f86(a927),x100054),x100055)),f335(f335(f42(a927),f335(f335(f86(a927),x100056),x100057)),x100053))),f51(a927,f335(f335(f86(a927),x100056),x100057),x100053)))) % 186.01/186.04 [10400]~P76(x104002)+~P1(f335(f67(x104003),x104005))+~P1(f335(f67(x104001),x104007))+E(f335(f335(f6(x104001,x104002),f335(f335(f18(x104001,f934(x104003,a922),x104002),f335(f335(f8(f934(x104003,x104002),f934(f934(x104003,a922),x104002),x104001),f6(x104003,x104002)),x104004)),f335(f335(f8(f934(x104003,a922),f934(x104003,a922),x104001),f270(x104003)),f335(f335(f8(f934(x104003,a922),f934(x104003,a922),x104001),f335(f18(x104003,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104003),a333),f335(f335(f7(x104003,f934(x104003,a922),a922),f337(x104003)),x104005)))),x104006)))),x104007),f335(f335(f6(x104003,x104002),f335(f335(f18(x104003,f934(x104001,a922),x104002),f335(f335(f8(f934(x104001,x104002),f934(f934(x104001,a922),x104002),x104003),f6(x104001,x104002)),f335(f7(x104001,x104003,x104002),x104004))),f335(f335(f8(f934(x104001,a922),f934(x104001,a922),x104003),f270(x104001)),f335(f335(f8(f934(x104001,a922),f934(x104001,a922),x104003),f335(f18(x104001,a922,a922),f335(f335(f8(a922,f934(a922,a922),x104001),a333),f335(f335(f7(x104001,f934(x104001,a922),a922),f337(x104001)),x104007)))),f335(f7(x104001,x104003,a922),x104006))))),x104005)) % 186.01/186.04 [10353]~P22(x103538,x103537,x103536,x103535,x103531)+~E(f335(x103532,f871(x103534,x103532,x103533,x103531,x103535,x103536,x103537)),f335(x103534,f871(x103534,x103532,x103533,x103531,x103535,x103536,x103537)))+E(f335(f335(x103531,x103532),x103533),f335(f335(x103531,x103534),x103533))+~P1(f335(f67(x103537),x103533)) % 186.01/186.04 [9877]~P23(x98777,x98776,x98771,x98778,x98772,x98774)+E(f335(f335(x98771,f335(x98772,x98773)),f335(x98774,x98775)),f335(x98774,x98775))+~P1(f335(f67(x98776),x98775))+~P1(f335(f335(f337(x98776),x98773),x98775)) % 186.01/186.04 [9882]~P13(x98826,x98821,x98822,x98828,x98823,x98824)+~P9(x98826,x98827,x98828)+P12(x98821,x98822,x98823,f335(x98824,x98825))+~P1(f335(f335(f337(x98826),x98825),x98827)) % 186.01/186.04 [10371]~P22(x103718,x103715,x103717,x103716,x103711)+E(f335(f335(x103711,x103712),x103713),f335(f335(x103711,x103714),x103713))+~P1(f335(f67(x103715),x103713))+P1(f335(f335(f337(x103715),f871(x103712,x103714,x103713,x103711,x103716,x103717,x103715)),x103713)) % 186.01/186.04 [10453]~P1(f335(f335(x104531,x104536),x104535))+P1(f335(f335(x104531,f857(x104531,x104534,x104535,x104536,x104533,x104532,x104537,x104538)),f862(x104531,x104534,x104535,x104536,x104533,x104532,x104537,x104538)))+P1(f335(f335(x104531,x104532),x104533))+~P1(f335(f335(f337(f933(f933(x104538,x104537),f933(x104538,x104537))),f335(f335(f260(f933(x104538,x104537),f933(x104538,x104537)),f335(f335(f260(x104538,x104537),x104532),x104533)),f335(f335(f260(x104538,x104537),x104536),x104535))),f315(f933(x104538,x104537),x104534))) % 186.01/186.04 [10454]~P1(f335(f335(x104541,x104546),x104545))+P1(f335(f335(x104541,f863(x104541,x104544,x104543,x104542,x104545,x104546,x104547,x104548)),f864(x104541,x104544,x104543,x104542,x104545,x104546,x104547,x104548)))+P1(f335(f335(x104541,x104542),x104543))+~P1(f335(f335(f337(f933(f933(x104548,x104547),f933(x104548,x104547))),f335(f335(f260(f933(x104548,x104547),f933(x104548,x104547)),f335(f335(f260(x104548,x104547),x104546),x104545)),f335(f335(f260(x104548,x104547),x104542),x104543))),f315(f933(x104548,x104547),x104544))) % 186.01/186.04 [10464]~P1(f335(f335(x104641,f858(x104641,x104646,x104645,x104644,x104643,x104642,x104647,x104648)),f861(x104641,x104646,x104645,x104644,x104643,x104642,x104647,x104648)))+P1(f335(f335(x104641,x104642),x104643))+~P1(f335(f335(x104641,x104644),x104645))+~P1(f335(f335(f337(f933(f933(x104648,x104647),f933(x104648,x104647))),f335(f335(f260(f933(x104648,x104647),f933(x104648,x104647)),f335(f335(f260(x104648,x104647),x104642),x104643)),f335(f335(f260(x104648,x104647),x104644),x104645))),f315(f933(x104648,x104647),x104646))) % 186.01/186.04 [10465]~P1(f335(f335(x104651,f865(x104651,x104656,x104653,x104652,x104655,x104654,x104657,x104658)),f866(x104651,x104656,x104653,x104652,x104655,x104654,x104657,x104658)))+P1(f335(f335(x104651,x104652),x104653))+~P1(f335(f335(x104651,x104654),x104655))+~P1(f335(f335(f337(f933(f933(x104658,x104657),f933(x104658,x104657))),f335(f335(f260(f933(x104658,x104657),f933(x104658,x104657)),f335(f335(f260(x104658,x104657),x104654),x104655)),f335(f335(f260(x104658,x104657),x104652),x104653))),f315(f933(x104658,x104657),x104656))) % 186.01/186.04 [10478]~P1(f335(f335(x104781,x104786),x104787))+P1(f335(f335(x104781,x104782),x104783))+P1(f335(f335(f337(f933(f933(x104784,x104785),f933(x104784,x104785))),f335(f335(f260(f933(x104784,x104785),f933(x104784,x104785)),f335(f335(f260(x104784,x104785),x104786),x104787)),f335(f335(f260(x104784,x104785),f863(x104781,x104788,x104783,x104782,x104787,x104786,x104785,x104784)),f864(x104781,x104788,x104783,x104782,x104787,x104786,x104785,x104784)))),f315(f933(x104784,x104785),x104788)))+~P1(f335(f335(f337(f933(f933(x104784,x104785),f933(x104784,x104785))),f335(f335(f260(f933(x104784,x104785),f933(x104784,x104785)),f335(f335(f260(x104784,x104785),x104786),x104787)),f335(f335(f260(x104784,x104785),x104782),x104783))),f315(f933(x104784,x104785),x104788))) % 186.01/186.04 [10480]~P1(f335(f335(x104801,x104808),x104807))+P1(f335(f335(x104801,x104802),x104803))+P1(f335(f335(f337(f933(f933(x104804,x104805),f933(x104804,x104805))),f335(f335(f260(f933(x104804,x104805),f933(x104804,x104805)),f335(f335(f260(x104804,x104805),f857(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804)),f862(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804))),f335(f335(f260(x104804,x104805),x104808),x104807))),f315(f933(x104804,x104805),x104806)))+~P1(f335(f335(f337(f933(f933(x104804,x104805),f933(x104804,x104805))),f335(f335(f260(f933(x104804,x104805),f933(x104804,x104805)),f335(f335(f260(x104804,x104805),x104802),x104803)),f335(f335(f260(x104804,x104805),x104808),x104807))),f315(f933(x104804,x104805),x104806))) % 186.01/186.04 [9498]~P20(x94987,x94981,x94988,x94983)+~P1(f335(f67(x94987),x94985))+~P1(f335(f67(x94987),x94984))+E(f335(f78(x94981,x94981,x94982,f335(x94983,x94984)),f335(f78(x94981,x94981,x94982,f335(x94983,x94985)),x94986)),f335(f78(x94981,x94981,x94982,f335(x94983,x94985)),f335(f78(x94981,x94981,x94982,f335(x94983,x94984)),x94986))) % 186.01/186.04 [9507]~P35(x95071,x95072,x95073,x95074,x95077)+P35(x95071,x95072,x95073,f335(f335(f166(x95071,x95074),x95075),x95076),f335(f335(f166(x95072,x95077),x95075),x95078))+~P1(f335(f335(x95073,x95076),x95078))+~P1(f335(f335(f244(a927),x95075),f335(f196(f928(x95071)),x95074))) % 186.01/186.04 [9508]~P35(x95081,x95082,x95083,x95084,x95087)+P35(x95081,x95082,x95083,f335(f335(f166(x95081,x95084),x95085),x95086),f335(f335(f166(x95082,x95087),x95085),x95088))+~P1(f335(f335(x95083,x95086),x95088))+~P1(f335(f335(f244(a927),x95085),f335(f196(f928(x95082)),x95087))) % 186.01/186.04 [9587]~P26(x95872,x95872,x95875,x95876)+~P22(x95873,x95872,x95877,x95878,x95871)+~P1(f335(f67(x95872),x95876))+E(f335(f335(x95871,f335(f78(x95872,x95873,x95872,x95874),x95875)),x95876),f335(f335(x95871,x95874),f335(f318(x95872,x95872,x95875),x95876))) % 186.01/186.04 [9842]P27(x98421,x98422,x98423,x98424,x98425)+~P27(x98422,x98426,x98427,x98425,x98428)+~P27(x98421,x98426,f335(f78(x98422,x98426,x98421,x98427),x98423),x98424,x98428)+~P1(f335(f335(f243(f934(x98422,a922)),f335(f318(x98421,x98422,x98423),x98424)),x98425)) % 186.01/186.04 [9879]~P24(x98797,x98792,x98795,x98798,x98796,x98791)+~P1(f335(f67(x98792),x98794))+E(f335(x98791,f335(f335(f317(x98792),x98793),x98794)),f335(f335(x98795,f335(x98796,x98793)),f335(x98791,x98794)))+P1(f335(f335(f337(x98792),x98793),x98794)) % 186.01/186.04 [9891]~P23(x98916,x98915,x98911,x98917,x98918,x98912)+E(f335(f335(x98911,f335(x98912,x98913)),f335(x98912,x98914)),f335(x98912,x98914))+~P1(f335(f67(x98915),x98914))+~P1(f335(f335(f243(f934(x98915,a922)),x98913),x98914)) % 186.01/186.04 [10398]P25(x103988,x103987,f335(f335(f317(f926(x103988)),f98(x103988,x103984,x103985,x103983)),f195(f934(f926(x103988),a922))))+~P25(x103988,x103987,f335(f335(f317(f926(x103988)),f98(x103988,x103986,x103985,x103981)),f195(f934(f926(x103988),a922))))+~P1(f335(f335(x103986,x103982),f920(x103983,x103984,x103981,x103985,x103986,x103987,x103988)))+P1(f335(f335(x103981,x103982),f353(x103983,x103984,x103981,x103985,x103986,x103987,x103988))) % 186.01/186.04 [9485]P1(f335(f335(f337(f933(f928(x94851),f928(x94851))),f335(f335(f260(f928(x94851),f928(x94851)),x94852),x94853)),f164(x94851,x94854)))+~E(x94853,f335(f335(f141(x94851),x94855),f335(f335(f158(x94851),x94856),x94857)))+~E(x94852,f335(f335(f141(x94851),x94855),f335(f335(f158(x94851),x94858),x94857)))+~P1(f335(f335(f337(f933(x94851,x94851)),f335(f335(f260(x94851,x94851),x94858),x94856)),x94854)) % 186.01/186.04 [9885]~P23(x98856,x98852,x98855,x98857,x98858,x98851)+~P1(f335(f67(x98852),x98854))+~P1(f335(f67(x98852),x98853))+E(f335(x98851,f335(f335(f117(f934(x98852,a922)),x98853),x98854)),f335(f335(x98855,f335(x98851,x98853)),f335(x98851,x98854))) % 186.01/186.04 [10443]~P26(x104434,x104432,x104435,x104438)+E(f335(f335(f46(x104431,f934(x104432,a922)),x104433),f335(f335(f8(f934(x104434,a922),f934(x104432,a922),x104431),f318(x104434,x104432,x104435)),x104436)),f335(f318(x104434,x104432,x104435),f335(f335(f46(x104431,f934(x104434,a922)),x104433),x104436)))+~P1(f335(f335(f337(x104431),x104437),x104433))+P1(f335(f335(f337(x104431),f658(x104437,x104436,x104433,x104431,x104438,x104435,x104432,x104434)),x104433)) % 186.01/186.04 [10469]~P26(x104694,x104692,x104695,x104697)+E(f335(f335(f46(x104691,f934(x104692,a922)),x104693),f335(f335(f8(f934(x104694,a922),f934(x104692,a922),x104691),f318(x104694,x104692,x104695)),x104696)),f335(f318(x104694,x104692,x104695),f335(f335(f46(x104691,f934(x104694,a922)),x104693),x104696)))+~P1(f335(f335(f337(x104691),x104698),x104693))+~P1(f335(f335(f243(f934(x104694,a922)),f335(x104696,f658(x104698,x104696,x104693,x104691,x104697,x104695,x104692,x104694))),x104697)) % 186.01/186.04 [10481]~P1(f335(f335(x104811,x104818),x104817))+P1(f335(f335(x104811,x104812),x104813))+~P1(f335(f335(f337(f933(f933(x104814,x104815),f933(x104814,x104815))),f335(f335(f260(f933(x104814,x104815),f933(x104814,x104815)),f335(f335(f260(x104814,x104815),x104812),x104813)),f335(f335(f260(x104814,x104815),x104818),x104817))),f315(f933(x104814,x104815),x104816)))+P1(f335(f335(f337(f933(f933(x104814,x104815),f933(x104814,x104815))),f335(f335(f260(f933(x104814,x104815),f933(x104814,x104815)),f335(f335(f260(x104814,x104815),f858(x104811,x104816,x104817,x104818,x104813,x104812,x104815,x104814)),f861(x104811,x104816,x104817,x104818,x104813,x104812,x104815,x104814))),f335(f335(f260(x104814,x104815),f857(x104811,x104816,x104817,x104818,x104813,x104812,x104815,x104814)),f862(x104811,x104816,x104817,x104818,x104813,x104812,x104815,x104814)))),x104816)) % 186.01/186.04 [10482]~P1(f335(f335(x104821,x104828),x104827))+P1(f335(f335(x104821,x104822),x104823))+~P1(f335(f335(f337(f933(f933(x104824,x104825),f933(x104824,x104825))),f335(f335(f260(f933(x104824,x104825),f933(x104824,x104825)),f335(f335(f260(x104824,x104825),x104828),x104827)),f335(f335(f260(x104824,x104825),x104822),x104823))),f315(f933(x104824,x104825),x104826)))+P1(f335(f335(f337(f933(f933(x104824,x104825),f933(x104824,x104825))),f335(f335(f260(f933(x104824,x104825),f933(x104824,x104825)),f335(f335(f260(x104824,x104825),f863(x104821,x104826,x104823,x104822,x104827,x104828,x104825,x104824)),f864(x104821,x104826,x104823,x104822,x104827,x104828,x104825,x104824))),f335(f335(f260(x104824,x104825),f865(x104821,x104826,x104823,x104822,x104827,x104828,x104825,x104824)),f866(x104821,x104826,x104823,x104822,x104827,x104828,x104825,x104824)))),x104826)) % 186.01/186.04 [9954]~P24(x99547,x99545,x99541,x99548,x99542,x99544)+~P1(f335(f67(x99545),x99546))+~P1(f335(f335(f337(x99545),x99543),x99546))+E(f335(f335(x99541,f335(x99542,x99543)),f335(x99544,f335(f335(f23(f934(x99545,a922)),x99546),f335(f335(f317(x99545),x99543),f195(f934(x99545,a922)))))),f335(x99544,x99546)) % 186.01/186.04 [9962]~P24(x99626,x99623,x99621,x99627,x99628,x99622)+~P1(f335(f67(x99623),x99625))+~P1(f335(f67(x99623),x99624))+E(f335(f335(x99621,f335(x99622,f335(f335(f117(f934(x99623,a922)),x99624),x99625))),f335(x99622,f335(f335(f108(f934(x99623,a922)),x99624),x99625))),f335(f335(x99621,f335(x99622,x99624)),f335(x99622,x99625))) % 186.01/186.04 [10045]P43(x100451,x100452,x100453,x100454,x100455,f335(f335(x100453,x100456),x100457))+~P43(x100451,x100452,x100453,x100454,f335(f335(f23(f934(x100451,a922)),x100455),f335(f335(f317(x100451),x100458),f195(f934(x100451,a922)))),x100459)+~E(f335(f335(x100453,x100456),x100457),f335(f335(x100453,x100458),x100459))+~P1(f335(f335(f337(x100451),x100458),x100455)) % 186.01/186.04 [9987]~P13(x99876,x99877,x99878,x99879,x998710,x99871)+E(f335(f335(x99871,x99872),x99873),f335(f335(x99871,x99874),x99875))+~P1(f335(f335(f337(f933(x99877,x99877)),f335(f335(f260(x99877,x99877),x99873),x99875)),x998710))+~P1(f335(f335(f337(f933(x99876,x99876)),f335(f335(f260(x99876,x99876),x99872),x99874)),x99879)) % 186.01/186.04 [9589]~P98(x95892)+E(x95891,f195(f934(x95892,a922)))+~P1(f335(f67(x95892),x95891))+P1(f335(f335(f337(x95892),f13(x95892,x95891)),x95891))+~P1(f335(f335(f337(x95892),f335(f335(f117(x95892),f370(x95891,x95892)),f377(x95891,x95892))),f335(f335(f317(x95892),f370(x95891,x95892)),f335(f335(f317(x95892),f377(x95891,x95892)),f195(f934(x95892,a922)))))) % 186.01/186.04 [9590]~P98(x95902)+E(x95901,f195(f934(x95902,a922)))+~P1(f335(f67(x95902),x95901))+P1(f335(f335(f337(x95902),f10(x95902,x95901)),x95901))+~P1(f335(f335(f337(x95902),f335(f335(f108(x95902),f371(x95901,x95902)),f372(x95901,x95902))),f335(f335(f317(x95902),f371(x95901,x95902)),f335(f335(f317(x95902),f372(x95901,x95902)),f195(f934(x95902,a922)))))) % 186.01/186.04 [9621]~P70(x96212)+E(x96211,f195(f934(x96212,a922)))+~P1(f335(f67(x96212),x96211))+P1(f335(f335(f337(x96212),f335(f69(x96212,f87(x96212)),x96211)),x96211))+~P1(f335(f335(f337(x96212),f335(f335(f87(x96212),f366(x96211,x96212)),f367(x96211,x96212))),f335(f335(f317(x96212),f366(x96211,x96212)),f335(f335(f317(x96212),f367(x96211,x96212)),f195(f934(x96212,a922)))))) % 186.01/186.04 [9626]~P109(x96262)+E(x96261,f195(f934(x96262,a922)))+~P1(f335(f67(x96262),x96261))+P1(f335(f335(f337(x96262),f11(x96262,f242(x96262),x96261)),x96261))+~P1(f335(f335(f337(x96262),f335(f335(f242(x96262),f411(x96261,x96262)),f413(x96261,x96262))),f335(f335(f317(x96262),f411(x96261,x96262)),f335(f335(f317(x96262),f413(x96261,x96262)),f195(f934(x96262,a922)))))) % 186.01/186.04 [9627]~P109(x96272)+E(x96271,f195(f934(x96272,a922)))+~P1(f335(f67(x96272),x96271))+P1(f335(f335(f337(x96272),f12(x96272,f241(x96272),x96271)),x96271))+~P1(f335(f335(f337(x96272),f335(f335(f241(x96272),f417(x96271,x96272)),f418(x96271,x96272))),f335(f335(f317(x96272),f417(x96271,x96272)),f335(f335(f317(x96272),f418(x96271,x96272)),f195(f934(x96272,a922)))))) % 186.01/186.04 [6766]~P89(x67662)+E(x67661,f2(x67662))+~E(f335(f335(f86(x67662),x67663),x67661),f2(x67662))+~P1(f335(f335(f243(x67662),f2(x67662)),x67663))+~P1(f335(f335(f243(x67662),f2(x67662)),x67661)) % 186.01/186.04 [6767]~P89(x67672)+E(x67671,f2(x67672))+~E(f335(f335(f86(x67672),x67671),x67673),f2(x67672))+~P1(f335(f335(f243(x67672),f2(x67672)),x67673))+~P1(f335(f335(f243(x67672),f2(x67672)),x67671)) % 186.01/186.04 [7294]~P109(x72942)+~P14(x72942,x72941)+E(x72941,f120(x72942))+~P1(f335(f335(f337(x72942),x72943),f335(f179(x72942),f731(x72941,x72942))))+P1(f335(f335(f243(x72942),f750(x72941,x72942)),x72943)) % 186.01/186.04 [7462]~P109(x74621)+E(f15(x74621,x74622),x74623)+~P1(f335(f67(x74621),x74622))+~P1(f335(f335(f243(x74621),x74623),f612(x74623,x74622,x74621)))+~P1(f335(f335(f337(x74621),x74623),x74622)) % 186.01/186.04 [7495]~P109(x74951)+~P14(x74951,x74952)+~P14(x74951,x74953)+P14(x74951,f335(f335(f141(x74951),x74952),x74953))+P1(f335(f335(f337(x74951),f737(x74953,x74952,x74951)),f335(f179(x74951),x74952))) % 186.01/186.04 [7496]~P109(x74961)+~P14(x74961,x74962)+~P14(x74961,x74963)+P14(x74961,f335(f335(f141(x74961),x74962),x74963))+P1(f335(f335(f337(x74961),f738(x74963,x74962,x74961)),f335(f179(x74961),x74963))) % 186.01/186.04 [7561]~P109(x75611)+E(f14(x75611,x75612),x75613)+~P1(f335(f67(x75611),x75612))+P1(f335(f335(f337(x75611),f614(x75613,x75612,x75611)),x75612))+~P1(f335(f335(f337(x75611),x75613),x75612)) % 186.01/186.04 [7562]~P109(x75621)+E(f15(x75621,x75622),x75623)+~P1(f335(f67(x75621),x75622))+P1(f335(f335(f337(x75621),f612(x75623,x75622,x75621)),x75622))+~P1(f335(f335(f337(x75621),x75623),x75622)) % 186.01/186.04 [8120]~P109(x81201)+E(f14(x81201,x81202),x81203)+~P1(f335(f67(x81201),x81202))+~P1(f335(f335(f337(x81201),x81203),x81202))+~P1(f335(f335(f243(x81201),f614(x81203,x81202,x81201)),x81203)) % 186.01/186.04 [8434]~P109(x84341)+~P14(x84341,x84342)+~P14(x84341,x84343)+P14(x84341,f335(f335(f141(x84341),x84342),x84343))+~P1(f335(f335(f243(x84341),f737(x84343,x84342,x84341)),f738(x84343,x84342,x84341))) % 186.01/186.04 [9230]~P98(x92302)+E(x92301,f195(f934(x92302,a922)))+~E(f335(f335(f117(x92302),f335(x92303,f375(x92301,x92303,x92302))),f335(x92303,f379(x92301,x92303,x92302))),f335(x92303,f335(f335(f117(x92302),f375(x92301,x92303,x92302)),f379(x92301,x92303,x92302))))+E(f13(x92302,f335(f318(x92302,x92302,x92303),x92301)),f335(x92303,f13(x92302,x92301)))+~P1(f335(f67(x92302),x92301)) % 186.01/186.04 [9231]~P98(x92312)+E(x92311,f195(f934(x92312,a922)))+~E(f335(f335(f108(x92312),f335(x92313,f376(x92311,x92313,x92312))),f335(x92313,f378(x92311,x92313,x92312))),f335(x92313,f335(f335(f108(x92312),f376(x92311,x92313,x92312)),f378(x92311,x92313,x92312))))+E(f10(x92312,f335(f318(x92312,x92312,x92313),x92311)),f335(x92313,f10(x92312,x92311)))+~P1(f335(f67(x92312),x92311)) % 186.01/186.04 [9232]~P109(x92322)+E(x92321,f195(f934(x92322,a922)))+~E(f335(f335(f242(x92322),f335(x92323,f501(x92321,x92323,x92322))),f335(x92323,f502(x92321,x92323,x92322))),f335(x92323,f335(f335(f242(x92322),f501(x92321,x92323,x92322)),f502(x92321,x92323,x92322))))+E(f14(x92322,f335(f318(x92322,x92322,x92323),x92321)),f335(x92323,f14(x92322,x92321)))+~P1(f335(f67(x92322),x92321)) % 186.01/186.04 [9233]~P109(x92332)+E(x92331,f195(f934(x92332,a922)))+~E(f335(f335(f241(x92332),f335(x92333,f503(x92331,x92333,x92332))),f335(x92333,f504(x92331,x92333,x92332))),f335(x92333,f335(f335(f241(x92332),f503(x92331,x92333,x92332)),f504(x92331,x92333,x92332))))+E(f15(x92332,f335(f318(x92332,x92332,x92333),x92331)),f335(x92333,f15(x92332,x92331)))+~P1(f335(f67(x92332),x92331)) % 186.01/186.04 [9301]~P109(x93012)+E(x93011,f195(f934(x93012,a922)))+~E(f335(f335(f242(x93012),f335(x93013,f490(x93011,x93013,x93012))),f335(x93013,f493(x93011,x93013,x93012))),f335(x93013,f335(f335(f242(x93012),f490(x93011,x93013,x93012)),f493(x93011,x93013,x93012))))+E(f11(x93012,f242(x93012),f335(f318(x93012,x93012,x93013),x93011)),f335(x93013,f11(x93012,f242(x93012),x93011)))+~P1(f335(f67(x93012),x93011)) % 186.01/186.04 [9302]~P109(x93022)+E(x93021,f195(f934(x93022,a922)))+~E(f335(f335(f241(x93022),f335(x93023,f494(x93021,x93023,x93022))),f335(x93023,f495(x93021,x93023,x93022))),f335(x93023,f335(f335(f241(x93022),f494(x93021,x93023,x93022)),f495(x93021,x93023,x93022))))+E(f12(x93022,f241(x93022),f335(f318(x93022,x93022,x93023),x93021)),f335(x93023,f12(x93022,f241(x93022),x93021)))+~P1(f335(f67(x93022),x93021)) % 186.01/186.04 [6783]~P70(x67832)+E(x67831,f195(f934(x67832,a922)))+~P1(f335(f67(x67832),x67831))+E(f335(f69(x67832,f87(x67832)),f335(f335(f317(x67832),x67833),x67831)),f335(f335(f87(x67832),x67833),f335(f69(x67832,f87(x67832)),x67831)))+P1(f335(f335(f337(x67832),x67833),x67831)) % 186.01/186.04 [7300]~P98(x73002)+E(f335(f335(f108(x73002),f10(x73002,x73001)),f10(x73002,x73003)),f10(x73002,x73003))+E(x73001,f195(f934(x73002,a922)))+~P1(f335(f67(x73002),x73003))+~P1(f335(f335(f243(f934(x73002,a922)),x73001),x73003)) % 186.01/186.04 [7301]~P98(x73012)+E(f335(f335(f117(x73012),f13(x73012,x73011)),f13(x73012,x73013)),f13(x73012,x73013))+E(x73011,f195(f934(x73012,a922)))+~P1(f335(f67(x73012),x73013))+~P1(f335(f335(f243(f934(x73012,a922)),x73011),x73013)) % 186.01/186.04 [7302]~P109(x73022)+E(f335(f335(f241(x73022),f15(x73022,x73021)),f15(x73022,x73023)),f15(x73022,x73023))+E(x73021,f195(f934(x73022,a922)))+~P1(f335(f67(x73022),x73023))+~P1(f335(f335(f243(f934(x73022,a922)),x73021),x73023)) % 186.01/186.04 [7303]~P109(x73032)+E(f335(f335(f242(x73032),f14(x73032,x73031)),f14(x73032,x73033)),f14(x73032,x73033))+E(x73031,f195(f934(x73032,a922)))+~P1(f335(f67(x73032),x73033))+~P1(f335(f335(f243(f934(x73032,a922)),x73031),x73033)) % 186.01/186.04 [7608]~P109(x76082)+E(x76081,f195(f934(x76082,a922)))+~P1(f335(f67(x76082),x76083))+P1(f335(f335(f243(x76082),f14(x76082,x76081)),f14(x76082,x76083)))+~P1(f335(f335(f243(f934(x76082,a922)),x76081),x76083)) % 186.01/186.04 [7609]~P109(x76092)+E(x76091,f195(f934(x76092,a922)))+~P1(f335(f67(x76092),x76093))+P1(f335(f335(f243(x76092),f15(x76092,x76093)),f15(x76092,x76091)))+~P1(f335(f335(f243(f934(x76092,a922)),x76091),x76093)) % 186.01/186.04 [7662]~P98(x76621)+E(f13(x76621,x76622),x76623)+~P1(f335(f67(x76621),x76622))+~E(f335(f335(f23(f934(x76621,a922)),x76622),f335(f335(f317(x76621),x76623),f195(f934(x76621,a922)))),f195(f934(x76621,a922)))+~P1(f335(f335(f337(x76621),x76623),x76622)) % 186.01/186.04 [7663]~P98(x76631)+E(f10(x76631,x76632),x76633)+~P1(f335(f67(x76631),x76632))+~E(f335(f335(f23(f934(x76631,a922)),x76632),f335(f335(f317(x76631),x76633),f195(f934(x76631,a922)))),f195(f934(x76631,a922)))+~P1(f335(f335(f337(x76631),x76633),x76632)) % 186.01/186.04 [7664]~P109(x76641)+E(f14(x76641,x76642),x76643)+~P1(f335(f67(x76641),x76642))+~E(f335(f335(f23(f934(x76641,a922)),x76642),f335(f335(f317(x76641),x76643),f195(f934(x76641,a922)))),f195(f934(x76641,a922)))+~P1(f335(f335(f337(x76641),x76643),x76642)) % 186.01/186.04 [7665]~P109(x76651)+E(f15(x76651,x76652),x76653)+~P1(f335(f67(x76651),x76652))+~E(f335(f335(f23(f934(x76651,a922)),x76652),f335(f335(f317(x76651),x76653),f195(f934(x76651,a922)))),f195(f934(x76651,a922)))+~P1(f335(f335(f337(x76651),x76653),x76652)) % 186.01/186.04 [7757]~P109(x77571)+E(f11(x77571,f242(x77571),x77572),x77573)+~P1(f335(f67(x77571),x77572))+~E(f335(f335(f23(f934(x77571,a922)),x77572),f335(f335(f317(x77571),x77573),f195(f934(x77571,a922)))),f195(f934(x77571,a922)))+~P1(f335(f335(f337(x77571),x77573),x77572)) % 186.01/186.04 [7758]~P109(x77581)+E(f12(x77581,f241(x77581),x77582),x77583)+~P1(f335(f67(x77581),x77582))+~E(f335(f335(f23(f934(x77581,a922)),x77582),f335(f335(f317(x77581),x77583),f195(f934(x77581,a922)))),f195(f934(x77581,a922)))+~P1(f335(f335(f337(x77581),x77583),x77582)) % 186.01/186.04 [7793]~P97(x77932)+E(x77931,f195(f934(x77932,a922)))+~P1(f335(f67(x77932),x77931))+~P1(f335(f335(f243(x77932),x77933),f364(x77933,x77931,x77932)))+P1(f335(f335(f243(x77932),x77933),f335(f69(x77932,f108(x77932)),x77931))) % 186.01/186.04 [7794]~P109(x77942)+E(x77941,f195(f934(x77942,a922)))+~P1(f335(f67(x77942),x77941))+~P1(f335(f335(f243(x77942),x77943),f394(x77943,x77941,x77942)))+P1(f335(f335(f243(x77942),x77943),f335(f69(x77942,f241(x77942)),x77941))) % 186.01/186.04 [7795]~P109(x77952)+E(x77951,f195(f934(x77952,a922)))+~P1(f335(f67(x77952),x77951))+~P1(f335(f335(f244(x77952),x77953),f395(x77953,x77951,x77952)))+P1(f335(f335(f244(x77952),x77953),f335(f69(x77952,f241(x77952)),x77951))) % 186.01/186.04 [7880]~P97(x78802)+E(x78801,f195(f934(x78802,a922)))+~P1(f335(f67(x78802),x78801))+P1(f335(f335(f337(x78802),f364(x78803,x78801,x78802)),x78801))+P1(f335(f335(f243(x78802),x78803),f335(f69(x78802,f108(x78802)),x78801))) % 186.01/186.04 [7881]~P109(x78812)+E(x78811,f195(f934(x78812,a922)))+~P1(f335(f67(x78812),x78811))+P1(f335(f335(f337(x78812),f394(x78813,x78811,x78812)),x78811))+P1(f335(f335(f243(x78812),x78813),f335(f69(x78812,f241(x78812)),x78811))) % 186.01/186.04 [7882]~P109(x78822)+E(x78821,f195(f934(x78822,a922)))+~P1(f335(f67(x78822),x78821))+P1(f335(f335(f337(x78822),f395(x78823,x78821,x78822)),x78821))+P1(f335(f335(f244(x78822),x78823),f335(f69(x78822,f241(x78822)),x78821))) % 186.01/186.04 [8001]~P109(x80012)+E(x80011,f195(f934(x80012,a922)))+E(f335(f335(f241(x80012),f12(x80012,f241(x80012),x80011)),f12(x80012,f241(x80012),x80013)),f12(x80012,f241(x80012),x80013))+~P1(f335(f67(x80012),x80013))+~P1(f335(f335(f243(f934(x80012,a922)),x80011),x80013)) % 186.01/186.04 [8002]~P109(x80022)+E(x80021,f195(f934(x80022,a922)))+E(f335(f335(f242(x80022),f11(x80022,f242(x80022),x80021)),f11(x80022,f242(x80022),x80023)),f11(x80022,f242(x80022),x80023))+~P1(f335(f67(x80022),x80023))+~P1(f335(f335(f243(f934(x80022,a922)),x80021),x80023)) % 186.01/186.04 [8198]~E(f583(x81981,x81983,x81982),f584(x81981,x81983,x81982))+~E(f335(f41(x81982),f585(x81981,x81983,x81982)),x81981)+E(f335(f335(f87(a927),x81981),f335(f41(f934(x81982,a922)),x81983)),f335(f41(x81982),f43(f934(x81982,a922),x81983)))+~P1(f335(f67(x81982),f43(f934(x81982,a922),x81983)))+~P1(f335(f67(f934(x81982,a922)),x81983)) % 186.01/186.04 [8374]~P109(x83742)+E(x83741,f195(f934(x83742,a922)))+~P1(f335(f67(x83742),x83743))+P1(f335(f335(f243(x83742),f335(f69(x83742,f241(x83742)),x83743)),f335(f69(x83742,f241(x83742)),x83741)))+~P1(f335(f335(f243(f934(x83742,a922)),x83741),x83743)) % 186.01/186.04 [8674]~E(f583(x86741,x86743,x86742),f584(x86741,x86743,x86742))+E(f335(f335(f87(a927),x86741),f335(f41(f934(x86742,a922)),x86743)),f335(f41(x86742),f43(f934(x86742,a922),x86743)))+P1(f335(f335(f337(f934(x86742,a922)),f585(x86741,x86743,x86742)),x86743))+~P1(f335(f67(x86742),f43(f934(x86742,a922),x86743)))+~P1(f335(f67(f934(x86742,a922)),x86743)) % 186.01/186.04 [8700]~E(f335(f41(x87002),f585(x87001,x87003,x87002)),x87001)+E(f335(f335(f87(a927),x87001),f335(f41(f934(x87002,a922)),x87003)),f335(f41(x87002),f43(f934(x87002,a922),x87003)))+P1(f335(f335(f337(f934(x87002,a922)),f584(x87001,x87003,x87002)),x87003))+~P1(f335(f67(x87002),f43(f934(x87002,a922),x87003)))+~P1(f335(f67(f934(x87002,a922)),x87003)) % 186.01/186.04 [8701]~E(f335(f41(x87012),f585(x87011,x87013,x87012)),x87011)+E(f335(f335(f87(a927),x87011),f335(f41(f934(x87012,a922)),x87013)),f335(f41(x87012),f43(f934(x87012,a922),x87013)))+P1(f335(f335(f337(f934(x87012,a922)),f583(x87011,x87013,x87012)),x87013))+~P1(f335(f67(x87012),f43(f934(x87012,a922),x87013)))+~P1(f335(f67(f934(x87012,a922)),x87013)) % 186.01/186.04 [8726]~E(f335(f41(x87262),f585(x87261,x87263,x87262)),x87261)+~E(f335(f335(f108(f934(x87262,a922)),f584(x87261,x87263,x87262)),f583(x87261,x87263,x87262)),f195(f934(x87262,a922)))+E(f335(f335(f87(a927),x87261),f335(f41(f934(x87262,a922)),x87263)),f335(f41(x87262),f43(f934(x87262,a922),x87263)))+~P1(f335(f67(f934(x87262,a922)),x87263))+~P1(f335(f67(x87262),f43(f934(x87262,a922),x87263))) % 186.01/186.04 [8990]E(f335(f335(f87(a927),x89901),f335(f41(f934(x89902,a922)),x89903)),f335(f41(x89902),f43(f934(x89902,a922),x89903)))+P1(f335(f335(f337(f934(x89902,a922)),f585(x89901,x89903,x89902)),x89903))+P1(f335(f335(f337(f934(x89902,a922)),f584(x89901,x89903,x89902)),x89903))+~P1(f335(f67(f934(x89902,a922)),x89903))+~P1(f335(f67(x89902),f43(f934(x89902,a922),x89903))) % 186.01/186.04 [8991]E(f335(f335(f87(a927),x89911),f335(f41(f934(x89912,a922)),x89913)),f335(f41(x89912),f43(f934(x89912,a922),x89913)))+P1(f335(f335(f337(f934(x89912,a922)),f585(x89911,x89913,x89912)),x89913))+P1(f335(f335(f337(f934(x89912,a922)),f583(x89911,x89913,x89912)),x89913))+~P1(f335(f67(f934(x89912,a922)),x89913))+~P1(f335(f67(x89912),f43(f934(x89912,a922),x89913))) % 186.01/186.04 [9017]~E(f335(f335(f108(f934(x90172,a922)),f584(x90171,x90173,x90172)),f583(x90171,x90173,x90172)),f195(f934(x90172,a922)))+E(f335(f335(f87(a927),x90171),f335(f41(f934(x90172,a922)),x90173)),f335(f41(x90172),f43(f934(x90172,a922),x90173)))+~P1(f335(f67(f934(x90172,a922)),x90173))+P1(f335(f335(f337(f934(x90172,a922)),f585(x90171,x90173,x90172)),x90173))+~P1(f335(f67(x90172),f43(f934(x90172,a922),x90173))) % 186.01/186.04 [9276]~P96(x92762)+E(x92761,f195(f934(x92762,a922)))+~E(f335(f335(f87(x92762),f335(x92763,f380(x92761,x92763,x92762))),f335(x92763,f381(x92761,x92763,x92762))),f335(x92763,f335(f335(f87(x92762),f380(x92761,x92763,x92762)),f381(x92761,x92763,x92762))))+~P1(f335(f67(x92762),x92761))+E(f335(f69(x92762,f87(x92762)),f335(f318(x92762,x92762,x92763),x92761)),f335(x92763,f335(f69(x92762,f87(x92762)),x92761))) % 186.01/186.04 [10208]P1(f335(f335(x102081,x102082),x102083))+P1(f335(f335(f244(a1),f479(x102081,x102083,x102082)),f487(x102081,x102083,x102082)))+P1(f335(f335(f243(a1),f487(x102081,x102083,x102082)),f2(a1)))+P1(f335(f335(x102081,f479(x102081,x102083,x102082)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f487(x102081,x102083,x102082))))+~P1(f335(f323(f933(a1,a1),a64),f335(f335(f260(a1,a1),x102082),x102083))) % 186.01/186.04 [10214]P1(f335(f335(x102141,x102142),x102143))+P1(f335(f335(f243(a1),f489(x102141,x102143,x102142)),f2(a1)))+P1(f335(f335(x102141,f488(x102141,x102143,x102142)),f335(f335(f87(a1),f335(f110(a1),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f489(x102141,x102143,x102142))))+P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),f488(x102141,x102143,x102142)),f489(x102141,x102143,x102142))))+~P1(f335(f323(f933(a1,a1),a58),f335(f335(f260(a1,a1),x102142),x102143))) % 186.01/186.04 [8169]~P113(x81691)+~P1(f335(f335(f243(x81691),x81692),f84(x81691)))+~P1(f335(f335(f243(x81691),f2(x81691)),x81692))+~P1(f335(f335(f243(x81691),f2(x81691)),x81693))+P1(f335(f335(f243(x81691),f335(f335(f87(x81691),x81692),x81693)),x81693)) % 186.01/186.04 [8170]~P113(x81701)+~P1(f335(f335(f243(x81701),x81703),f84(x81701)))+~P1(f335(f335(f243(x81701),f2(x81701)),x81703))+~P1(f335(f335(f243(x81701),f2(x81701)),x81702))+P1(f335(f335(f243(x81701),f335(f335(f87(x81701),x81702),x81703)),x81702)) % 186.01/186.04 [8521]~P109(x85212)+E(x85211,f195(f934(x85212,a922)))+~P1(f335(f67(x85212),x85211))+P1(f335(f335(f337(x85212),f396(x85213,x85211,x85212)),x85211))+~P1(f335(f335(f243(x85212),f335(f69(x85212,f241(x85212)),x85211)),x85213)) % 186.01/186.04 [8522]~P109(x85222)+E(x85221,f195(f934(x85222,a922)))+~P1(f335(f67(x85222),x85221))+P1(f335(f335(f337(x85222),f397(x85223,x85221,x85222)),x85221))+~P1(f335(f335(f244(x85222),f335(f69(x85222,f241(x85222)),x85221)),x85223)) % 186.01/186.04 [8523]~P109(x85232)+E(x85231,f195(f934(x85232,a922)))+~P1(f335(f67(x85232),x85231))+P1(f335(f335(f243(x85232),f396(x85233,x85231,x85232)),x85233))+~P1(f335(f335(f243(x85232),f335(f69(x85232,f241(x85232)),x85231)),x85233)) % 186.01/186.04 [8524]~P109(x85242)+E(x85241,f195(f934(x85242,a922)))+~P1(f335(f67(x85242),x85241))+P1(f335(f335(f244(x85242),f397(x85243,x85241,x85242)),x85243))+~P1(f335(f335(f244(x85242),f335(f69(x85242,f241(x85242)),x85241)),x85243)) % 186.01/186.04 [8610]~P1(f335(x86101,x86103))+P1(f335(x86101,f528(x86101,x86102)))+P1(f335(x86101,f521(x86101,x86102)))+~P1(f335(f335(f244(a1),f2(a1)),x86102))+P1(f335(x86101,f335(f335(f23(a1),f521(x86101,x86102)),f335(f335(f87(a1),f529(x86101,x86102)),x86102)))) % 186.01/186.04 [8827]~P1(f335(x88271,x88273))+P1(f335(x88271,f521(x88271,x88272)))+~P1(f335(f335(f244(a1),f2(a1)),x88272))+P1(f335(f335(f337(a1),f528(x88271,x88272)),f311(a1,f84(a1),x88272)))+P1(f335(x88271,f335(f335(f23(a1),f521(x88271,x88272)),f335(f335(f87(a1),f529(x88271,x88272)),x88272)))) % 186.01/186.04 [9039]~P1(f335(x90391,x90393))+~P1(f335(x90391,f521(x90391,x90392)))+P1(f335(x90391,f528(x90391,x90392)))+~P1(f335(f335(f244(a1),f2(a1)),x90392))+~P1(f335(x90391,f335(f335(f23(a1),f521(x90391,x90392)),f335(f335(f87(a1),f529(x90391,x90392)),x90392)))) % 186.01/186.04 [9167]~P1(f335(x91671,x91673))+~P1(f335(x91671,f521(x91671,x91672)))+~P1(f335(f335(f244(a1),f2(a1)),x91672))+P1(f335(f335(f337(a1),f528(x91671,x91672)),f311(a1,f84(a1),x91672)))+~P1(f335(x91671,f335(f335(f23(a1),f521(x91671,x91672)),f335(f335(f87(a1),f529(x91671,x91672)),x91672)))) % 186.01/186.04 [8945]~P98(x89451)+~P1(f335(f67(x89451),x89452))+E(f335(f335(f23(f934(x89451,a922)),x89452),f335(f335(f317(x89451),x89453),f195(f934(x89451,a922)))),f195(f934(x89451,a922)))+~P1(f335(f335(f337(x89451),x89453),x89452))+E(f335(f335(f117(x89451),x89453),f13(x89451,f335(f335(f23(f934(x89451,a922)),x89452),f335(f335(f317(x89451),x89453),f195(f934(x89451,a922)))))),f13(x89451,x89452)) % 186.01/186.04 [8946]~P98(x89461)+~P1(f335(f67(x89461),x89462))+E(f335(f335(f23(f934(x89461,a922)),x89462),f335(f335(f317(x89461),x89463),f195(f934(x89461,a922)))),f195(f934(x89461,a922)))+~P1(f335(f335(f337(x89461),x89463),x89462))+E(f335(f335(f108(x89461),x89463),f10(x89461,f335(f335(f23(f934(x89461,a922)),x89462),f335(f335(f317(x89461),x89463),f195(f934(x89461,a922)))))),f10(x89461,x89462)) % 186.01/186.04 [8947]~P109(x89471)+~P1(f335(f67(x89471),x89472))+E(f335(f335(f23(f934(x89471,a922)),x89472),f335(f335(f317(x89471),x89473),f195(f934(x89471,a922)))),f195(f934(x89471,a922)))+~P1(f335(f335(f337(x89471),x89473),x89472))+E(f335(f335(f242(x89471),x89473),f14(x89471,f335(f335(f23(f934(x89471,a922)),x89472),f335(f335(f317(x89471),x89473),f195(f934(x89471,a922)))))),f14(x89471,x89472)) % 186.01/186.04 [8948]~P109(x89481)+~P1(f335(f67(x89481),x89482))+E(f335(f335(f23(f934(x89481,a922)),x89482),f335(f335(f317(x89481),x89483),f195(f934(x89481,a922)))),f195(f934(x89481,a922)))+~P1(f335(f335(f337(x89481),x89483),x89482))+E(f335(f335(f241(x89481),x89483),f15(x89481,f335(f335(f23(f934(x89481,a922)),x89482),f335(f335(f317(x89481),x89483),f195(f934(x89481,a922)))))),f15(x89481,x89482)) % 186.01/186.04 [9010]~P109(x90101)+~P1(f335(f67(x90101),x90102))+E(f335(f335(f23(f934(x90101,a922)),x90102),f335(f335(f317(x90101),x90103),f195(f934(x90101,a922)))),f195(f934(x90101,a922)))+~P1(f335(f335(f337(x90101),x90103),x90102))+E(f335(f335(f242(x90101),x90103),f11(x90101,f242(x90101),f335(f335(f23(f934(x90101,a922)),x90102),f335(f335(f317(x90101),x90103),f195(f934(x90101,a922)))))),f11(x90101,f242(x90101),x90102)) % 186.01/186.04 [9011]~P109(x90111)+~P1(f335(f67(x90111),x90112))+E(f335(f335(f23(f934(x90111,a922)),x90112),f335(f335(f317(x90111),x90113),f195(f934(x90111,a922)))),f195(f934(x90111,a922)))+~P1(f335(f335(f337(x90111),x90113),x90112))+E(f335(f335(f241(x90111),x90113),f12(x90111,f241(x90111),f335(f335(f23(f934(x90111,a922)),x90112),f335(f335(f317(x90111),x90113),f195(f934(x90111,a922)))))),f12(x90111,f241(x90111),x90112)) % 186.01/186.04 [9026]~P98(x90261)+~P1(f335(f67(x90261),x90263))+~P1(f335(f67(x90261),x90262))+E(f335(f335(f108(f934(x90261,a922)),x90262),x90263),f195(f934(x90261,a922)))+E(f335(f335(f108(x90261),f10(x90261,f335(f335(f117(f934(x90261,a922)),x90262),x90263))),f10(x90261,f335(f335(f108(f934(x90261,a922)),x90262),x90263))),f335(f335(f108(x90261),f10(x90261,x90262)),f10(x90261,x90263))) % 186.01/186.04 [9027]~P98(x90271)+~P1(f335(f67(x90271),x90273))+~P1(f335(f67(x90271),x90272))+E(f335(f335(f108(f934(x90271,a922)),x90272),x90273),f195(f934(x90271,a922)))+E(f335(f335(f117(x90271),f13(x90271,f335(f335(f117(f934(x90271,a922)),x90272),x90273))),f13(x90271,f335(f335(f108(f934(x90271,a922)),x90272),x90273))),f335(f335(f117(x90271),f13(x90271,x90272)),f13(x90271,x90273))) % 186.01/186.04 [9028]~P109(x90281)+~P1(f335(f67(x90281),x90283))+~P1(f335(f67(x90281),x90282))+E(f335(f335(f108(f934(x90281,a922)),x90282),x90283),f195(f934(x90281,a922)))+E(f335(f335(f241(x90281),f15(x90281,f335(f335(f117(f934(x90281,a922)),x90282),x90283))),f15(x90281,f335(f335(f108(f934(x90281,a922)),x90282),x90283))),f335(f335(f241(x90281),f15(x90281,x90282)),f15(x90281,x90283))) % 186.01/186.04 [9029]~P109(x90291)+~P1(f335(f67(x90291),x90293))+~P1(f335(f67(x90291),x90292))+E(f335(f335(f108(f934(x90291,a922)),x90292),x90293),f195(f934(x90291,a922)))+E(f335(f335(f242(x90291),f14(x90291,f335(f335(f117(f934(x90291,a922)),x90292),x90293))),f14(x90291,f335(f335(f108(f934(x90291,a922)),x90292),x90293))),f335(f335(f242(x90291),f14(x90291,x90292)),f14(x90291,x90293))) % 186.01/186.04 [9248]~P109(x92481)+~P1(f335(f67(x92481),x92483))+~P1(f335(f67(x92481),x92482))+E(f335(f335(f108(f934(x92481,a922)),x92482),x92483),f195(f934(x92481,a922)))+E(f335(f335(f241(x92481),f12(x92481,f241(x92481),f335(f335(f117(f934(x92481,a922)),x92482),x92483))),f12(x92481,f241(x92481),f335(f335(f108(f934(x92481,a922)),x92482),x92483))),f335(f335(f241(x92481),f12(x92481,f241(x92481),x92482)),f12(x92481,f241(x92481),x92483))) % 186.01/186.04 [9249]~P109(x92491)+~P1(f335(f67(x92491),x92493))+~P1(f335(f67(x92491),x92492))+E(f335(f335(f108(f934(x92491,a922)),x92492),x92493),f195(f934(x92491,a922)))+E(f335(f335(f242(x92491),f11(x92491,f242(x92491),f335(f335(f117(f934(x92491,a922)),x92492),x92493))),f11(x92491,f242(x92491),f335(f335(f108(f934(x92491,a922)),x92492),x92493))),f335(f335(f242(x92491),f11(x92491,f242(x92491),x92492)),f11(x92491,f242(x92491),x92493))) % 186.01/186.04 [10042]~P125(x100423)+E(x100421,x100422)+~P1(f335(f335(f243(x100423),f2(x100423)),x100422))+~P1(f335(f335(f243(x100423),f2(x100423)),x100421))+~E(f335(f335(f252(x100423),x100421),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)))),f335(f335(f252(x100423),x100422),f335(f110(a927),f335(f335(f86(a1),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104)),f335(f335(f23(a1),f335(f335(f86(a1),a89),a89)),a104))))) % 186.01/186.04 [6582]E(f401(x65821,x65822,x65823),x65824)+E(f335(x65821,x65824),f2(a927))+~E(f335(f335(f6(x65823,a927),x65821),x65822),f84(a927))+~P1(f335(f67(x65823),x65822))+~P1(f335(f335(f337(x65823),x65824),x65822)) % 186.01/186.04 [6644]E(f404(x66441,x66442,x66443),x66444)+E(f335(x66441,x66444),f2(a927))+~E(f335(f335(f6(x66443,a927),x66441),x66442),f335(a119,f2(a927)))+~P1(f335(f67(x66443),x66442))+~P1(f335(f335(f337(x66443),x66444),x66442)) % 186.01/186.04 [6752]~P109(x67521)+~P6(x67521)+P1(f335(f335(f244(x67521),x67522),f43(x67521,x67523)))+~P1(f335(f335(f244(x67521),x67522),x67524))+~P1(f335(f335(f337(x67521),x67524),x67523)) % 186.01/186.04 [6926]~P109(x69261)+~P6(x69261)+~P1(f335(f335(f244(x69261),x69264),x69263))+P1(f335(f335(f244(x69261),f44(x69261,x69262)),x69263))+~P1(f335(f335(f337(x69261),x69264),x69262)) % 186.01/186.04 [7179]~P125(x71793)+E(x71791,x71792)+~E(f335(f335(f252(x71793),x71791),f335(a119,x71794)),f335(f335(f252(x71793),x71792),f335(a119,x71794)))+~P1(f335(f335(f243(x71793),f2(x71793)),x71792))+~P1(f335(f335(f243(x71793),f2(x71793)),x71791)) % 186.01/186.04 [7389]~E(f407(x73892,x73893,x73891,x73894),x73894)+~E(f335(x73892,x73894),f84(a927))+E(f335(f335(f6(x73891,a927),x73892),x73893),f84(a927))+~P1(f335(f67(x73891),x73893))+~P1(f335(f335(f337(x73891),x73894),x73893)) % 186.01/186.04 [7396]~P118(x73964)+~P129(x73964)+E(f335(x73961,f470(x73961,x73962,x73963,x73964)),f2(x73964))+~E(f335(f335(f9(x73963,x73964),x73961),x73962),f2(x73964))+~P1(f335(f67(x73963),x73962)) % 186.01/186.04 [7485]~E(f405(x74852,x74853,x74851,x74854),x74854)+~E(f335(x74852,x74854),f335(a119,f2(a927)))+E(f335(f335(f6(x74851,a927),x74852),x74853),f335(a119,f2(a927)))+~P1(f335(f67(x74851),x74853))+~P1(f335(f335(f337(x74851),x74854),x74853)) % 186.01/186.04 [8210]~E(f335(x82102,x82104),f84(a927))+~E(f335(x82102,f407(x82102,x82103,x82101,x82104)),f2(a927))+E(f335(f335(f6(x82101,a927),x82102),x82103),f84(a927))+~P1(f335(f67(x82101),x82103))+~P1(f335(f335(f337(x82101),x82104),x82103)) % 186.01/186.04 [8248]~E(f335(x82482,x82484),f335(a119,f2(a927)))+~E(f335(x82482,f405(x82482,x82483,x82481,x82484)),f2(a927))+E(f335(f335(f6(x82481,a927),x82482),x82483),f335(a119,f2(a927)))+~P1(f335(f67(x82481),x82483))+~P1(f335(f335(f337(x82481),x82484),x82483)) % 186.01/186.04 [8794]~P109(x87941)+~P14(x87941,x87944)+P14(x87941,x87942)+~E(x87942,f335(f335(f158(x87941),x87943),x87944))+~P1(f335(f335(f243(x87941),x87943),f751(x87942,x87941,x87944,x87943))) % 186.01/186.04 [8831]E(x88311,x88312)+E(f335(f335(f23(a1),f514(x88313,x88312,x88314,x88311)),f515(x88313,x88312,x88314,x88311)),x88311)+~E(f335(f335(f86(a1),x88311),x88314),x88312)+~P1(f335(f335(f244(a1),f2(a1)),x88314))+~P1(f335(f335(f337(a1),x88312),x88313)) % 186.01/186.04 [8832]E(x88321,x88322)+E(f335(f335(f86(a1),f516(x88323,x88322,x88324,x88321)),f517(x88323,x88322,x88324,x88321)),x88321)+~E(f335(f335(f23(a1),x88321),x88324),x88322)+~P1(f335(f335(f244(a1),f2(a1)),x88324))+~P1(f335(f335(f337(a1),x88322),x88323)) % 186.01/186.04 [9024]E(f335(x90241,f634(x90242,x90241,x90243,x90244)),x90242)+P1(f335(f335(f243(a927),x90244),f635(x90242,x90241,x90243,x90244)))+~P1(f335(f335(f243(a1),x90242),f335(x90241,x90243)))+~P1(f335(f335(f244(a927),x90244),x90243))+~P1(f335(f335(f243(a1),f335(x90241,x90244)),x90242)) % 186.01/186.04 [9025]~P109(x90251)+~P14(x90251,x90253)+P14(x90251,x90252)+~E(x90252,f335(f335(f158(x90251),x90254),x90253))+P1(f335(f335(f337(x90251),f751(x90252,x90251,x90253,x90254)),f335(f179(x90251),x90253))) % 186.01/186.04 [9043]~P118(x90434)+~P129(x90434)+~E(f335(f335(f9(x90431,x90434),x90432),x90433),f2(x90434))+~P1(f335(f67(x90431),x90433))+P1(f335(f335(f337(x90431),f470(x90432,x90433,x90431,x90434)),x90433)) % 186.01/186.04 [9081]~E(f335(x90812,x90814),f84(a927))+E(f335(f335(f6(x90811,a927),x90812),x90813),f84(a927))+~P1(f335(f67(x90811),x90813))+~P1(f335(f335(f337(x90811),x90814),x90813))+P1(f335(f335(f337(x90811),f407(x90812,x90813,x90811,x90814)),x90813)) % 186.01/186.04 [9093]E(x90931,x90932)+~E(f335(f335(f86(a1),x90932),x90934),x90931)+~P1(f335(f335(f244(a1),f2(a1)),x90934))+~P1(f335(f335(f337(a1),x90931),x90933))+P1(f335(f335(f337(a1),f514(x90933,x90931,x90934,x90932)),x90933)) % 186.01/186.04 [9094]E(x90941,x90942)+~E(f335(f335(f23(a1),x90942),x90944),x90941)+~P1(f335(f335(f244(a1),f2(a1)),x90944))+~P1(f335(f335(f337(a1),x90941),x90943))+P1(f335(f335(f337(a1),f516(x90943,x90941,x90944,x90942)),x90943)) % 186.01/186.04 [9096]~E(f335(x90962,x90964),f335(a119,f2(a927)))+E(f335(f335(f6(x90961,a927),x90962),x90963),f335(a119,f2(a927)))+~P1(f335(f67(x90961),x90963))+~P1(f335(f335(f337(x90961),x90964),x90963))+P1(f335(f335(f337(x90961),f405(x90962,x90963,x90961,x90964)),x90963)) % 186.01/186.04 [9101]P60(x91012,x91013,x91014,x91011)+E(x91011,f195(f934(x91012,a922)))+~P1(f335(f67(x91012),x91014))+~P1(f335(f67(x91012),x91011))+P1(f335(f335(f337(x91012),f822(x91013,x91011,x91014,x91012)),x91014)) % 186.01/186.04 [9102]P60(x91022,x91023,x91024,x91021)+E(x91021,f195(f934(x91022,a922)))+~P1(f335(f67(x91022),x91024))+~P1(f335(f67(x91022),x91021))+P1(f335(f335(f337(x91022),f359(x91021,x91024,x91023,x91022)),x91024)) % 186.01/186.04 [9103]P60(x91032,x91033,x91034,x91031)+E(x91031,f195(f934(x91032,a922)))+~P1(f335(f67(x91032),x91034))+~P1(f335(f67(x91032),x91031))+P1(f335(f335(f337(x91032),f823(x91031,x91034,x91033,x91032)),x91034)) % 186.01/186.04 [9180]E(x91801,x91802)+~E(f335(f335(f86(a1),x91802),x91804),x91801)+~P1(f335(f335(f244(a1),f2(a1)),x91804))+~P1(f335(f335(f337(a1),x91801),x91803))+P1(f335(f335(f337(a1),f515(x91803,x91801,x91804,x91802)),f311(a1,f84(a1),x91804))) % 186.01/186.04 [9181]E(x91811,x91812)+~E(f335(f335(f23(a1),x91812),x91814),x91811)+~P1(f335(f335(f244(a1),f2(a1)),x91814))+~P1(f335(f335(f337(a1),x91811),x91813))+P1(f335(f335(f337(a1),f517(x91813,x91811,x91814,x91812)),f311(a1,f84(a1),x91814))) % 186.01/186.04 [9254]P1(f335(f335(f243(a927),x92541),f634(x92542,x92543,x92544,x92541)))+~P1(f335(f335(f243(a1),x92542),f335(x92543,x92544)))+P1(f335(f335(f243(a927),x92541),f635(x92542,x92543,x92544,x92541)))+~P1(f335(f335(f244(a927),x92541),x92544))+~P1(f335(f335(f243(a1),f335(x92543,x92541)),x92542)) % 186.01/186.04 [9369]E(f335(x93691,f634(x93692,x93691,x93693,x93694)),x93692)+~P1(f335(f335(f243(a1),x93692),f335(x93691,x93693)))+P1(f335(f335(f244(a927),f635(x93692,x93691,x93693,x93694)),x93693))+~P1(f335(f335(f244(a927),x93694),x93693))+~P1(f335(f335(f243(a1),f335(x93691,x93694)),x93692)) % 186.01/186.04 [9495]~P1(f335(f335(f243(a1),x94952),f335(x94953,x94954)))+P1(f335(f335(f243(a927),x94951),f635(x94952,x94953,x94954,x94951)))+P1(f335(f335(f243(a927),f634(x94952,x94953,x94954,x94951)),x94954))+~P1(f335(f335(f244(a927),x94951),x94954))+~P1(f335(f335(f243(a1),f335(x94953,x94951)),x94952)) % 186.01/186.04 [9496]~P1(f335(f335(f243(a1),x94962),f335(x94963,x94964)))+P1(f335(f335(f243(a927),x94961),f634(x94962,x94963,x94964,x94961)))+P1(f335(f335(f244(a927),f635(x94962,x94963,x94964,x94961)),x94964))+~P1(f335(f335(f244(a927),x94961),x94964))+~P1(f335(f335(f243(a1),f335(x94963,x94961)),x94962)) % 186.01/186.04 [9604]~P1(f335(f335(f243(a1),x96041),f335(x96042,x96043)))+P1(f335(f335(f244(a927),f635(x96041,x96042,x96043,x96044)),x96043))+~P1(f335(f335(f244(a927),x96044),x96043))+~P1(f335(f335(f243(a1),f335(x96042,x96044)),x96041))+P1(f335(f335(f243(a927),f634(x96041,x96042,x96043,x96044)),x96043)) % 186.01/186.04 [9688]E(x96881,f195(f934(x96882,a922)))+~P1(f335(f67(x96882),x96884))+~P1(f335(f67(x96882),x96881))+P1(f335(f335(f337(f933(f934(x96882,a922),f934(x96882,a922))),f335(f335(f260(f934(x96882,a922),f934(x96882,a922)),x96884),x96881)),f327(x96882,x96883)))+P1(f335(f335(f337(x96882),f361(x96883,x96881,x96884,x96882)),x96884)) % 186.01/186.04 [9689]E(x96891,f195(f934(x96892,a922)))+~P1(f335(f67(x96892),x96894))+~P1(f335(f67(x96892),x96891))+P1(f335(f335(f337(f933(f934(x96892,a922),f934(x96892,a922))),f335(f335(f260(f934(x96892,a922),f934(x96892,a922)),x96894),x96891)),f327(x96892,x96893)))+P1(f335(f335(f337(x96892),f610(x96893,x96891,x96894,x96892)),x96894)) % 186.01/186.04 [10366]E(f335(x103661,f634(x103662,x103661,x103663,x103664)),x103662)+~P1(f335(f335(f243(a1),x103662),f335(x103661,x103663)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x103661,f335(f335(f86(a927),f635(x103662,x103661,x103663,x103664)),f84(a927)))),f335(x103661,f635(x103662,x103661,x103663,x103664))))),f84(a1)))+~P1(f335(f335(f244(a927),x103664),x103663))+~P1(f335(f335(f243(a1),f335(x103661,x103664)),x103662)) % 186.01/186.04 [10367]~P1(f335(f335(f243(a1),x103672),f335(x103673,x103674)))+P1(f335(f335(f243(a927),x103671),f634(x103672,x103673,x103674,x103671)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x103673,f335(f335(f86(a927),f635(x103672,x103673,x103674,x103671)),f84(a927)))),f335(x103673,f635(x103672,x103673,x103674,x103671))))),f84(a1)))+~P1(f335(f335(f244(a927),x103671),x103674))+~P1(f335(f335(f243(a1),f335(x103673,x103671)),x103672)) % 186.01/186.04 [10368]~P1(f335(f335(f243(a1),x103681),f335(x103682,x103683)))+~P1(f335(f335(f243(a1),f335(f81(a1),f335(f335(f23(a1),f335(x103682,f335(f335(f86(a927),f635(x103681,x103682,x103683,x103684)),f84(a927)))),f335(x103682,f635(x103681,x103682,x103683,x103684))))),f84(a1)))+~P1(f335(f335(f244(a927),x103684),x103683))+~P1(f335(f335(f243(a1),f335(x103682,x103684)),x103681))+P1(f335(f335(f243(a927),f634(x103681,x103682,x103683,x103684)),x103683)) % 186.01/186.04 [7448]~P68(x74481)+P1(f335(f335(f244(x74481),x74482),f2(x74481)))+~P1(f335(f335(f243(x74481),x74483),f2(x74481)))+P1(f335(f335(f244(x74481),f2(x74481)),x74482))+P1(f335(f335(f243(x74481),x74483),f335(f335(f299(x74481),x74484),x74482))) % 186.01/186.04 [7449]~P68(x74491)+P1(f335(f335(f244(x74491),x74492),f2(x74491)))+~P1(f335(f335(f244(x74491),x74493),f2(x74491)))+P1(f335(f335(f244(x74491),f2(x74491)),x74492))+P1(f335(f335(f244(x74491),x74493),f335(f335(f299(x74491),x74494),x74492))) % 186.01/186.04 [7699]~P68(x76991)+P1(f335(f335(f243(x76991),x76992),f2(x76991)))+P1(f335(f335(f244(x76991),x76993),f2(x76991)))+P1(f335(f335(f244(x76991),f2(x76991)),x76993))+~P1(f335(f335(f243(x76991),x76992),f335(f335(f299(x76991),x76994),x76993))) % 186.01/186.04 [7700]~P68(x77001)+P1(f335(f335(f244(x77001),x77002),f2(x77001)))+P1(f335(f335(f244(x77001),x77003),f2(x77001)))+P1(f335(f335(f244(x77001),f2(x77001)),x77003))+~P1(f335(f335(f244(x77001),x77002),f335(f335(f299(x77001),x77004),x77003))) % 186.01/186.04 [7814]E(x78141,x78142)+~E(f335(f335(f171(x78143),x78144),x78141),f335(f335(f171(x78143),x78144),x78142))+~P1(f335(f144(x78143),x78144))+~P1(f335(f335(f244(a927),x78142),f335(f196(f928(x78143)),x78144)))+~P1(f335(f335(f244(a927),x78141),f335(f196(f928(x78143)),x78144))) % 186.01/186.04 [8171]~P68(x81711)+~P1(f335(f335(f243(x81711),x81713),f2(x81711)))+P1(f335(f335(f244(x81711),f2(x81711)),x81712))+~P1(f335(f335(f243(x81711),x81714),f335(f335(f87(x81711),x81713),x81712)))+P1(f335(f335(f243(x81711),x81713),f335(f335(f299(x81711),x81714),x81712))) % 186.01/186.04 [8172]~P68(x81721)+~P1(f335(f335(f244(x81721),x81723),f2(x81721)))+P1(f335(f335(f244(x81721),f2(x81721)),x81722))+~P1(f335(f335(f244(x81721),x81724),f335(f335(f87(x81721),x81723),x81722)))+P1(f335(f335(f244(x81721),x81723),f335(f335(f299(x81721),x81724),x81722))) % 186.01/186.04 [8173]~P68(x81731)+~P1(f335(f335(f244(x81731),x81732),f2(x81731)))+P1(f335(f335(f244(x81731),f2(x81731)),x81732))+~P1(f335(f335(f243(x81731),x81734),f335(f335(f87(x81731),x81733),x81732)))+P1(f335(f335(f243(x81731),x81733),f335(f335(f299(x81731),x81734),x81732))) % 186.01/186.04 [8174]~P68(x81741)+~P1(f335(f335(f244(x81741),x81742),f2(x81741)))+P1(f335(f335(f244(x81741),f2(x81741)),x81742))+~P1(f335(f335(f243(x81741),x81744),f335(f335(f299(x81741),x81743),x81742)))+P1(f335(f335(f243(x81741),x81743),f335(f335(f87(x81741),x81744),x81742))) % 186.01/186.04 [8175]~P68(x81751)+~P1(f335(f335(f244(x81751),x81752),f2(x81751)))+P1(f335(f335(f244(x81751),f2(x81751)),x81752))+~P1(f335(f335(f244(x81751),x81754),f335(f335(f87(x81751),x81753),x81752)))+P1(f335(f335(f244(x81751),x81753),f335(f335(f299(x81751),x81754),x81752))) % 186.01/186.04 [8176]~P68(x81761)+~P1(f335(f335(f244(x81761),x81762),f2(x81761)))+P1(f335(f335(f244(x81761),f2(x81761)),x81762))+~P1(f335(f335(f244(x81761),x81764),f335(f335(f299(x81761),x81763),x81762)))+P1(f335(f335(f244(x81761),x81763),f335(f335(f87(x81761),x81764),x81762))) % 186.01/186.04 [8302]~P63(x83021)+~P1(f335(f335(f295(x83021),x83023),x83024))+~P1(f335(f335(f295(x83021),x83023),x83022))+~P1(f335(f335(f295(x83021),x83022),x83024))+P1(f335(f335(f295(x83021),f335(f335(f42(x83021),x83022),x83023)),f335(f335(f42(x83021),x83024),x83023))) % 186.01/186.04 [8317]~P109(x83171)+~P14(x83171,x83172)+~P1(f335(f335(f243(a927),x83173),x83174))+P1(f335(f335(f243(x83171),f335(f335(f171(x83171),x83172),x83173)),f335(f335(f171(x83171),x83172),x83174)))+~P1(f335(f335(f244(a927),x83174),f335(f196(f928(x83171)),x83172))) % 186.01/186.04 [8365]~P125(x83651)+~P1(f335(f335(f243(x83651),x83652),f84(x83651)))+~P1(f335(f335(f243(x83651),f2(x83651)),x83652))+~P1(f335(f335(f243(a927),x83654),x83653))+P1(f335(f335(f243(x83651),f335(f335(f252(x83651),x83652),x83653)),f335(f335(f252(x83651),x83652),x83654))) % 186.01/186.04 [8366]~P125(x83661)+~P1(f335(f335(f244(x83661),x83662),f84(x83661)))+~P1(f335(f335(f244(x83661),f2(x83661)),x83662))+~P1(f335(f335(f244(a927),x83664),x83663))+P1(f335(f335(f244(x83661),f335(f335(f252(x83661),x83662),x83663)),f335(f335(f252(x83661),x83662),x83664))) % 186.01/186.04 [8367]~P125(x83671)+~P1(f335(f335(f243(x83671),f2(x83671)),x83672))+~P1(f335(f335(f244(a927),f2(a927)),x83673))+~P1(f335(f335(f244(x83671),x83672),x83674))+P1(f335(f335(f244(x83671),f335(f335(f252(x83671),x83672),x83673)),f335(f335(f252(x83671),x83674),x83673))) % 186.01/186.04 [8385]~P109(x83851)+~P14(x83851,f335(f175(x83851),x83852))+~P1(f335(f335(f243(a927),x83854),x83853))+P1(f335(f335(f243(x83851),f335(f335(f171(x83851),x83852),x83853)),f335(f335(f171(x83851),x83852),x83854)))+~P1(f335(f335(f244(a927),x83853),f335(f196(f928(x83851)),x83852))) % 186.01/186.04 [8616]~P63(x86161)+P1(f335(f335(f295(x86161),x86162),x86163))+~P1(f335(f335(f295(x86161),x86164),x86163))+~P1(f335(f335(f295(x86161),x86164),x86162))+~P1(f335(f335(f295(x86161),f335(f335(f42(x86161),x86162),x86164)),f335(f335(f42(x86161),x86163),x86164))) % 186.01/186.04 [8631]~P68(x86311)+~P1(f335(f335(f243(x86311),x86312),f2(x86311)))+~P1(f335(f335(f243(x86311),x86313),x86314))+~P1(f335(f335(f244(x86311),f2(x86311)),f335(f335(f87(x86311),x86313),x86314)))+P1(f335(f335(f243(x86311),f335(f335(f299(x86311),x86312),x86313)),f335(f335(f299(x86311),x86312),x86314))) % 186.01/186.04 [8632]~P69(x86321)+~P1(f335(f335(f244(x86321),x86322),f2(x86321)))+~P1(f335(f335(f244(x86321),x86323),x86324))+~P1(f335(f335(f244(x86321),f2(x86321)),f335(f335(f87(x86321),x86323),x86324)))+P1(f335(f335(f244(x86321),f335(f335(f299(x86321),x86322),x86323)),f335(f335(f299(x86321),x86322),x86324))) % 186.01/186.04 [8641]~P69(x86411)+~P1(f335(f335(f243(x86411),x86414),x86413))+~P1(f335(f335(f243(x86411),f2(x86411)),x86412))+~P1(f335(f335(f244(x86411),f2(x86411)),f335(f335(f87(x86411),x86413),x86414)))+P1(f335(f335(f243(x86411),f335(f335(f299(x86411),x86412),x86413)),f335(f335(f299(x86411),x86412),x86414))) % 186.01/186.04 [8642]~P69(x86421)+~P1(f335(f335(f244(x86421),x86424),x86423))+~P1(f335(f335(f244(x86421),f2(x86421)),x86422))+~P1(f335(f335(f244(x86421),f2(x86421)),f335(f335(f87(x86421),x86423),x86424)))+P1(f335(f335(f244(x86421),f335(f335(f299(x86421),x86422),x86423)),f335(f335(f299(x86421),x86422),x86424))) % 186.01/186.04 [8742]P1(f335(x87421,x87422))+~P1(f335(f67(x87424),x87422))+P1(f335(x87421,f356(x87421,x87423,x87422,x87424)))+~P1(f335(x87421,f195(f934(x87424,a922))))+~P1(f335(f335(f243(f934(x87424,a922)),x87422),x87423)) % 186.01/186.04 [8751]P1(f335(x87511,x87512))+P1(f335(f67(x87513),f356(x87511,x87514,x87512,x87513)))+~P1(f335(f67(x87513),x87512))+~P1(f335(x87511,f195(f934(x87513,a922))))+~P1(f335(f335(f243(f934(x87513,a922)),x87512),x87514)) % 186.01/186.04 [9019]E(f335(f335(f86(a1),f518(x90191,x90192,x90193,x90194)),f519(x90191,x90192,x90193,x90194)),x90194)+~P1(f335(f335(f244(a1),f2(a1)),x90193))+~P1(f335(f335(f244(a1),x90192),x90194))+~P1(f335(f335(f337(a1),x90192),x90191))+P1(f335(f335(f244(a1),x90192),f335(f335(f23(a1),x90194),x90193))) % 186.01/186.04 [9236]~P1(f335(f335(f244(a1),f2(a1)),x92363))+~P1(f335(f335(f244(a1),x92362),x92364))+~P1(f335(f335(f337(a1),x92362),x92361))+P1(f335(f335(f337(a1),f518(x92361,x92362,x92363,x92364)),x92361))+P1(f335(f335(f244(a1),x92362),f335(f335(f23(a1),x92364),x92363))) % 186.01/186.04 [9247]P1(f335(x92471,x92472))+~P1(f335(f67(x92473),x92472))+P1(f335(f335(f337(x92473),f357(x92471,x92474,x92472,x92473)),x92474))+~P1(f335(x92471,f195(f934(x92473,a922))))+~P1(f335(f335(f243(f934(x92473,a922)),x92472),x92474)) % 186.01/186.04 [9264]E(f335(f335(f86(a1),f505(x92641,x92642,x92643,x92644)),f506(x92641,x92642,x92643,x92644)),x92644)+~P1(f335(f335(f244(a1),f2(a1)),x92643))+~P1(f335(f335(f243(a1),x92642),x92644))+P1(f335(f335(f243(a1),x92642),f335(f335(f23(a1),x92644),x92643)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x92642),f84(a1))),x92641)) % 186.01/186.04 [9319]~P1(f335(f335(f244(a1),f2(a1)),x93193))+~P1(f335(f335(f244(a1),x93191),x93192))+~P1(f335(f335(f337(a1),x93191),x93194))+P1(f335(f335(f337(a1),f519(x93194,x93191,x93193,x93192)),f311(a1,f84(a1),x93193)))+P1(f335(f335(f244(a1),x93191),f335(f335(f23(a1),x93192),x93193))) % 186.01/186.04 [9345]~P76(x93452)+~E(f808(x93453,x93454,x93451,x93452),f809(x93453,x93454,x93451,x93452))+~P1(f335(f67(x93451),f810(x93453,x93454,x93451,x93452)))+E(f335(f335(f6(f934(x93451,a922),x93452),f335(f6(x93451,x93452),x93453)),x93454),f335(f335(f6(x93451,x93452),x93453),f43(f934(x93451,a922),x93454)))+~P1(f335(f67(f934(x93451,a922)),x93454)) % 186.01/186.04 [9349]~P76(x93492)+~E(f335(x93493,f811(x93493,x93494,x93491,x93492)),f2(x93492))+~P1(f335(f67(x93491),f810(x93493,x93494,x93491,x93492)))+E(f335(f335(f6(f934(x93491,a922),x93492),f335(f6(x93491,x93492),x93493)),x93494),f335(f335(f6(x93491,x93492),x93493),f43(f934(x93491,a922),x93494)))+~P1(f335(f67(f934(x93491,a922)),x93494)) % 186.01/186.04 [9412]~P1(f335(f335(f244(a1),f2(a1)),x94123))+~P1(f335(f335(f243(a1),x94122),x94124))+P1(f335(f335(f337(a1),f505(x94121,x94122,x94123,x94124)),x94121))+P1(f335(f335(f243(a1),x94122),f335(f335(f23(a1),x94124),x94123)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x94122),f84(a1))),x94121)) % 186.01/186.04 [9454]~P1(f335(f335(f244(a1),f2(a1)),x94543))+~P1(f335(f335(f243(a1),x94541),x94542))+P1(f335(f335(f337(a1),f506(x94544,x94541,x94543,x94542)),f311(a1,f84(a1),x94543)))+P1(f335(f335(f243(a1),x94541),f335(f335(f23(a1),x94542),x94543)))+~P1(f335(f335(f337(a1),f335(f335(f23(a1),x94541),f84(a1))),x94544)) % 186.01/186.04 [9475]~P76(x94752)+~E(f808(x94753,x94754,x94751,x94752),f809(x94753,x94754,x94751,x94752))+E(f335(f335(f6(f934(x94751,a922),x94752),f335(f6(x94751,x94752),x94753)),x94754),f335(f335(f6(x94751,x94752),x94753),f43(f934(x94751,a922),x94754)))+P1(f335(f335(f337(f934(x94751,a922)),f810(x94753,x94754,x94751,x94752)),x94754))+~P1(f335(f67(f934(x94751,a922)),x94754)) % 186.01/186.04 [9480]~P76(x94802)+~E(f335(x94803,f811(x94803,x94804,x94801,x94802)),f2(x94802))+E(f335(f335(f6(f934(x94801,a922),x94802),f335(f6(x94801,x94802),x94803)),x94804),f335(f335(f6(x94801,x94802),x94803),f43(f934(x94801,a922),x94804)))+P1(f335(f335(f337(f934(x94801,a922)),f810(x94803,x94804,x94801,x94802)),x94804))+~P1(f335(f67(f934(x94801,a922)),x94804)) % 186.01/186.04 [9581]~P76(x95812)+~P1(f335(f67(x95811),f810(x95813,x95814,x95811,x95812)))+E(f335(f335(f6(f934(x95811,a922),x95812),f335(f6(x95811,x95812),x95813)),x95814),f335(f335(f6(x95811,x95812),x95813),f43(f934(x95811,a922),x95814)))+P1(f335(f335(f337(f934(x95811,a922)),f809(x95813,x95814,x95811,x95812)),x95814))+~P1(f335(f67(f934(x95811,a922)),x95814)) % 186.01/186.04 [9582]~P76(x95822)+~P1(f335(f67(x95821),f810(x95823,x95824,x95821,x95822)))+E(f335(f335(f6(f934(x95821,a922),x95822),f335(f6(x95821,x95822),x95823)),x95824),f335(f335(f6(x95821,x95822),x95823),f43(f934(x95821,a922),x95824)))+P1(f335(f335(f337(f934(x95821,a922)),f808(x95823,x95824,x95821,x95822)),x95824))+~P1(f335(f67(f934(x95821,a922)),x95824)) % 186.01/186.04 [9659]~P76(x96592)+E(f335(f335(f6(f934(x96591,a922),x96592),f335(f6(x96591,x96592),x96593)),x96594),f335(f335(f6(x96591,x96592),x96593),f43(f934(x96591,a922),x96594)))+P1(f335(f335(f337(f934(x96591,a922)),f810(x96593,x96594,x96591,x96592)),x96594))+P1(f335(f335(f337(f934(x96591,a922)),f809(x96593,x96594,x96591,x96592)),x96594))+~P1(f335(f67(f934(x96591,a922)),x96594)) % 186.01/186.04 [9660]~P76(x96602)+E(f335(f335(f6(f934(x96601,a922),x96602),f335(f6(x96601,x96602),x96603)),x96604),f335(f335(f6(x96601,x96602),x96603),f43(f934(x96601,a922),x96604)))+P1(f335(f335(f337(f934(x96601,a922)),f810(x96603,x96604,x96601,x96602)),x96604))+P1(f335(f335(f337(f934(x96601,a922)),f808(x96603,x96604,x96601,x96602)),x96604))+~P1(f335(f67(f934(x96601,a922)),x96604)) % 186.01/186.04 [9677]~P76(x96772)+P1(f335(f335(f337(x96771),f811(x96773,x96774,x96771,x96772)),f809(x96773,x96774,x96771,x96772)))+~P1(f335(f67(x96771),f810(x96773,x96774,x96771,x96772)))+E(f335(f335(f6(f934(x96771,a922),x96772),f335(f6(x96771,x96772),x96773)),x96774),f335(f335(f6(x96771,x96772),x96773),f43(f934(x96771,a922),x96774)))+~P1(f335(f67(f934(x96771,a922)),x96774)) % 186.01/186.04 [9678]~P76(x96782)+P1(f335(f335(f337(x96781),f811(x96783,x96784,x96781,x96782)),f808(x96783,x96784,x96781,x96782)))+~P1(f335(f67(x96781),f810(x96783,x96784,x96781,x96782)))+E(f335(f335(f6(f934(x96781,a922),x96782),f335(f6(x96781,x96782),x96783)),x96784),f335(f335(f6(x96781,x96782),x96783),f43(f934(x96781,a922),x96784)))+~P1(f335(f67(f934(x96781,a922)),x96784)) % 186.01/186.04 [9691]P1(f335(x96911,x96912))+~P1(f335(f335(f337(x96913),f357(x96911,x96914,x96912,x96913)),f356(x96911,x96914,x96912,x96913)))+~P1(f335(f67(x96913),x96912))+~P1(f335(x96911,f195(f934(x96913,a922))))+~P1(f335(f335(f243(f934(x96913,a922)),x96912),x96914)) % 186.01/186.04 [9728]~P76(x97282)+P1(f335(f335(f337(x97281),f811(x97283,x97284,x97281,x97282)),f809(x97283,x97284,x97281,x97282)))+E(f335(f335(f6(f934(x97281,a922),x97282),f335(f6(x97281,x97282),x97283)),x97284),f335(f335(f6(x97281,x97282),x97283),f43(f934(x97281,a922),x97284)))+P1(f335(f335(f337(f934(x97281,a922)),f810(x97283,x97284,x97281,x97282)),x97284))+~P1(f335(f67(f934(x97281,a922)),x97284)) % 186.01/186.04 [9729]~P76(x97292)+P1(f335(f335(f337(x97291),f811(x97293,x97294,x97291,x97292)),f808(x97293,x97294,x97291,x97292)))+E(f335(f335(f6(f934(x97291,a922),x97292),f335(f6(x97291,x97292),x97293)),x97294),f335(f335(f6(x97291,x97292),x97293),f43(f934(x97291,a922),x97294)))+P1(f335(f335(f337(f934(x97291,a922)),f810(x97293,x97294,x97291,x97292)),x97294))+~P1(f335(f67(f934(x97291,a922)),x97294)) % 186.01/186.04 [9905]P1(f335(x99051,x99052))+~P1(f335(f67(x99053),x99052))+~P1(f335(x99051,f335(f335(f317(x99053),f357(x99051,x99054,x99052,x99053)),f356(x99051,x99054,x99052,x99053))))+~P1(f335(x99051,f195(f934(x99053,a922))))+~P1(f335(f335(f243(f934(x99053,a922)),x99052),x99054)) % 186.01/186.04 [7946]~P68(x79461)+P1(f335(f335(f244(x79461),x79462),f2(x79461)))+~P1(f335(f335(f243(x79461),f2(x79461)),x79464))+P1(f335(f335(f244(x79461),f2(x79461)),x79462))+P1(f335(f335(f243(x79461),f335(f335(f299(x79461),x79463),x79462)),x79464)) % 186.01/186.04 [7947]~P68(x79471)+P1(f335(f335(f244(x79471),x79472),f2(x79471)))+P1(f335(f335(f244(x79471),f2(x79471)),x79472))+~P1(f335(f335(f244(x79471),f2(x79471)),x79474))+P1(f335(f335(f244(x79471),f335(f335(f299(x79471),x79473),x79472)),x79474)) % 186.01/186.04 [8223]~P1(f335(f335(f243(a1),x82234),f2(a1)))+~E(x82232,f335(f335(f86(a1),f335(f335(f87(a1),x82231),x82233)),x82234))+P1(f335(f335(f244(a1),f2(a1)),x82231))+~P1(f335(f335(f244(a1),x82231),x82234))+P1(f335(f55(x82232,x82231),f335(f335(f260(a1,a1),x82233),x82234))) % 186.01/186.04 [8257]~P1(f335(x82571,x82574))+P1(f335(x82571,f507(x82572,x82571,x82573)))+~P1(f335(f335(f243(a1),f2(a1)),x82572))+~P1(f335(f335(f244(a1),f2(a1)),x82573))+P1(f335(x82571,f335(f335(f23(a1),x82574),f335(f335(f87(a1),x82572),x82573)))) % 186.01/186.04 [8258]~P1(f335(x82581,x82584))+P1(f335(x82581,f537(x82582,x82581,x82583)))+~P1(f335(f335(f243(a1),f2(a1)),x82582))+~P1(f335(f335(f244(a1),f2(a1)),x82583))+P1(f335(x82581,f335(f335(f86(a1),x82584),f335(f335(f87(a1),x82582),x82583)))) % 186.01/186.04 [8259]~P68(x82591)+P1(f335(f335(f244(x82591),x82592),f2(x82591)))+P1(f335(f335(f244(x82591),f2(x82591)),x82592))+P1(f335(f335(f243(x82591),f2(x82591)),x82593))+~P1(f335(f335(f243(x82591),f335(f335(f299(x82591),x82594),x82592)),x82593)) % 186.01/186.04 [8260]~P68(x82601)+P1(f335(f335(f244(x82601),x82602),f2(x82601)))+P1(f335(f335(f244(x82601),f2(x82601)),x82602))+P1(f335(f335(f244(x82601),f2(x82601)),x82603))+~P1(f335(f335(f244(x82601),f335(f335(f299(x82601),x82604),x82602)),x82603)) % 186.01/186.04 [8312]~E(x83121,f335(f335(f86(a1),f335(f335(f87(a1),x83122),x83123)),x83124))+~P1(f335(f335(f243(a1),f2(a1)),x83124))+~P1(f335(f335(f244(a1),f2(a1)),x83122))+~P1(f335(f335(f244(a1),x83124),x83122))+P1(f335(f55(x83121,x83122),f335(f335(f260(a1,a1),x83123),x83124))) % 186.01/186.04 [8424]~P68(x84241)+P1(f335(f335(f244(x84241),x84242),f2(x84241)))+~P1(f335(f335(f243(x84241),f2(x84241)),x84244))+~P1(f335(f335(f243(x84241),x84243),f335(f335(f87(x84241),x84244),x84242)))+P1(f335(f335(f243(x84241),f335(f335(f299(x84241),x84243),x84242)),x84244)) % 186.01/186.04 [8425]~P68(x84251)+P1(f335(f335(f244(x84251),x84252),f2(x84251)))+~P1(f335(f335(f244(x84251),f2(x84251)),x84254))+~P1(f335(f335(f244(x84251),x84253),f335(f335(f87(x84251),x84254),x84252)))+P1(f335(f335(f244(x84251),f335(f335(f299(x84251),x84253),x84252)),x84254)) % 186.01/186.04 [8511]~P68(x85111)+P1(f335(f335(f244(x85111),x85112),f2(x85111)))+~P1(f335(f335(f243(x85111),x85113),f2(x85111)))+P1(f335(f335(f243(x85111),x85113),f335(f335(f299(x85111),x85114),x85112)))+~P1(f335(f335(f243(x85111),f335(f335(f87(x85111),x85113),x85112)),x85114)) % 186.01/186.04 [8512]~P68(x85121)+P1(f335(f335(f244(x85121),x85122),f2(x85121)))+~P1(f335(f335(f244(x85121),x85123),f2(x85121)))+P1(f335(f335(f244(x85121),x85123),f335(f335(f299(x85121),x85124),x85122)))+~P1(f335(f335(f244(x85121),f335(f335(f87(x85121),x85123),x85122)),x85124)) % 186.01/186.04 [8663]~P68(x86631)+~P1(f335(f335(f244(x86631),x86632),f2(x86631)))+P1(f335(f335(f244(x86631),f2(x86631)),x86632))+~P1(f335(f335(f243(x86631),f335(f335(f299(x86631),x86634),x86632)),x86633))+P1(f335(f335(f243(x86631),f335(f335(f87(x86631),x86633),x86632)),x86634)) % 186.01/186.04 [8664]~P68(x86641)+~P1(f335(f335(f244(x86641),x86642),f2(x86641)))+P1(f335(f335(f244(x86641),f2(x86641)),x86642))+~P1(f335(f335(f243(x86641),f335(f335(f87(x86641),x86644),x86642)),x86643))+P1(f335(f335(f243(x86641),f335(f335(f299(x86641),x86643),x86642)),x86644)) % 186.01/186.04 [8665]~P68(x86651)+~P1(f335(f335(f244(x86651),x86652),f2(x86651)))+P1(f335(f335(f244(x86651),f2(x86651)),x86652))+~P1(f335(f335(f244(x86651),f335(f335(f299(x86651),x86654),x86652)),x86653))+P1(f335(f335(f244(x86651),f335(f335(f87(x86651),x86653),x86652)),x86654)) % 186.01/186.04 [8666]~P68(x86661)+~P1(f335(f335(f244(x86661),x86662),f2(x86661)))+P1(f335(f335(f244(x86661),f2(x86661)),x86662))+~P1(f335(f335(f244(x86661),f335(f335(f87(x86661),x86664),x86662)),x86663))+P1(f335(f335(f244(x86661),f335(f335(f299(x86661),x86663),x86662)),x86664)) % 186.01/186.04 [8682]~P68(x86821)+~P1(f335(f335(f243(x86821),f2(x86821)),x86824))+P1(f335(f335(f244(x86821),f2(x86821)),x86822))+~P1(f335(f335(f243(x86821),f335(f335(f87(x86821),x86824),x86822)),x86823))+P1(f335(f335(f243(x86821),f335(f335(f299(x86821),x86823),x86822)),x86824)) % 186.01/186.04 [8683]~P68(x86831)+~P1(f335(f335(f244(x86831),f2(x86831)),x86834))+P1(f335(f335(f244(x86831),f2(x86831)),x86832))+~P1(f335(f335(f244(x86831),f335(f335(f87(x86831),x86834),x86832)),x86833))+P1(f335(f335(f244(x86831),f335(f335(f299(x86831),x86833),x86832)),x86834)) % 186.01/186.04 [8759]~P68(x87591)+~P1(f335(f335(f244(x87591),x87594),f2(x87591)))+~P1(f335(f335(f243(x87591),x87593),f335(f335(f87(x87591),x87592),x87594)))+P1(f335(f335(f243(x87591),x87592),f335(f335(f299(x87591),x87593),x87594)))+~P1(f335(f335(f243(x87591),f335(f335(f87(x87591),x87592),x87594)),x87593)) % 186.01/186.04 [8760]~P68(x87601)+~P1(f335(f335(f243(x87601),x87602),f2(x87601)))+~P1(f335(f335(f243(x87601),x87603),f335(f335(f87(x87601),x87602),x87604)))+P1(f335(f335(f243(x87601),x87602),f335(f335(f299(x87601),x87603),x87604)))+~P1(f335(f335(f243(x87601),f335(f335(f87(x87601),x87602),x87604)),x87603)) % 186.01/186.04 [8761]~P68(x87611)+~P1(f335(f335(f244(x87611),x87614),f2(x87611)))+~P1(f335(f335(f244(x87611),x87613),f335(f335(f87(x87611),x87612),x87614)))+P1(f335(f335(f244(x87611),x87612),f335(f335(f299(x87611),x87613),x87614)))+~P1(f335(f335(f244(x87611),f335(f335(f87(x87611),x87612),x87614)),x87613)) % 186.01/186.04 [8762]~P68(x87621)+~P1(f335(f335(f244(x87621),x87622),f2(x87621)))+~P1(f335(f335(f244(x87621),x87623),f335(f335(f87(x87621),x87622),x87624)))+P1(f335(f335(f244(x87621),x87622),f335(f335(f299(x87621),x87623),x87624)))+~P1(f335(f335(f244(x87621),f335(f335(f87(x87621),x87622),x87624)),x87623)) % 186.01/186.04 [8884]~P68(x88841)+~P1(f335(f335(f244(x88841),x88843),f2(x88841)))+~P1(f335(f335(f243(x88841),x88842),f335(f335(f87(x88841),x88844),x88843)))+~P1(f335(f335(f243(x88841),f335(f335(f87(x88841),x88844),x88843)),x88842))+P1(f335(f335(f243(x88841),f335(f335(f299(x88841),x88842),x88843)),x88844)) % 186.01/186.04 [8885]~P68(x88851)+~P1(f335(f335(f244(x88851),x88853),f2(x88851)))+~P1(f335(f335(f244(x88851),x88852),f335(f335(f87(x88851),x88854),x88853)))+~P1(f335(f335(f244(x88851),f335(f335(f87(x88851),x88854),x88853)),x88852))+P1(f335(f335(f244(x88851),f335(f335(f299(x88851),x88852),x88853)),x88854)) % 186.01/186.04 [8902]~P68(x89021)+~P1(f335(f335(f243(x89021),f2(x89021)),x89024))+~P1(f335(f335(f243(x89021),x89022),f335(f335(f87(x89021),x89024),x89023)))+~P1(f335(f335(f243(x89021),f335(f335(f87(x89021),x89024),x89023)),x89022))+P1(f335(f335(f243(x89021),f335(f335(f299(x89021),x89022),x89023)),x89024)) % 186.01/186.04 [8903]~P68(x89031)+~P1(f335(f335(f244(x89031),f2(x89031)),x89034))+~P1(f335(f335(f244(x89031),x89032),f335(f335(f87(x89031),x89034),x89033)))+~P1(f335(f335(f244(x89031),f335(f335(f87(x89031),x89034),x89033)),x89032))+P1(f335(f335(f244(x89031),f335(f335(f299(x89031),x89032),x89033)),x89034)) % 186.01/186.04 [9086]E(f335(f335(f23(a1),f524(x90861,x90862,x90863,x90864)),f525(x90861,x90862,x90863,x90864)),x90864)+~P1(f335(f335(f244(a1),f2(a1)),x90863))+~P1(f335(f335(f337(a1),x90862),x90861))+~P1(f335(f335(f244(a1),x90864),x90862))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x90864),x90863)),x90862)) % 186.01/186.04 [9161]~P1(f335(x91611,x91612))+~P1(f335(f335(f243(a1),f2(a1)),x91613))+~P1(f335(f335(f244(a1),f2(a1)),x91614))+~P1(f335(x91611,f335(f335(f23(a1),f507(x91613,x91611,x91614)),x91614)))+P1(f335(x91611,f335(f335(f23(a1),x91612),f335(f335(f87(a1),x91613),x91614)))) % 186.01/186.04 [9162]~P1(f335(x91621,x91622))+~P1(f335(f335(f243(a1),f2(a1)),x91623))+~P1(f335(f335(f244(a1),f2(a1)),x91624))+~P1(f335(x91621,f335(f335(f86(a1),f537(x91623,x91621,x91624)),x91624)))+P1(f335(x91621,f335(f335(f86(a1),x91622),f335(f335(f87(a1),x91623),x91624)))) % 186.01/186.04 [9312]~P1(f335(f335(f244(a1),f2(a1)),x93123))+~P1(f335(f335(f337(a1),x93122),x93121))+~P1(f335(f335(f244(a1),x93124),x93122))+P1(f335(f335(f337(a1),f524(x93121,x93122,x93123,x93124)),x93121))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x93124),x93123)),x93122)) % 186.01/186.04 [9332]E(f335(f335(f23(a1),f510(x93321,x93322,x93323,x93324)),f511(x93321,x93322,x93323,x93324)),x93324)+~P1(f335(f335(f244(a1),f2(a1)),x93323))+~P1(f335(f335(f243(a1),x93324),x93322))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x93322),f84(a1))),x93321))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x93324),x93323)),x93322)) % 186.01/186.04 [9360]~P1(f335(f335(f244(a1),f2(a1)),x93602))+~P1(f335(f335(f337(a1),x93603),x93604))+~P1(f335(f335(f244(a1),x93601),x93603))+P1(f335(f335(f337(a1),f525(x93604,x93603,x93602,x93601)),f311(a1,f84(a1),x93602)))+P1(f335(f335(f244(a1),f335(f335(f86(a1),x93601),x93602)),x93603)) % 186.01/186.04 [9446]~P1(f335(f335(f244(a1),f2(a1)),x94463))+~P1(f335(f335(f243(a1),x94464),x94462))+P1(f335(f335(f337(a1),f510(x94461,x94462,x94463,x94464)),x94461))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x94462),f84(a1))),x94461))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x94464),x94463)),x94462)) % 186.01/186.04 [9491]~P1(f335(f335(f244(a1),f2(a1)),x94912))+~P1(f335(f335(f243(a1),x94911),x94913))+P1(f335(f335(f337(a1),f511(x94914,x94913,x94912,x94911)),f311(a1,f84(a1),x94912)))+~P1(f335(f335(f337(a1),f335(f335(f86(a1),x94913),f84(a1))),x94914))+P1(f335(f335(f243(a1),f335(f335(f86(a1),x94911),x94912)),x94913)) % 186.01/186.04 [9782]~P38(x97821,x97823)+~P28(x97821,x97824)+P38(x97821,f335(f335(f117(f934(f933(x97821,x97821),a922)),x97822),x97823))+~P1(f335(f335(f243(f934(f933(x97821,x97821),a922)),x97822),f335(f259(f934(f933(x97821,x97821),a922),f934(f933(x97821,x97821),a922)),x97824)))+~P1(f335(f335(f243(f934(f933(x97821,x97821),a922)),x97823),f335(f264(f934(f933(x97821,x97821),a922),f934(f933(x97821,x97821),a922)),x97824))) % 186.01/186.04 [10177]~P19(x101772,x101774,x101773)+E(x101771,f195(f934(x101772,a922)))+~P1(f335(f67(x101772),x101771))+P1(f335(f335(f337(x101772),f335(x101773,x101771)),x101771))+~P1(f335(f335(f337(x101772),f335(f335(x101774,f346(x101771,x101773,x101774,x101772)),f348(x101771,x101773,x101774,x101772))),f335(f335(f317(x101772),f346(x101771,x101773,x101774,x101772)),f335(f335(f317(x101772),f348(x101771,x101773,x101774,x101772)),f195(f934(x101772,a922)))))) % 186.01/186.04 [10098]~P110(x100982)+~P65(x100981)+~P1(f335(f335(f243(f934(x100981,x100982)),x100983),x100984))+P1(f335(f335(f244(f934(x100981,x100982)),x100983),x100984))+~P1(f335(f62(x100981),f335(f335(f8(a922,a922,x100981),a330),f335(f335(f18(x100981,x100982,a922),f335(f335(f8(x100982,f934(x100982,a922),x100981),a332),x100983)),x100984)))) % 186.01/186.04 [9697]~P56(x96971,x96971,x96974)+P1(f335(f335(f337(f933(x96971,x96971)),f335(f335(f260(x96971,x96971),x96972),x96973)),f315(x96971,x96974)))+P1(f335(f335(f337(f933(x96971,x96971)),f335(f335(f260(x96971,x96971),x96973),x96972)),f315(x96971,x96974)))+~P1(f335(f335(f337(f933(x96971,x96971)),f335(f335(f260(x96971,x96971),x96975),x96972)),f315(x96971,x96974)))+~P1(f335(f335(f337(f933(x96971,x96971)),f335(f335(f260(x96971,x96971),x96975),x96973)),f315(x96971,x96974))) % 186.01/186.04 [5864]E(x58641,f2(a927))+~E(f335(f41(x58642),x58645),x58641)+E(f335(f41(x58642),x58643),f335(a119,x58641))+~E(x58643,f335(f335(f317(x58642),x58644),x58645))+P1(f335(f335(f337(x58642),x58644),x58645)) % 186.01/186.04 [5986]~P67(x59862)+E(x59861,f2(x59862))+E(x59863,f2(x59862))+~E(f335(f335(f299(x59862),x59864),x59863),f335(f335(f299(x59862),x59865),x59861))+E(f335(f335(f87(x59862),x59864),x59861),f335(f335(f87(x59862),x59865),x59863)) % 186.01/186.04 [5987]~P67(x59872)+E(x59871,f2(x59872))+E(x59873,f2(x59872))+~E(f335(f335(f87(x59872),x59874),x59873),f335(f335(f87(x59872),x59875),x59871))+E(f335(f335(f299(x59872),x59874),x59871),f335(f335(f299(x59872),x59875),x59873)) % 186.01/186.04 [6056]~E(f335(f41(x60561),x60565),x60563)+~E(x60565,f195(f934(x60561,a922)))+E(f335(f41(x60561),x60562),f335(a119,x60563))+~E(x60562,f335(f335(f317(x60561),x60564),x60565))+P1(f335(f335(f337(x60561),x60564),x60565)) % 186.01/186.04 [6289]~P118(x62892)+~E(f335(x62893,x62895),f2(x62892))+E(f335(f335(f9(x62891,x62892),x62893),x62894),f2(x62892))+~P1(f335(f67(x62891),x62894))+~P1(f335(f335(f337(x62891),x62895),x62894)) % 186.01/186.04 [6657]~P109(x66573)+E(x66571,x66572)+~E(f335(f310(x66573,x66574),x66571),f335(f310(x66573,x66575),x66572))+~P1(f335(f335(f244(x66573),x66575),x66572))+~P1(f335(f335(f244(x66573),x66574),x66571)) % 186.01/186.04 [6658]~P109(x66583)+E(x66581,x66582)+~E(f335(f310(x66583,x66581),x66584),f335(f310(x66583,x66582),x66585))+~P1(f335(f335(f244(x66583),x66582),x66585))+~P1(f335(f335(f244(x66583),x66581),x66584)) % 186.01/186.04 [7716]~P109(x77161)+~P14(x77161,f335(f335(f141(x77161),x77164),x77165))+~P1(f335(f335(f337(x77161),x77163),f335(f179(x77161),x77165)))+~P1(f335(f335(f337(x77161),x77162),f335(f179(x77161),x77164)))+P1(f335(f335(f243(x77161),x77162),x77163)) % 186.01/186.04 [8796]~P110(x87961)+~P1(f335(f335(f244(f934(x87961,a922)),f311(x87961,x87965,x87962)),f311(x87961,x87964,x87963)))+~P1(f335(f335(f243(x87961),x87965),x87962))+P1(f335(f335(f244(x87961),x87962),x87963))+P1(f335(f335(f244(x87961),x87964),x87965)) % 186.01/186.04 [10220]~P18(x102202,x102205,x102203)+E(x102201,f195(f934(x102202,a922)))+~E(f335(f335(x102205,f335(x102204,f388(x102201,x102204,x102203,x102205,x102202))),f335(x102204,f390(x102201,x102204,x102203,x102205,x102202))),f335(x102204,f335(f335(x102205,f388(x102201,x102204,x102203,x102205,x102202)),f390(x102201,x102204,x102203,x102205,x102202))))+E(f335(x102203,f335(f318(x102202,x102202,x102204),x102201)),f335(x102204,f335(x102203,x102201)))+~P1(f335(f67(x102202),x102201)) % 186.01/186.04 [6654]~P19(x66542,x66545,x66543)+E(x66541,f195(f934(x66542,a922)))+~P1(f335(f67(x66542),x66541))+E(f335(x66543,f335(f335(f317(x66542),x66544),x66541)),f335(f335(x66545,x66544),f335(x66543,x66541)))+P1(f335(f335(f337(x66542),x66544),x66541)) % 186.01/186.04 [7476]~P18(x74762,x74763,x74764)+E(f335(f335(x74763,f335(x74764,x74761)),f335(x74764,x74765)),f335(x74764,x74765))+E(x74761,f195(f934(x74762,a922)))+~P1(f335(f67(x74762),x74765))+~P1(f335(f335(f243(f934(x74762,a922)),x74761),x74765)) % 186.01/186.04 [7847]~P19(x78474,x78475,x78471)+E(f335(x78471,x78472),x78473)+~P1(f335(f67(x78474),x78472))+~E(f335(f335(f23(f934(x78474,a922)),x78472),f335(f335(f317(x78474),x78473),f195(f934(x78474,a922)))),f195(f934(x78474,a922)))+~P1(f335(f335(f337(x78474),x78473),x78472)) % 186.01/186.04 [8717]~P72(x87171)+~P120(x87171)+~P1(f335(f67(x87172),x87175))+P1(f335(f335(f295(x87171),f335(f335(f9(x87172,x87171),x87173),x87174)),f335(f335(f9(x87172,x87171),x87173),x87175)))+~P1(f335(f335(f243(f934(x87172,a922)),x87174),x87175)) % 186.01/186.04 [8766]E(x87661,x87662)+~P9(x87663,x87664,x87665)+E(f335(f335(f108(f934(x87663,a922)),x87661),x87662),f195(f934(x87663,a922)))+~P1(f335(f335(f337(f934(x87663,a922)),x87662),f335(f335(f66(x87663),x87664),x87665)))+~P1(f335(f335(f337(f934(x87663,a922)),x87661),f335(f335(f66(x87663),x87664),x87665))) % 186.01/186.04 [9574]~P76(x95742)+~E(f335(x95743,f546(x95743,x95744,x95745,x95741,x95742)),f2(x95742))+E(f335(f335(f6(x95741,x95742),x95743),x95744),f335(f335(f6(x95741,x95742),x95743),x95745))+~P1(f335(f67(x95741),x95745))+~P1(f335(f335(f243(f934(x95741,a922)),x95744),x95745)) % 186.01/186.04 [9575]~P76(x95752)+~E(f335(x95753,f547(x95753,x95754,x95755,x95751,x95752)),f2(x95752))+E(f335(f335(f6(x95751,x95752),x95753),x95754),f335(f335(f6(x95751,x95752),x95753),x95755))+~P1(f335(f67(x95751),x95755))+~P1(f335(f335(f243(f934(x95751,a922)),x95754),x95755)) % 186.01/186.04 [9576]~P72(x95762)+~E(f335(x95763,f539(x95763,x95764,x95765,x95761,x95762)),f84(x95762))+E(f335(f335(f9(x95761,x95762),x95763),x95764),f335(f335(f9(x95761,x95762),x95763),x95765))+~P1(f335(f67(x95761),x95765))+~P1(f335(f335(f243(f934(x95761,a922)),x95764),x95765)) % 186.01/186.04 [9577]~P72(x95772)+~E(f335(x95773,f541(x95773,x95774,x95775,x95771,x95772)),f84(x95772))+E(f335(f335(f9(x95771,x95772),x95773),x95774),f335(f335(f9(x95771,x95772),x95773),x95775))+~P1(f335(f67(x95771),x95775))+~P1(f335(f335(f243(f934(x95771,a922)),x95774),x95775)) % 186.01/186.04 [10051]~P89(x100511)+~P1(f335(f67(x100512),x100515))+~P1(f335(f335(f243(x100511),f2(x100511)),f335(x100513,f412(x100513,x100514,x100515,x100512,x100511))))+P1(f335(f335(f243(x100511),f335(f335(f6(x100512,x100511),x100513),x100514)),f335(f335(f6(x100512,x100511),x100513),x100515)))+~P1(f335(f335(f243(f934(x100512,a922)),x100514),x100515)) % 186.01/186.04 [7713]E(x77131,f2(a927))+P1(f335(x77132,x77133))+~E(x77134,f335(f335(f86(a927),f335(f335(f87(a927),x77131),x77133)),x77135))+~P1(f335(f335(f244(a927),x77135),x77131))+~P1(f335(x77132,f335(f335(f42(a927),x77134),x77131))) % 186.01/186.04 [7787]E(x77871,f2(a927))+P1(f335(x77872,x77873))+~P1(f335(x77872,f51(a927,x77874,x77871)))+~E(x77874,f335(f335(f86(a927),f335(f335(f87(a927),x77871),x77875)),x77873))+~P1(f335(f335(f244(a927),x77873),x77871)) % 186.01/186.04 [8073]~P67(x80733)+E(f335(x80731,x80732),f2(x80733))+~P1(f335(f67(x80734),x80735))+E(f335(f335(f9(x80734,x80733),x80731),f335(f335(f23(f934(x80734,a922)),x80735),f335(f335(f317(x80734),x80732),f195(f934(x80734,a922))))),f335(f335(f9(x80734,x80733),x80731),x80735))+P1(f335(f335(f337(x80734),x80732),x80735)) % 186.01/186.04 [8465]~P76(x84651)+~P1(f335(f67(x84652),x84655))+~P1(f335(f67(x84652),x84654))+~E(f335(f335(f108(f934(x84652,a922)),x84654),x84655),f195(f934(x84652,a922)))+E(f335(f335(f86(x84651),f335(f335(f6(x84652,x84651),x84653),x84654)),f335(f335(f6(x84652,x84651),x84653),x84655)),f335(f335(f6(x84652,x84651),x84653),f335(f335(f117(f934(x84652,a922)),x84654),x84655))) % 186.01/186.04 [8467]~P72(x84671)+~P1(f335(f67(x84672),x84675))+~P1(f335(f67(x84672),x84674))+~E(f335(f335(f108(f934(x84672,a922)),x84674),x84675),f195(f934(x84672,a922)))+E(f335(f335(f87(x84671),f335(f335(f9(x84672,x84671),x84673),x84674)),f335(f335(f9(x84672,x84671),x84673),x84675)),f335(f335(f9(x84672,x84671),x84673),f335(f335(f117(f934(x84672,a922)),x84674),x84675))) % 186.01/186.04 [8566]~P67(x85663)+E(f335(x85661,x85662),f2(x85663))+~P1(f335(f67(x85664),x85665))+E(f335(f335(f9(x85664,x85663),x85661),f335(f335(f23(f934(x85664,a922)),x85665),f335(f335(f317(x85664),x85662),f195(f934(x85664,a922))))),f335(f335(f299(x85663),f335(f335(f9(x85664,x85663),x85661),x85665)),f335(x85661,x85662)))+~P1(f335(f335(f337(x85664),x85662),x85665)) % 186.01/186.04 [9289]~P9(x92891,x92895,x92894)+~E(f335(f335(f66(x92891),f335(f335(f317(x92891),x92892),f195(f934(x92891,a922)))),x92894),f335(f335(f66(x92891),f335(f335(f317(x92891),x92893),f195(f934(x92891,a922)))),x92894))+~P1(f335(f335(f337(x92891),x92893),x92895))+~P1(f335(f335(f337(x92891),x92892),x92895))+P1(f335(f335(f337(f933(x92891,x92891)),f335(f335(f260(x92891,x92891),x92892),x92893)),x92894)) % 186.01/186.04 [9311]~P9(x93111,x93115,x93113)+E(f335(f335(f66(x93111),f335(f335(f317(x93111),x93112),f195(f934(x93111,a922)))),x93113),f335(f335(f66(x93111),f335(f335(f317(x93111),x93114),f195(f934(x93111,a922)))),x93113))+~P1(f335(f335(f337(x93111),x93114),x93115))+~P1(f335(f335(f337(x93111),x93112),x93115))+~P1(f335(f335(f337(f933(x93111,x93111)),f335(f335(f260(x93111,x93111),x93112),x93114)),x93113)) % 186.01/186.04 [9603]~P72(x96031)+~P1(f335(f67(x96032),x96035))+~P1(f335(f67(x96032),x96034))+~E(f335(f335(f108(f934(x96032,a922)),x96034),x96035),f195(f934(x96032,a922)))+E(f335(f335(f87(x96031),f335(f335(f335(f71(x96031,x96032,f87(x96031)),x96033),f84(x96031)),x96034)),f335(f335(f335(f71(x96031,x96032,f87(x96031)),x96033),f84(x96031)),x96035)),f335(f335(f335(f71(x96031,x96032,f87(x96031)),x96033),f84(x96031)),f335(f335(f117(f934(x96032,a922)),x96034),x96035))) % 186.01/186.04 [9612]~P76(x96121)+~E(f335(x96123,f422(x96123,x96125,x96124,x96122,x96121)),f2(x96121))+~P1(f335(f67(x96122),x96124))+~P1(f335(f67(x96122),x96125))+E(f335(f335(f86(x96121),f335(f335(f6(x96122,x96121),x96123),x96124)),f335(f335(f6(x96122,x96121),x96123),x96125)),f335(f335(f6(x96122,x96121),x96123),f335(f335(f117(f934(x96122,a922)),x96124),x96125))) % 186.01/186.04 [9613]~P76(x96131)+~E(f335(x96133,f423(x96133,x96135,x96134,x96132,x96131)),f2(x96131))+~P1(f335(f67(x96132),x96134))+~P1(f335(f67(x96132),x96135))+E(f335(f335(f86(x96131),f335(f335(f6(x96132,x96131),x96133),x96134)),f335(f335(f6(x96132,x96131),x96133),x96135)),f335(f335(f6(x96132,x96131),x96133),f335(f335(f117(f934(x96132,a922)),x96134),x96135))) % 186.01/186.04 [9614]~P72(x96141)+~E(f335(x96143,f481(x96143,x96145,x96144,x96142,x96141)),f84(x96141))+~P1(f335(f67(x96142),x96144))+~P1(f335(f67(x96142),x96145))+E(f335(f335(f87(x96141),f335(f335(f9(x96142,x96141),x96143),x96144)),f335(f335(f9(x96142,x96141),x96143),x96145)),f335(f335(f9(x96142,x96141),x96143),f335(f335(f117(f934(x96142,a922)),x96144),x96145))) % 186.01/186.04 [9615]~P72(x96151)+~E(f335(x96153,f482(x96153,x96155,x96154,x96152,x96151)),f84(x96151))+~P1(f335(f67(x96152),x96154))+~P1(f335(f67(x96152),x96155))+E(f335(f335(f87(x96151),f335(f335(f9(x96152,x96151),x96153),x96154)),f335(f335(f9(x96152,x96151),x96153),x96155)),f335(f335(f9(x96152,x96151),x96153),f335(f335(f117(f934(x96152,a922)),x96154),x96155))) % 186.01/186.04 [9825]~P72(x98251)+~E(f335(x98253,f384(x98253,x98255,x98254,x98252,x98251)),f84(x98251))+~P1(f335(f67(x98252),x98254))+~P1(f335(f67(x98252),x98255))+E(f335(f335(f87(x98251),f335(f335(f335(f71(x98251,x98252,f87(x98251)),x98253),f84(x98251)),x98254)),f335(f335(f335(f71(x98251,x98252,f87(x98251)),x98253),f84(x98251)),x98255)),f335(f335(f335(f71(x98251,x98252,f87(x98251)),x98253),f84(x98251)),f335(f335(f117(f934(x98252,a922)),x98254),x98255))) % 186.01/186.04 [9937]~P76(x99372)+E(f335(f335(f6(x99371,x99372),x99373),x99374),f335(f335(f6(x99371,x99372),x99373),x99375))+~P1(f335(f67(x99371),x99375))+~P1(f335(f335(f243(f934(x99371,a922)),x99374),x99375))+P1(f335(f335(f337(x99371),f546(x99373,x99374,x99375,x99371,x99372)),f335(f335(f23(f934(x99371,a922)),x99375),x99374))) % 186.01/186.04 [9938]~P76(x99382)+E(f335(f335(f6(x99381,x99382),x99383),x99384),f335(f335(f6(x99381,x99382),x99383),x99385))+~P1(f335(f67(x99381),x99385))+~P1(f335(f335(f243(f934(x99381,a922)),x99384),x99385))+P1(f335(f335(f337(x99381),f547(x99383,x99384,x99385,x99381,x99382)),f335(f335(f23(f934(x99381,a922)),x99385),x99384))) % 186.01/186.04 [9939]~P72(x99392)+E(f335(f335(f9(x99391,x99392),x99393),x99394),f335(f335(f9(x99391,x99392),x99393),x99395))+~P1(f335(f67(x99391),x99395))+~P1(f335(f335(f243(f934(x99391,a922)),x99394),x99395))+P1(f335(f335(f337(x99391),f539(x99393,x99394,x99395,x99391,x99392)),f335(f335(f23(f934(x99391,a922)),x99395),x99394))) % 186.01/186.04 [9940]~P72(x99402)+E(f335(f335(f9(x99401,x99402),x99403),x99404),f335(f335(f9(x99401,x99402),x99403),x99405))+~P1(f335(f67(x99401),x99405))+~P1(f335(f335(f243(f934(x99401,a922)),x99404),x99405))+P1(f335(f335(f337(x99401),f541(x99403,x99404,x99405,x99401,x99402)),f335(f335(f23(f934(x99401,a922)),x99405),x99404))) % 186.01/186.04 [9958]~P76(x99581)+~P1(f335(f67(x99582),x99584))+~P1(f335(f67(x99582),x99585))+E(f335(f335(f86(x99581),f335(f335(f6(x99582,x99581),x99583),x99584)),f335(f335(f6(x99582,x99581),x99583),x99585)),f335(f335(f6(x99582,x99581),x99583),f335(f335(f117(f934(x99582,a922)),x99584),x99585)))+P1(f335(f335(f337(x99582),f422(x99583,x99585,x99584,x99582,x99581)),f335(f335(f108(f934(x99582,a922)),x99584),x99585))) % 186.01/186.04 [9959]~P76(x99591)+~P1(f335(f67(x99592),x99594))+~P1(f335(f67(x99592),x99595))+E(f335(f335(f86(x99591),f335(f335(f6(x99592,x99591),x99593),x99594)),f335(f335(f6(x99592,x99591),x99593),x99595)),f335(f335(f6(x99592,x99591),x99593),f335(f335(f117(f934(x99592,a922)),x99594),x99595)))+P1(f335(f335(f337(x99592),f423(x99593,x99595,x99594,x99592,x99591)),f335(f335(f108(f934(x99592,a922)),x99594),x99595))) % 186.01/186.04 [9960]~P72(x99601)+~P1(f335(f67(x99602),x99604))+~P1(f335(f67(x99602),x99605))+E(f335(f335(f87(x99601),f335(f335(f9(x99602,x99601),x99603),x99604)),f335(f335(f9(x99602,x99601),x99603),x99605)),f335(f335(f9(x99602,x99601),x99603),f335(f335(f117(f934(x99602,a922)),x99604),x99605)))+P1(f335(f335(f337(x99602),f481(x99603,x99605,x99604,x99602,x99601)),f335(f335(f108(f934(x99602,a922)),x99604),x99605))) % 186.01/186.04 [9961]~P72(x99611)+~P1(f335(f67(x99612),x99614))+~P1(f335(f67(x99612),x99615))+E(f335(f335(f87(x99611),f335(f335(f9(x99612,x99611),x99613),x99614)),f335(f335(f9(x99612,x99611),x99613),x99615)),f335(f335(f9(x99612,x99611),x99613),f335(f335(f117(f934(x99612,a922)),x99614),x99615)))+P1(f335(f335(f337(x99612),f482(x99613,x99615,x99614,x99612,x99611)),f335(f335(f108(f934(x99612,a922)),x99614),x99615))) % 186.01/186.04 [9968]~P89(x99685)+~P1(f335(f67(x99681),x99684))+P1(f335(f335(f243(x99685),f335(f335(f6(x99681,x99685),x99682),x99683)),f335(f335(f6(x99681,x99685),x99682),x99684)))+~P1(f335(f335(f243(f934(x99681,a922)),x99683),x99684))+P1(f335(f335(f337(x99681),f412(x99682,x99683,x99684,x99681,x99685)),f335(f335(f23(f934(x99681,a922)),x99684),x99683))) % 186.01/186.04 [10012]~P72(x100121)+~P1(f335(f67(x100122),x100124))+~P1(f335(f67(x100122),x100125))+E(f335(f335(f87(x100121),f335(f335(f335(f71(x100121,x100122,f87(x100121)),x100123),f84(x100121)),x100124)),f335(f335(f335(f71(x100121,x100122,f87(x100121)),x100123),f84(x100121)),x100125)),f335(f335(f335(f71(x100121,x100122,f87(x100121)),x100123),f84(x100121)),f335(f335(f117(f934(x100122,a922)),x100124),x100125)))+P1(f335(f335(f337(x100122),f384(x100123,x100125,x100124,x100122,x100121)),f335(f335(f108(f934(x100122,a922)),x100124),x100125))) % 186.01/186.04 [8975]~P19(x89751,x89754,x89755)+~P1(f335(f67(x89751),x89752))+E(f335(f335(f23(f934(x89751,a922)),x89752),f335(f335(f317(x89751),x89753),f195(f934(x89751,a922)))),f195(f934(x89751,a922)))+~P1(f335(f335(f337(x89751),x89753),x89752))+E(f335(f335(x89754,x89753),f335(x89755,f335(f335(f23(f934(x89751,a922)),x89752),f335(f335(f317(x89751),x89753),f195(f934(x89751,a922)))))),f335(x89755,x89752)) % 186.01/186.04 [9053]~P19(x90531,x90534,x90535)+~P1(f335(f67(x90531),x90533))+~P1(f335(f67(x90531),x90532))+E(f335(f335(f108(f934(x90531,a922)),x90532),x90533),f195(f934(x90531,a922)))+E(f335(f335(x90534,f335(x90535,f335(f335(f117(f934(x90531,a922)),x90532),x90533))),f335(x90535,f335(f335(f108(f934(x90531,a922)),x90532),x90533))),f335(f335(x90534,f335(x90535,x90532)),f335(x90535,x90533))) % 186.01/186.04 [9617]~P1(f335(f335(f243(a1),x96174),f2(a1)))+~P1(f335(f335(f244(a1),x96173),x96175))+P1(f335(f335(f243(a1),x96171),x96172))+~P1(f335(f335(f244(a1),x96173),x96174))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),f335(f335(f87(a1),x96173),x96172)),x96175)),f335(f335(f86(a1),f335(f335(f87(a1),x96173),x96171)),x96174))) % 186.01/186.04 [9619]~P1(f335(f335(f243(a1),f2(a1)),x96195))+P1(f335(f335(f243(a1),x96191),x96192))+~P1(f335(f335(f244(a1),x96193),x96194))+~P1(f335(f335(f244(a1),x96195),x96194))+~P1(f335(f335(f243(a1),f335(f335(f86(a1),f335(f335(f87(a1),x96194),x96191)),x96195)),f335(f335(f86(a1),f335(f335(f87(a1),x96194),x96192)),x96193))) % 186.01/186.04 [9734]~P67(x97345)+E(f335(x97341,f484(x97341,x97342,x97343,x97344,x97345)),f2(x97345))+~P1(f335(f67(x97344),x97343))+~P1(f335(f67(x97344),x97342))+E(f335(f335(f299(x97345),f335(f335(f87(x97345),f335(f335(f9(x97344,x97345),x97341),x97343)),f335(f335(f9(x97344,x97345),x97341),x97342))),f335(f335(f9(x97344,x97345),x97341),f335(f335(f108(f934(x97344,a922)),x97343),x97342))),f335(f335(f9(x97344,x97345),x97341),f335(f335(f117(f934(x97344,a922)),x97343),x97342))) % 186.01/186.04 [10004]~P67(x100041)+~P1(f335(f67(x100042),x100044))+~P1(f335(f67(x100042),x100045))+E(f335(f335(f299(x100041),f335(f335(f87(x100041),f335(f335(f9(x100042,x100041),x100043),x100044)),f335(f335(f9(x100042,x100041),x100043),x100045))),f335(f335(f9(x100042,x100041),x100043),f335(f335(f108(f934(x100042,a922)),x100044),x100045))),f335(f335(f9(x100042,x100041),x100043),f335(f335(f117(f934(x100042,a922)),x100044),x100045)))+P1(f335(f335(f337(x100042),f484(x100043,x100045,x100044,x100042,x100041)),f335(f335(f108(f934(x100042,a922)),x100044),x100045))) % 186.01/186.04 [9331]E(f335(f335(f141(x93311),x93312),x93313),f335(f335(f141(x93311),x93314),x93315))+~E(f335(f335(f182(x93311),f335(f196(f928(x93311)),x93314)),x93312),x93314)+~E(f335(f335(f182(x93311),f335(f196(f928(x93311)),x93312)),x93314),x93312)+~E(x93315,f335(f335(f141(x93311),f335(f335(f145(x93311),f335(f196(f928(x93311)),x93314)),x93312)),x93313))+~E(f335(f335(f141(x93311),f335(f335(f145(x93311),f335(f196(f928(x93311)),x93312)),x93314)),x93315),x93313) % 186.01/186.04 [9732]~P109(x97322)+E(f335(f335(f155(x97321,x97322,x97323),x97324),f177(x97321,x97324,x97325)),x97325)+~P14(x97322,f335(f335(f161(x97321,x97322),x97323),x97325))+~P1(f335(f335(f337(x97321),x97324),f335(f179(x97321),x97325)))+~E(f335(f148(x97321),f335(f143(x97321,f335(f335(f8(x97322,a922,x97321),f335(a332,f335(x97323,x97324))),x97323)),x97325)),x97324) % 186.01/186.04 [10069]~P70(x100691)+~P1(f335(f72(x100691,x100691,f87(x100691),x100692,x100693),x100695))+~P1(f335(f335(f337(x100691),x100694),x100693))+P1(f335(f335(f337(x100691),x100692),x100693))+P1(f335(f72(x100691,x100691,f87(x100691),x100694,f335(f335(f317(x100691),x100692),f335(f335(f23(f934(x100691,a922)),x100693),f335(f335(f317(x100691),x100694),f195(f934(x100691,a922)))))),x100695)) % 186.01/186.04 [7484]E(x74841,x74842)+~P26(x74844,x74845,x74843,x74846)+~E(f335(x74843,x74841),f335(x74843,x74842))+~P1(f335(f335(f337(x74844),x74842),x74846))+~P1(f335(f335(f337(x74844),x74841),x74846)) % 186.01/186.04 [6746]~P143(x67464)+E(x67461,x67462)+~E(x67465,x67466)+E(x67463,f2(x67464))+~E(f335(f335(f86(x67464),x67465),f335(f335(f87(x67464),x67463),x67461)),f335(f335(f86(x67464),x67466),f335(f335(f87(x67464),x67463),x67462))) % 186.01/186.04 [7767]~P109(x77671)+~P6(x77671)+~P1(f335(f335(f244(x77671),x77672),f335(x77675,x77676)))+~P1(f335(f335(f337(x77673),x77676),x77674))+P1(f335(f335(f244(x77671),x77672),f335(f335(f45(x77673,x77671),x77674),x77675))) % 186.01/186.04 [10065]~P26(x100652,x100651,x100653,x100654)+~P26(x100651,x100652,x100656,x100655)+P27(x100651,x100652,f563(x100653,x100654,x100655,x100656,x100652,x100651),x100655,x100654)+~P1(f335(f335(f243(f934(x100652,a922)),f335(f318(x100651,x100652,x100656),x100655)),x100654))+~P1(f335(f335(f243(f934(x100651,a922)),f335(f318(x100652,x100651,x100653),x100654)),x100655)) % 186.01/186.04 [8435]~P109(x84351)+~P6(x84351)+~P1(f335(f335(f244(x84351),f335(x84354,x84356)),x84355))+~P1(f335(f335(f337(x84352),x84356),x84353))+P1(f335(f335(f244(x84351),f335(f335(f46(x84352,x84351),x84353),x84354)),x84355)) % 186.01/186.04 [8689]~P20(x86892,x86895,x86896,x86891)+~P1(f335(f67(x86892),x86894))+~P1(f335(f67(x86892),x86893))+~E(f335(f335(f108(f934(x86892,a922)),x86893),x86894),f195(f934(x86892,a922)))+E(f335(x86891,f335(f335(f117(f934(x86892,a922)),x86893),x86894)),f335(f78(x86895,x86895,x86895,f335(x86891,x86893)),f335(x86891,x86894))) % 186.01/186.04 [10281]~P72(x102811)+~E(f836(x102814,x102815,x102813,x102816,x102812,x102811),f837(x102814,x102815,x102813,x102816,x102812,x102811))+~P1(f335(f67(x102812),x102816))+E(f335(f335(f335(f71(x102811,x102812,f87(x102811)),f335(f335(f8(f934(x102813,a922),x102811,x102812),f335(f335(f71(x102811,x102813,f87(x102811)),x102814),f84(x102811))),x102815)),f84(x102811)),x102816),f335(f335(f335(f71(x102811,x102813,f87(x102811)),x102814),f84(x102811)),f335(f335(f45(x102812,f934(x102813,a922)),x102816),x102815)))+P1(f335(f335(f337(x102812),f834(x102814,x102815,x102813,x102816,x102812,x102811)),x102816)) % 186.01/186.04 [10311]~P72(x103111)+~E(f836(x103114,x103115,x103113,x103116,x103112,x103111),f837(x103114,x103115,x103113,x103116,x103112,x103111))+~P1(f335(f67(x103112),x103116))+E(f335(f335(f335(f71(x103111,x103112,f87(x103111)),f335(f335(f8(f934(x103113,a922),x103111,x103112),f335(f335(f71(x103111,x103113,f87(x103111)),x103114),f84(x103111))),x103115)),f84(x103111)),x103116),f335(f335(f335(f71(x103111,x103113,f87(x103111)),x103114),f84(x103111)),f335(f335(f45(x103112,f934(x103113,a922)),x103116),x103115)))+~P1(f335(f67(x103113),f335(x103115,f834(x103114,x103115,x103113,x103116,x103112,x103111)))) % 186.01/186.04 [10314]~P72(x103141)+~P1(f335(f67(x103142),x103146))+E(f335(f335(f335(f71(x103141,x103142,f87(x103141)),f335(f335(f8(f934(x103143,a922),x103141,x103142),f335(f335(f71(x103141,x103143,f87(x103141)),x103144),f84(x103141))),x103145)),f84(x103141)),x103146),f335(f335(f335(f71(x103141,x103143,f87(x103141)),x103144),f84(x103141)),f335(f335(f45(x103142,f934(x103143,a922)),x103146),x103145)))+P1(f335(f335(f337(x103142),f834(x103144,x103145,x103143,x103146,x103142,x103141)),x103146))+P1(f335(f335(f337(x103142),f837(x103144,x103145,x103143,x103146,x103142,x103141)),x103146)) % 186.01/186.04 [10315]~P72(x103151)+~P1(f335(f67(x103152),x103156))+E(f335(f335(f335(f71(x103151,x103152,f87(x103151)),f335(f335(f8(f934(x103153,a922),x103151,x103152),f335(f335(f71(x103151,x103153,f87(x103151)),x103154),f84(x103151))),x103155)),f84(x103151)),x103156),f335(f335(f335(f71(x103151,x103153,f87(x103151)),x103154),f84(x103151)),f335(f335(f45(x103152,f934(x103153,a922)),x103156),x103155)))+P1(f335(f335(f337(x103152),f834(x103154,x103155,x103153,x103156,x103152,x103151)),x103156))+P1(f335(f335(f337(x103152),f836(x103154,x103155,x103153,x103156,x103152,x103151)),x103156)) % 186.01/186.04 [10334]~P72(x103341)+~P1(f335(f67(x103342),x103346))+E(f335(f335(f335(f71(x103341,x103342,f87(x103341)),f335(f335(f8(f934(x103343,a922),x103341,x103342),f335(f335(f71(x103341,x103343,f87(x103341)),x103344),f84(x103341))),x103345)),f84(x103341)),x103346),f335(f335(f335(f71(x103341,x103343,f87(x103341)),x103344),f84(x103341)),f335(f335(f45(x103342,f934(x103343,a922)),x103346),x103345)))+P1(f335(f335(f337(x103342),f837(x103344,x103345,x103343,x103346,x103342,x103341)),x103346))+~P1(f335(f67(x103343),f335(x103345,f834(x103344,x103345,x103343,x103346,x103342,x103341)))) % 186.01/186.04 [10335]~P72(x103351)+~P1(f335(f67(x103352),x103356))+E(f335(f335(f335(f71(x103351,x103352,f87(x103351)),f335(f335(f8(f934(x103353,a922),x103351,x103352),f335(f335(f71(x103351,x103353,f87(x103351)),x103354),f84(x103351))),x103355)),f84(x103351)),x103356),f335(f335(f335(f71(x103351,x103353,f87(x103351)),x103354),f84(x103351)),f335(f335(f45(x103352,f934(x103353,a922)),x103356),x103355)))+P1(f335(f335(f337(x103352),f836(x103354,x103355,x103353,x103356,x103352,x103351)),x103356))+~P1(f335(f67(x103353),f335(x103355,f834(x103354,x103355,x103353,x103356,x103352,x103351)))) % 186.01/186.04 [10346]~P72(x103461)+~E(f335(f335(f108(f934(x103463,a922)),f335(x103465,f837(x103464,x103465,x103463,x103466,x103462,x103461))),f335(x103465,f836(x103464,x103465,x103463,x103466,x103462,x103461))),f195(f934(x103463,a922)))+~P1(f335(f67(x103462),x103466))+E(f335(f335(f335(f71(x103461,x103462,f87(x103461)),f335(f335(f8(f934(x103463,a922),x103461,x103462),f335(f335(f71(x103461,x103463,f87(x103461)),x103464),f84(x103461))),x103465)),f84(x103461)),x103466),f335(f335(f335(f71(x103461,x103463,f87(x103461)),x103464),f84(x103461)),f335(f335(f45(x103462,f934(x103463,a922)),x103466),x103465)))+P1(f335(f335(f337(x103462),f834(x103464,x103465,x103463,x103466,x103462,x103461)),x103466)) % 186.01/186.04 [10357]~P72(x103571)+~E(f335(f335(f108(f934(x103573,a922)),f335(x103575,f837(x103574,x103575,x103573,x103576,x103572,x103571))),f335(x103575,f836(x103574,x103575,x103573,x103576,x103572,x103571))),f195(f934(x103573,a922)))+~P1(f335(f67(x103572),x103576))+E(f335(f335(f335(f71(x103571,x103572,f87(x103571)),f335(f335(f8(f934(x103573,a922),x103571,x103572),f335(f335(f71(x103571,x103573,f87(x103571)),x103574),f84(x103571))),x103575)),f84(x103571)),x103576),f335(f335(f335(f71(x103571,x103573,f87(x103571)),x103574),f84(x103571)),f335(f335(f45(x103572,f934(x103573,a922)),x103576),x103575)))+~P1(f335(f67(x103573),f335(x103575,f834(x103574,x103575,x103573,x103576,x103572,x103571)))) % 186.01/186.04 [9023]E(x90231,x90232)+~P58(x90234,x90235,x90236,x90233,x90237)+~E(f335(x90233,x90231),f335(x90233,x90232))+~P1(f335(f335(f337(x90235),x90232),x90237))+~P1(f335(f335(f337(x90235),x90231),x90237)) % 186.01/186.04 [10324]~P1(f335(x103242,x103244))+~E(x103245,f335(f143(x103241,x103242),x103247))+E(f335(f143(x103241,x103242),x103243),f335(f335(f158(x103241),x103244),x103245))+~E(x103243,f335(f335(f141(x103241),x103246),f335(f335(f158(x103241),x103244),x103247)))+P1(f335(x103242,f771(x103245,x103244,x103243,x103242,x103241,x103246,x103247))) % 186.01/186.04 [10325]~P1(f335(x103254,x103252))+~E(x103253,f335(f143(x103251,x103254),x103257))+E(f335(f335(f158(x103251),x103252),x103253),f335(f143(x103251,x103254),x103255))+~E(x103255,f335(f335(f141(x103251),x103256),f335(f335(f158(x103251),x103252),x103257)))+P1(f335(x103254,f770(x103255,x103254,x103253,x103252,x103251,x103256,x103257))) % 186.01/186.04 [10369]~P1(f335(x103692,x103694))+~E(x103695,f335(f143(x103691,x103692),x103697))+E(f335(f143(x103691,x103692),x103693),f335(f335(f158(x103691),x103694),x103695))+~E(x103693,f335(f335(f141(x103691),x103696),f335(f335(f158(x103691),x103694),x103697)))+P1(f335(f335(f337(x103691),f771(x103695,x103694,x103693,x103692,x103691,x103696,x103697)),f335(f179(x103691),x103696))) % 186.01/186.04 [10370]~P1(f335(x103704,x103702))+~E(x103703,f335(f143(x103701,x103704),x103707))+E(f335(f335(f158(x103701),x103702),x103703),f335(f143(x103701,x103704),x103705))+~E(x103705,f335(f335(f141(x103701),x103706),f335(f335(f158(x103701),x103702),x103707)))+P1(f335(f335(f337(x103701),f770(x103705,x103704,x103703,x103702,x103701,x103706,x103707)),f335(f179(x103701),x103706))) % 186.01/186.04 [10374]~P9(x103741,x103747,x103746)+~P12(x103741,f934(x103745,a922),x103746,x103744)+P1(f335(f335(f337(x103741),f755(x103742,x103743,x103744,x103745,x103746,x103747,x103741)),x103747))+~P1(f335(f335(f337(f934(x103741,a922)),x103743),f335(f335(f66(x103741),x103747),x103746)))+P1(f335(f335(f337(f934(x103745,a922)),f335(f335(f45(x103741,f934(x103745,a922)),x103743),x103744)),x103742)) % 186.01/186.04 [10434]~P9(x104342,x104346,x104347)+~P12(x104342,f934(x104341,a922),x104347,x104344)+~P1(f335(f335(f337(f934(x104342,a922)),x104343),f335(f335(f66(x104342),x104346),x104347)))+~P1(f335(f335(f337(f934(x104341,a922)),f335(x104344,f755(x104345,x104343,x104344,x104341,x104347,x104346,x104342))),x104345))+P1(f335(f335(f337(f934(x104341,a922)),f335(f335(f45(x104342,f934(x104341,a922)),x104343),x104344)),x104345)) % 186.01/186.04 [8609]~P72(x86092)+~P26(x86091,x86095,x86098,x86094)+~E(x86093,f335(f78(x86095,x86092,x86091,x86096),x86098))+~E(x86097,f335(f318(x86091,x86095,x86098),x86094))+E(f335(f335(f9(x86091,x86092),x86093),x86094),f335(f335(f9(x86095,x86092),x86096),x86097)) % 186.01/186.04 [10438]~P72(x104382)+~P26(x104385,x104381,x104388,x104387)+~E(f335(x104386,f540(x104383,x104386,x104384,x104387,x104388,x104381,x104385,x104382)),f335(f335(f78(x104381,x104382,x104385,x104383),x104388),f540(x104383,x104386,x104384,x104387,x104388,x104381,x104385,x104382)))+~E(x104384,f335(f318(x104385,x104381,x104388),x104387))+E(f335(f335(f9(x104381,x104382),x104383),x104384),f335(f335(f9(x104385,x104382),x104386),x104387)) % 186.01/186.04 [10441]~P76(x104412)+~P26(x104411,x104415,x104418,x104414)+~E(x104417,f335(f318(x104411,x104415,x104418),x104414))+E(f335(f335(f6(x104411,x104412),x104413),x104414),f335(f335(f6(x104415,x104412),x104416),x104417))+P1(f335(f335(f337(x104411),f645(x104416,x104413,x104417,x104414,x104418,x104415,x104411,x104412)),x104414)) % 186.01/186.04 [10442]~P72(x104422)+~P26(x104421,x104425,x104428,x104424)+~E(x104427,f335(f318(x104421,x104425,x104428),x104424))+E(f335(f335(f9(x104421,x104422),x104423),x104424),f335(f335(f9(x104425,x104422),x104426),x104427))+P1(f335(f335(f337(x104421),f540(x104426,x104423,x104427,x104424,x104428,x104425,x104421,x104422)),x104424)) % 186.01/186.04 [10447]~P76(x104472)+~P26(x104475,x104471,x104478,x104477)+~E(x104474,f335(f318(x104475,x104471,x104478),x104477))+~E(f335(x104476,f645(x104473,x104476,x104474,x104477,x104478,x104471,x104475,x104472)),f335(x104473,f335(x104478,f645(x104473,x104476,x104474,x104477,x104478,x104471,x104475,x104472))))+E(f335(f335(f6(x104471,x104472),x104473),x104474),f335(f335(f6(x104475,x104472),x104476),x104477)) % 186.01/186.04 [9899]~P24(x98996,x98992,x98995,x98997,x98998,x98991)+~P1(f335(f67(x98992),x98994))+~P1(f335(f67(x98992),x98993))+~E(f335(f335(f108(f934(x98992,a922)),x98993),x98994),f195(f934(x98992,a922)))+E(f335(x98991,f335(f335(f117(f934(x98992,a922)),x98993),x98994)),f335(f335(x98995,f335(x98991,x98993)),f335(x98991,x98994))) % 186.01/186.04 [10308]~P24(x103088,x103082,x103085,x103087,x103086,x103081)+~E(f335(x103086,f571(x103084,x103083,x103081,x103086,x103087,x103085,x103082)),x103087)+~P1(f335(f67(x103082),x103083))+~P1(f335(f67(x103082),x103084))+E(f335(x103081,f335(f335(f117(f934(x103082,a922)),x103083),x103084)),f335(f335(x103085,f335(x103081,x103083)),f335(x103081,x103084))) % 186.01/186.04 [10381]~P24(x103818,x103812,x103815,x103817,x103816,x103811)+~P1(f335(f67(x103812),x103813))+~P1(f335(f67(x103812),x103814))+E(f335(x103811,f335(f335(f117(f934(x103812,a922)),x103813),x103814)),f335(f335(x103815,f335(x103811,x103813)),f335(x103811,x103814)))+P1(f335(f335(f337(x103812),f571(x103814,x103813,x103811,x103816,x103817,x103815,x103812)),f335(f335(f108(f934(x103812,a922)),x103813),x103814))) % 186.01/186.04 [10056]~P9(x100564,x100568,x100565)+~P9(x100561,x100569,x100563)+~P13(x100561,x100564,f934(x100562,a922),x100563,x100565,x100567)+P12(x100561,f934(x100562,a922),x100563,f335(f335(f8(f934(x100564,f934(x100562,a922)),f934(x100562,a922),x100561),f335(f45(x100564,f934(x100562,a922)),f335(f293(x100564,x100564,x100565),f335(f335(f317(x100564),x100566),f195(f934(x100564,a922)))))),x100567))+~P1(f335(f335(f337(x100564),x100566),x100568)) % 186.01/186.04 [5663]~P109(x56633)+~P14(x56633,x56631)+E(x56631,f748(x56632,x56633))+~E(f335(f179(x56633),x56631),x56632)+~P1(f335(f67(x56633),x56632))+~P1(f335(f144(x56633),x56631)) % 186.01/186.04 [7475]P16(x74751,x74752)+~E(f335(x74752,f831(x74752)),f335(x74752,f832(x74752)))+~P1(f335(f335(x74752,f831(x74752)),f831(x74752)))+~P1(f335(f335(x74752,f831(x74752)),f832(x74752)))+~P1(f335(f335(x74752,f832(x74752)),f832(x74752)))+~P1(f335(f335(x74752,x74753),x74753)) % 186.01/186.04 [5288]~P129(x52882)+~P130(x52882)+~P144(x52882)+~P117(x52882)+E(x52881,f2(x52882))+~E(f335(f335(f252(x52882),x52881),x52883),f2(x52882)) % 186.01/186.04 [5289]~P129(x52892)+~P130(x52892)+~P144(x52892)+~P117(x52892)+~E(x52891,f2(a927))+~E(f335(f335(f252(x52892),x52893),x52891),f2(x52892)) % 186.01/186.04 [6728]~P89(x67281)+~E(x67283,f2(x67281))+~E(x67282,f2(x67281))+E(f335(f335(f86(x67281),x67282),x67283),f2(x67281))+~P1(f335(f335(f243(x67281),f2(x67281)),x67283))+~P1(f335(f335(f243(x67281),f2(x67281)),x67282)) % 186.01/186.04 [9091]~E(f335(f259(a927,a927),x90913),f2(a927))+~E(x90911,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x90913)),x90912)),f335(f264(a927,a927),x90913)))+P1(f335(f54(x90911,x90912),x90913))+~P1(f335(f335(f243(a927),f335(f264(a927,a927),x90913)),f2(a927)))+P1(f335(f335(f244(a927),f2(a927)),x90912))+~P1(f335(f335(f244(a927),x90912),f335(f264(a927,a927),x90913))) % 186.01/186.04 [9099]E(x90991,f2(a927))+~E(x90992,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x90993)),x90991)),f335(f264(a927,a927),x90993)))+P1(f335(f54(x90992,x90991),x90993))+~P1(f335(f335(f244(a927),f2(a927)),x90991))+~P1(f335(f335(f243(a927),f2(a927)),f335(f264(a927,a927),x90993)))+~P1(f335(f335(f244(a927),f335(f264(a927,a927),x90993)),x90991)) % 186.01/186.04 [9117]~E(f335(f259(a927,a927),x91173),f2(a927))+~E(x91171,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x91173)),x91172)),f335(f264(a927,a927),x91173)))+P1(f335(f54(x91171,x91172),x91173))+~P1(f335(f335(f244(a927),f2(a927)),x91172))+~P1(f335(f335(f243(a927),f2(a927)),f335(f264(a927,a927),x91173)))+~P1(f335(f335(f244(a927),f335(f264(a927,a927),x91173)),x91172)) % 186.01/186.04 [7107]~P98(x71072)+E(x71071,f195(f934(x71072,a922)))+E(x71073,f195(f934(x71072,a922)))+~P1(f335(f67(x71072),x71071))+~P1(f335(f67(x71072),x71073))+E(f13(x71072,f335(f335(f117(f934(x71072,a922)),x71073),x71071)),f335(f335(f117(x71072),f13(x71072,x71073)),f13(x71072,x71071))) % 186.01/186.04 [7108]~P98(x71082)+E(x71081,f195(f934(x71082,a922)))+E(x71083,f195(f934(x71082,a922)))+~P1(f335(f67(x71082),x71081))+~P1(f335(f67(x71082),x71083))+E(f10(x71082,f335(f335(f117(f934(x71082,a922)),x71083),x71081)),f335(f335(f108(x71082),f10(x71082,x71083)),f10(x71082,x71081))) % 186.01/186.04 [7109]~P109(x71092)+E(x71091,f195(f934(x71092,a922)))+E(x71093,f195(f934(x71092,a922)))+~P1(f335(f67(x71092),x71091))+~P1(f335(f67(x71092),x71093))+E(f14(x71092,f335(f335(f117(f934(x71092,a922)),x71093),x71091)),f335(f335(f242(x71092),f14(x71092,x71093)),f14(x71092,x71091))) % 186.01/186.04 [7110]~P109(x71102)+E(x71101,f195(f934(x71102,a922)))+E(x71103,f195(f934(x71102,a922)))+~P1(f335(f67(x71102),x71101))+~P1(f335(f67(x71102),x71103))+E(f15(x71102,f335(f335(f117(f934(x71102,a922)),x71103),x71101)),f335(f335(f241(x71102),f15(x71102,x71103)),f15(x71102,x71101))) % 186.01/186.04 [7744]~P96(x77442)+E(x77441,f195(f934(x77442,a922)))+E(x77443,f195(f934(x77442,a922)))+~P1(f335(f67(x77442),x77441))+~P1(f335(f67(x77442),x77443))+E(f335(f335(f87(x77442),f335(f69(x77442,f87(x77442)),x77443)),f335(f69(x77442,f87(x77442)),x77441)),f335(f69(x77442,f87(x77442)),f335(f335(f117(f934(x77442,a922)),x77443),x77441))) % 186.01/186.04 [7900]~P109(x79002)+E(x79001,f195(f934(x79002,a922)))+E(x79003,f195(f934(x79002,a922)))+~P1(f335(f67(x79002),x79001))+~P1(f335(f67(x79002),x79003))+E(f335(f335(f242(x79002),f11(x79002,f242(x79002),x79003)),f11(x79002,f242(x79002),x79001)),f11(x79002,f242(x79002),f335(f335(f117(f934(x79002,a922)),x79003),x79001))) % 186.01/186.04 [7901]~P109(x79012)+E(x79011,f195(f934(x79012,a922)))+E(x79013,f195(f934(x79012,a922)))+~P1(f335(f67(x79012),x79011))+~P1(f335(f67(x79012),x79013))+E(f335(f335(f241(x79012),f12(x79012,f241(x79012),x79013)),f12(x79012,f241(x79012),x79011)),f12(x79012,f241(x79012),f335(f335(f117(f934(x79012,a922)),x79013),x79011))) % 186.01/186.04 [8924]~P1(f335(x89241,x89243))+P1(f335(x89241,f531(x89241,x89242)))+P1(f335(x89241,f521(x89241,x89242)))+~P1(f335(f335(f244(a1),f2(a1)),x89242))+~P1(f335(f335(f337(a1),x89243),f311(a1,f84(a1),x89242)))+P1(f335(x89241,f335(f335(f23(a1),f521(x89241,x89242)),f335(f335(f87(a1),f529(x89241,x89242)),x89242)))) % 186.01/186.04 [9229]~P1(f335(x92291,x92293))+~P1(f335(x92291,f521(x92291,x92292)))+P1(f335(x92291,f531(x92291,x92292)))+~P1(f335(f335(f244(a1),f2(a1)),x92292))+~P1(f335(f335(f337(a1),x92293),f311(a1,f84(a1),x92292)))+~P1(f335(x92291,f335(f335(f23(a1),f521(x92291,x92292)),f335(f335(f87(a1),f529(x92291,x92292)),x92292)))) % 186.01/186.04 [10474]~P102(x104742)+E(x104741,f195(f934(x104742,a922)))+E(x104743,f195(f934(x104742,a922)))+~P1(f335(f67(x104742),x104741))+~P1(f335(f67(x104742),x104743))+E(f13(x104742,f335(f270(x104742),f335(f335(f8(f934(x104742,a922),a922,x104742),f93(x104742)),f335(f335(f8(f934(x104742,f934(x104742,a922)),f934(x104742,a922),x104742),f335(f8(f934(x104742,a922),a922,x104742),f93(x104742))),f335(f335(f7(x104742,f934(x104742,f934(x104742,a922)),f934(x104742,f934(x104742,a922))),f335(f335(f8(f934(x104742,f934(f934(x104742,a922),f934(x104742,a922))),f934(f934(x104742,f934(x104742,a922)),f934(x104742,f934(x104742,a922))),x104742),f18(x104742,f934(x104742,a922),f934(x104742,a922))),f335(f335(f8(f934(x104742,f934(x104742,f934(a922,a922))),f934(x104742,f934(f934(x104742,a922),f934(x104742,a922))),x104742),f335(f8(f934(x104742,f934(a922,a922)),f934(f934(x104742,a922),f934(x104742,a922)),x104742),f18(x104742,a922,a922))),f335(f335(f8(f934(x104742,f934(x104742,a922)),f934(x104742,f934(x104742,f934(a922,a922))),x104742),f335(f8(f934(x104742,a922),f934(x104742,f934(a922,a922)),x104742),f335(f8(a922,f934(a922,a922),x104742),a333))),f335(f335(f7(x104742,f934(x104742,f934(x104742,x104742)),f934(x104742,f934(x104742,a922))),f335(f335(f8(f934(f934(x104742,x104742),f934(x104742,a922)),f934(f934(x104742,f934(x104742,x104742)),f934(x104742,f934(x104742,a922))),x104742),f8(f934(x104742,x104742),f934(x104742,a922),x104742)),f335(f335(f8(f934(x104742,a922),f934(f934(x104742,x104742),f934(x104742,a922)),x104742),f8(x104742,a922,x104742)),a332))),f108(x104742)))))),f335(f335(f7(x104742,f934(x104742,a922),f934(x104742,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x104742,a922),f934(x104742,a922)),x104742),f8(a922,a922,x104742)),f335(f335(f8(a922,f934(a922,a922),x104742),a333),f335(f335(f7(x104742,f934(x104742,a922),a922),f337(x104742)),x104743)))),f335(f335(f7(x104742,f934(x104742,a922),a922),f337(x104742)),x104741))))))),f335(f335(f108(x104742),f13(x104742,x104743)),f13(x104742,x104741))) % 186.01/186.04 [10475]~P102(x104752)+E(x104751,f195(f934(x104752,a922)))+E(x104753,f195(f934(x104752,a922)))+~P1(f335(f67(x104752),x104751))+~P1(f335(f67(x104752),x104753))+E(f10(x104752,f335(f270(x104752),f335(f335(f8(f934(x104752,a922),a922,x104752),f93(x104752)),f335(f335(f8(f934(x104752,f934(x104752,a922)),f934(x104752,a922),x104752),f335(f8(f934(x104752,a922),a922,x104752),f93(x104752))),f335(f335(f7(x104752,f934(x104752,f934(x104752,a922)),f934(x104752,f934(x104752,a922))),f335(f335(f8(f934(x104752,f934(f934(x104752,a922),f934(x104752,a922))),f934(f934(x104752,f934(x104752,a922)),f934(x104752,f934(x104752,a922))),x104752),f18(x104752,f934(x104752,a922),f934(x104752,a922))),f335(f335(f8(f934(x104752,f934(x104752,f934(a922,a922))),f934(x104752,f934(f934(x104752,a922),f934(x104752,a922))),x104752),f335(f8(f934(x104752,f934(a922,a922)),f934(f934(x104752,a922),f934(x104752,a922)),x104752),f18(x104752,a922,a922))),f335(f335(f8(f934(x104752,f934(x104752,a922)),f934(x104752,f934(x104752,f934(a922,a922))),x104752),f335(f8(f934(x104752,a922),f934(x104752,f934(a922,a922)),x104752),f335(f8(a922,f934(a922,a922),x104752),a333))),f335(f335(f7(x104752,f934(x104752,f934(x104752,x104752)),f934(x104752,f934(x104752,a922))),f335(f335(f8(f934(f934(x104752,x104752),f934(x104752,a922)),f934(f934(x104752,f934(x104752,x104752)),f934(x104752,f934(x104752,a922))),x104752),f8(f934(x104752,x104752),f934(x104752,a922),x104752)),f335(f335(f8(f934(x104752,a922),f934(f934(x104752,x104752),f934(x104752,a922)),x104752),f8(x104752,a922,x104752)),a332))),f117(x104752)))))),f335(f335(f7(x104752,f934(x104752,a922),f934(x104752,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x104752,a922),f934(x104752,a922)),x104752),f8(a922,a922,x104752)),f335(f335(f8(a922,f934(a922,a922),x104752),a333),f335(f335(f7(x104752,f934(x104752,a922),a922),f337(x104752)),x104753)))),f335(f335(f7(x104752,f934(x104752,a922),a922),f337(x104752)),x104751))))))),f335(f335(f117(x104752),f10(x104752,x104753)),f10(x104752,x104751))) % 186.01/186.04 [10476]~P109(x104762)+E(x104761,f195(f934(x104762,a922)))+E(x104763,f195(f934(x104762,a922)))+~P1(f335(f67(x104762),x104761))+~P1(f335(f67(x104762),x104763))+E(f11(x104762,f242(x104762),f335(f270(x104762),f335(f335(f8(f934(x104762,a922),a922,x104762),f93(x104762)),f335(f335(f8(f934(x104762,f934(x104762,a922)),f934(x104762,a922),x104762),f335(f8(f934(x104762,a922),a922,x104762),f93(x104762))),f335(f335(f7(x104762,f934(x104762,f934(x104762,a922)),f934(x104762,f934(x104762,a922))),f335(f335(f8(f934(x104762,f934(f934(x104762,a922),f934(x104762,a922))),f934(f934(x104762,f934(x104762,a922)),f934(x104762,f934(x104762,a922))),x104762),f18(x104762,f934(x104762,a922),f934(x104762,a922))),f335(f335(f8(f934(x104762,f934(x104762,f934(a922,a922))),f934(x104762,f934(f934(x104762,a922),f934(x104762,a922))),x104762),f335(f8(f934(x104762,f934(a922,a922)),f934(f934(x104762,a922),f934(x104762,a922)),x104762),f18(x104762,a922,a922))),f335(f335(f8(f934(x104762,f934(x104762,a922)),f934(x104762,f934(x104762,f934(a922,a922))),x104762),f335(f8(f934(x104762,a922),f934(x104762,f934(a922,a922)),x104762),f335(f8(a922,f934(a922,a922),x104762),a333))),f335(f335(f7(x104762,f934(x104762,f934(x104762,x104762)),f934(x104762,f934(x104762,a922))),f335(f335(f8(f934(f934(x104762,x104762),f934(x104762,a922)),f934(f934(x104762,f934(x104762,x104762)),f934(x104762,f934(x104762,a922))),x104762),f8(f934(x104762,x104762),f934(x104762,a922),x104762)),f335(f335(f8(f934(x104762,a922),f934(f934(x104762,x104762),f934(x104762,a922)),x104762),f8(x104762,a922,x104762)),a332))),f241(x104762)))))),f335(f335(f7(x104762,f934(x104762,a922),f934(x104762,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x104762,a922),f934(x104762,a922)),x104762),f8(a922,a922,x104762)),f335(f335(f8(a922,f934(a922,a922),x104762),a333),f335(f335(f7(x104762,f934(x104762,a922),a922),f337(x104762)),x104763)))),f335(f335(f7(x104762,f934(x104762,a922),a922),f337(x104762)),x104761))))))),f335(f335(f241(x104762),f11(x104762,f242(x104762),x104763)),f11(x104762,f242(x104762),x104761))) % 186.01/186.04 [10477]~P109(x104772)+E(x104771,f195(f934(x104772,a922)))+E(x104773,f195(f934(x104772,a922)))+~P1(f335(f67(x104772),x104771))+~P1(f335(f67(x104772),x104773))+E(f12(x104772,f241(x104772),f335(f270(x104772),f335(f335(f8(f934(x104772,a922),a922,x104772),f93(x104772)),f335(f335(f8(f934(x104772,f934(x104772,a922)),f934(x104772,a922),x104772),f335(f8(f934(x104772,a922),a922,x104772),f93(x104772))),f335(f335(f7(x104772,f934(x104772,f934(x104772,a922)),f934(x104772,f934(x104772,a922))),f335(f335(f8(f934(x104772,f934(f934(x104772,a922),f934(x104772,a922))),f934(f934(x104772,f934(x104772,a922)),f934(x104772,f934(x104772,a922))),x104772),f18(x104772,f934(x104772,a922),f934(x104772,a922))),f335(f335(f8(f934(x104772,f934(x104772,f934(a922,a922))),f934(x104772,f934(f934(x104772,a922),f934(x104772,a922))),x104772),f335(f8(f934(x104772,f934(a922,a922)),f934(f934(x104772,a922),f934(x104772,a922)),x104772),f18(x104772,a922,a922))),f335(f335(f8(f934(x104772,f934(x104772,a922)),f934(x104772,f934(x104772,f934(a922,a922))),x104772),f335(f8(f934(x104772,a922),f934(x104772,f934(a922,a922)),x104772),f335(f8(a922,f934(a922,a922),x104772),a333))),f335(f335(f7(x104772,f934(x104772,f934(x104772,x104772)),f934(x104772,f934(x104772,a922))),f335(f335(f8(f934(f934(x104772,x104772),f934(x104772,a922)),f934(f934(x104772,f934(x104772,x104772)),f934(x104772,f934(x104772,a922))),x104772),f8(f934(x104772,x104772),f934(x104772,a922),x104772)),f335(f335(f8(f934(x104772,a922),f934(f934(x104772,x104772),f934(x104772,a922)),x104772),f8(x104772,a922,x104772)),a332))),f242(x104772)))))),f335(f335(f7(x104772,f934(x104772,a922),f934(x104772,a922)),f335(f335(f8(f934(a922,a922),f934(f934(x104772,a922),f934(x104772,a922)),x104772),f8(a922,a922,x104772)),f335(f335(f8(a922,f934(a922,a922),x104772),a333),f335(f335(f7(x104772,f934(x104772,a922),a922),f337(x104772)),x104773)))),f335(f335(f7(x104772,f934(x104772,a922),a922),f337(x104772)),x104771))))))),f335(f335(f242(x104772),f12(x104772,f241(x104772),x104773)),f12(x104772,f241(x104772),x104771))) % 186.01/186.04 [7431]~P125(x74313)+E(x74311,x74312)+~E(f335(f335(f252(x74313),x74311),x74314),f335(f335(f252(x74313),x74312),x74314))+~P1(f335(f335(f243(x74313),f2(x74313)),x74312))+~P1(f335(f335(f243(x74313),f2(x74313)),x74311))+~P1(f335(f335(f244(a927),f2(a927)),x74314)) % 186.01/186.04 [7705]~P109(x77052)+E(x77051,f195(f934(x77052,a922)))+~P1(f335(f67(x77052),x77051))+~P1(f335(f335(f337(x77052),x77054),x77051))+P1(f335(f335(f243(x77052),x77053),x77054))+~P1(f335(f335(f243(x77052),x77053),f335(f69(x77052,f241(x77052)),x77051))) % 186.01/186.04 [7706]~P97(x77062)+E(x77061,f195(f934(x77062,a922)))+~P1(f335(f67(x77062),x77061))+~P1(f335(f335(f337(x77062),x77064),x77061))+P1(f335(f335(f243(x77062),x77063),x77064))+~P1(f335(f335(f243(x77062),x77063),f335(f69(x77062,f108(x77062)),x77061))) % 186.01/186.04 [7707]~P109(x77072)+E(x77071,f195(f934(x77072,a922)))+~P1(f335(f67(x77072),x77071))+~P1(f335(f335(f337(x77072),x77074),x77071))+P1(f335(f335(f244(x77072),x77073),x77074))+~P1(f335(f335(f244(x77072),x77073),f335(f69(x77072,f241(x77072)),x77071))) % 186.01/186.04 [7612]E(x76121,f2(a1))+E(f335(f335(f42(a1),x76122),x76121),x76123)+~P1(f335(f335(f243(a1),x76124),f2(a1)))+~E(x76122,f335(f335(f86(a1),f335(f335(f87(a1),x76121),x76123)),x76124))+P1(f335(f335(f244(a1),f2(a1)),x76121))+~P1(f335(f335(f244(a1),x76121),x76124)) % 186.01/186.04 [7627]E(f51(a1,x76272,x76271),x76273)+E(x76271,f2(a1))+~P1(f335(f335(f243(a1),x76273),f2(a1)))+~E(x76272,f335(f335(f86(a1),f335(f335(f87(a1),x76271),x76274)),x76273))+P1(f335(f335(f244(a1),f2(a1)),x76271))+~P1(f335(f335(f244(a1),x76271),x76273)) % 186.01/186.04 [7743]E(x77431,f2(a1))+E(f335(f335(f42(a1),x77432),x77431),x77433)+~E(x77432,f335(f335(f86(a1),f335(f335(f87(a1),x77431),x77433)),x77434))+~P1(f335(f335(f243(a1),f2(a1)),x77434))+~P1(f335(f335(f244(a1),f2(a1)),x77431))+~P1(f335(f335(f244(a1),x77434),x77431)) % 186.01/186.04 [7763]E(f51(a1,x77632,x77631),x77633)+E(x77631,f2(a1))+~E(x77632,f335(f335(f86(a1),f335(f335(f87(a1),x77631),x77634)),x77633))+~P1(f335(f335(f243(a1),f2(a1)),x77633))+~P1(f335(f335(f244(a1),f2(a1)),x77631))+~P1(f335(f335(f244(a1),x77633),x77631)) % 186.01/186.04 [7904]~P109(x79042)+E(x79041,f195(f934(x79042,a922)))+~P1(f335(f67(x79042),x79041))+~P1(f335(f335(f243(x79042),x79044),x79043))+~P1(f335(f335(f337(x79042),x79044),x79041))+P1(f335(f335(f243(x79042),f335(f69(x79042,f241(x79042)),x79041)),x79043)) % 186.01/186.04 [7905]~P109(x79052)+E(x79051,f195(f934(x79052,a922)))+~P1(f335(f67(x79052),x79051))+~P1(f335(f335(f244(x79052),x79054),x79053))+~P1(f335(f335(f337(x79052),x79054),x79051))+P1(f335(f335(f244(x79052),f335(f69(x79052,f241(x79052)),x79051)),x79053)) % 186.01/186.04 [8460]~P1(f335(f335(f243(a1),x84604),f2(a1)))+~E(x84601,f335(f335(f86(a1),f335(f335(f87(a1),x84602),x84603)),x84604))+~P1(f335(f335(f243(a1),f2(a1)),x84604))+~P1(f335(f335(f244(a1),x84604),x84602))+~P1(f335(f335(f244(a1),x84602),x84604))+P1(f335(f55(x84601,x84602),f335(f335(f260(a1,a1),x84603),x84604))) % 186.01/186.04 [8628]~P110(x86281)+P1(f335(f335(f244(f934(x86281,a922)),f311(x86281,x86282,x86283)),f311(x86281,x86284,x86285)))+~P1(f335(f335(f243(x86281),x86284),x86282))+~P1(f335(f335(f243(x86281),x86284),x86285))+~P1(f335(f335(f243(x86281),x86283),x86285))+~P1(f335(f335(f244(x86281),x86283),x86285)) % 186.01/186.04 [8629]~P110(x86291)+P1(f335(f335(f244(f934(x86291,a922)),f311(x86291,x86292,x86293)),f311(x86291,x86294,x86295)))+~P1(f335(f335(f243(x86291),x86293),x86295))+~P1(f335(f335(f243(x86291),x86294),x86295))+~P1(f335(f335(f243(x86291),x86294),x86292))+~P1(f335(f335(f244(x86291),x86294),x86292)) % 186.01/186.04 [9487]P60(x94872,x94873,x94874,x94871)+E(x94871,f195(f934(x94872,a922)))+~P1(f335(f67(x94872),x94874))+~P1(f335(f67(x94872),x94871))+~P1(f335(f335(x94873,f359(x94871,x94874,x94873,x94872)),x94875))+~P1(f335(f335(f337(x94872),x94875),x94871)) % 186.01/186.04 [9488]P60(x94882,x94883,x94884,x94881)+E(x94881,f195(f934(x94882,a922)))+~P1(f335(f67(x94882),x94884))+~P1(f335(f67(x94882),x94881))+~P1(f335(f335(x94883,f822(x94883,x94881,x94884,x94882)),x94885))+~P1(f335(f335(f337(x94882),x94885),x94881)) % 186.01/186.04 [9489]P60(x94892,x94893,x94894,x94891)+E(x94891,f195(f934(x94892,a922)))+~P1(f335(f67(x94892),x94894))+~P1(f335(f67(x94892),x94891))+~P1(f335(f335(x94893,f823(x94891,x94894,x94893,x94892)),x94895))+~P1(f335(f335(f337(x94892),x94895),x94891)) % 186.01/186.04 [9635]~E(x96353,x96355)+~P72(x96351)+~P76(x96351)+~P41(x96353)+E(f335(f335(f6(a1,x96351),x96352),x96353),f335(f335(f6(a1,x96351),x96354),x96355))+P1(f335(f335(f243(a1),f2(a1)),f555(x96352,x96354,x96353,x96355,x96351))) % 186.01/186.04 [9636]~E(x96363,x96365)+~P72(x96361)+~P76(x96361)+~P41(x96363)+E(f335(f335(f9(a1,x96361),x96362),x96363),f335(f335(f9(a1,x96361),x96364),x96365))+P1(f335(f335(f243(a1),f2(a1)),f553(x96362,x96364,x96363,x96365,x96361))) % 186.01/186.04 [9808]~E(x98085,x98083)+~P72(x98081)+~P76(x98081)+~P41(x98085)+~E(f335(x98082,f555(x98084,x98082,x98085,x98083,x98081)),f335(x98084,f555(x98084,x98082,x98085,x98083,x98081)))+E(f335(f335(f6(a1,x98081),x98082),x98083),f335(f335(f6(a1,x98081),x98084),x98085)) % 186.01/186.04 [9809]~E(x98095,x98093)+~P72(x98091)+~P76(x98091)+~P41(x98095)+~E(f335(x98092,f553(x98094,x98092,x98095,x98093,x98091)),f335(x98094,f553(x98094,x98092,x98095,x98093,x98091)))+E(f335(f335(f9(a1,x98091),x98092),x98093),f335(f335(f9(a1,x98091),x98094),x98095)) % 186.01/186.04 [9897]~P79(x98973)+E(f335(x98971,x98972),f2(x98973))+~E(f335(f335(f6(x98974,x98973),x98971),x98975),f2(x98973))+~P1(f335(f67(x98974),x98975))+P1(f335(f335(f337(x98974),f485(x98972,x98971,x98975,x98974,x98973)),x98975))+~P1(f335(f335(f337(x98974),x98972),x98975)) % 186.01/186.04 [10026]~P79(x100263)+E(f335(x100261,x100262),f2(x100263))+~E(f335(f335(f6(x100264,x100263),x100261),x100265),f2(x100263))+~P1(f335(f67(x100264),x100265))+~P1(f335(f335(f337(x100264),x100262),x100265))+~P1(f335(f335(f243(x100263),f2(x100263)),f335(x100261,f485(x100262,x100261,x100265,x100264,x100263)))) % 186.01/186.04 [8546]~P137(x85461)+~P1(f335(f335(f243(x85461),x85463),x85465))+~P1(f335(f335(f243(x85461),x85462),x85464))+~P1(f335(f335(f243(x85461),f2(x85461)),x85463))+~P1(f335(f335(f243(x85461),f2(x85461)),x85464))+P1(f335(f335(f243(x85461),f335(f335(f87(x85461),x85462),x85463)),f335(f335(f87(x85461),x85464),x85465))) % 186.01/186.04 [8547]~P137(x85471)+~P1(f335(f335(f243(x85471),x85473),x85475))+~P1(f335(f335(f243(x85471),x85472),x85474))+~P1(f335(f335(f243(x85471),f2(x85471)),x85473))+~P1(f335(f335(f243(x85471),f2(x85471)),x85472))+P1(f335(f335(f243(x85471),f335(f335(f87(x85471),x85472),x85473)),f335(f335(f87(x85471),x85474),x85475))) % 186.01/186.04 [8548]~P69(x85481)+~P1(f335(f335(f244(x85481),f2(x85481)),x85485))+~P1(f335(f335(f243(x85481),x85485),x85483))+~P1(f335(f335(f243(x85481),x85482),x85484))+~P1(f335(f335(f243(x85481),f2(x85481)),x85482))+P1(f335(f335(f243(x85481),f335(f335(f299(x85481),x85482),x85483)),f335(f335(f299(x85481),x85484),x85485))) % 186.01/186.04 [8549]~P131(x85491)+~P1(f335(f335(f243(x85491),x85493),x85495))+~P1(f335(f335(f243(x85491),f2(x85491)),x85492))+~P1(f335(f335(f244(x85491),x85492),x85494))+~P1(f335(f335(f244(x85491),f2(x85491)),x85493))+P1(f335(f335(f244(x85491),f335(f335(f87(x85491),x85492),x85493)),f335(f335(f87(x85491),x85494),x85495))) % 186.01/186.04 [8550]~P131(x85501)+~P1(f335(f335(f243(x85501),x85502),x85504))+~P1(f335(f335(f243(x85501),f2(x85501)),x85503))+~P1(f335(f335(f244(x85501),x85503),x85505))+~P1(f335(f335(f244(x85501),f2(x85501)),x85502))+P1(f335(f335(f244(x85501),f335(f335(f87(x85501),x85502),x85503)),f335(f335(f87(x85501),x85504),x85505))) % 186.01/186.04 [8551]~P131(x85511)+~P1(f335(f335(f243(x85511),f2(x85511)),x85513))+~P1(f335(f335(f243(x85511),f2(x85511)),x85512))+~P1(f335(f335(f244(x85511),x85513),x85515))+~P1(f335(f335(f244(x85511),x85512),x85514))+P1(f335(f335(f244(x85511),f335(f335(f87(x85511),x85512),x85513)),f335(f335(f87(x85511),x85514),x85515))) % 186.01/186.04 [8552]~P131(x85521)+~P1(f335(f335(f243(x85521),f2(x85521)),x85523))+~P1(f335(f335(f244(x85521),x85523),x85525))+~P1(f335(f335(f244(x85521),x85522),x85524))+~P1(f335(f335(f244(x85521),f2(x85521)),x85524))+P1(f335(f335(f244(x85521),f335(f335(f87(x85521),x85522),x85523)),f335(f335(f87(x85521),x85524),x85525))) % 186.01/186.04 [8553]~P69(x85531)+~P1(f335(f335(f243(x85531),x85535),x85533))+~P1(f335(f335(f243(x85531),f2(x85531)),x85532))+~P1(f335(f335(f244(x85531),x85532),x85534))+~P1(f335(f335(f244(x85531),f2(x85531)),x85535))+P1(f335(f335(f244(x85531),f335(f335(f299(x85531),x85532),x85533)),f335(f335(f299(x85531),x85534),x85535))) % 186.01/186.04 [8554]~P69(x85541)+~P1(f335(f335(f243(x85541),x85542),x85544))+~P1(f335(f335(f244(x85541),x85545),x85543))+~P1(f335(f335(f244(x85541),f2(x85541)),x85545))+~P1(f335(f335(f244(x85541),f2(x85541)),x85542))+P1(f335(f335(f244(x85541),f335(f335(f299(x85541),x85542),x85543)),f335(f335(f299(x85541),x85544),x85545))) % 186.01/186.04 [9941]~P88(x99415)+~P76(x99415)+E(x99411,f195(f934(x99412,a922)))+~P1(f335(f67(x99412),x99411))+P1(f335(f335(f337(x99412),f551(x99413,x99414,x99411,x99412,x99415)),x99411))+P1(f335(f335(f244(x99415),f335(f335(f6(x99412,x99415),x99414),x99411)),f335(f335(f6(x99412,x99415),x99413),x99411))) % 186.01/186.04 [10052]~P86(x100521)+~P76(x100521)+~P1(f335(f67(x100522),x100525))+~P1(f335(f335(f243(x100521),f2(x100521)),f335(x100523,f429(x100523,x100524,x100525,x100522,x100521))))+P1(f335(f335(f243(x100521),f335(f335(f6(x100522,x100521),x100523),x100524)),f335(f335(f6(x100522,x100521),x100523),x100525)))+~P1(f335(f335(f243(f934(x100522,a922)),x100524),x100525)) % 186.01/186.04 [10225]~P88(x102253)+~P76(x102253)+E(x102251,f195(f934(x102252,a922)))+~P1(f335(f67(x102252),x102251))+~P1(f335(f335(f244(x102253),f335(x102254,f551(x102255,x102254,x102251,x102252,x102253))),f335(x102255,f551(x102255,x102254,x102251,x102252,x102253))))+P1(f335(f335(f244(x102253),f335(f335(f6(x102252,x102253),x102254),x102251)),f335(f335(f6(x102252,x102253),x102255),x102251))) % 186.01/186.04 [7288]~P18(x72882,x72885,x72884)+E(x72881,f195(f934(x72882,a922)))+E(x72883,f195(f934(x72882,a922)))+~P1(f335(f67(x72882),x72881))+~P1(f335(f67(x72882),x72883))+E(f335(x72884,f335(f335(f117(f934(x72882,a922)),x72883),x72881)),f335(f335(x72885,f335(x72884,x72883)),f335(x72884,x72881))) % 186.01/186.04 [7871]~P148(x78711,x78714,x78713)+P1(f335(x78711,x78712))+~P1(f335(f335(f244(a1),x78714),f2(a1)))+~P1(f335(f335(f243(a1),x78715),f2(a1)))+~E(x78713,f335(f335(f86(a1),f335(f335(f87(a1),x78714),x78712)),x78715))+~P1(f335(f335(f244(a1),x78714),x78715)) % 186.01/186.04 [7872]~P147(x78721,x78724,x78723)+P1(f335(x78721,x78722))+~P1(f335(f335(f244(a1),x78724),f2(a1)))+~P1(f335(f335(f243(a1),x78722),f2(a1)))+~E(x78723,f335(f335(f86(a1),f335(f335(f87(a1),x78724),x78725)),x78722))+~P1(f335(f335(f244(a1),x78724),x78722)) % 186.01/186.04 [7913]~P148(x79131,x79134,x79133)+P1(f335(x79131,x79132))+~E(x79133,f335(f335(f86(a1),f335(f335(f87(a1),x79134),x79132)),x79135))+~P1(f335(f335(f243(a1),f2(a1)),x79135))+~P1(f335(f335(f244(a1),f2(a1)),x79134))+~P1(f335(f335(f244(a1),x79135),x79134)) % 186.01/186.04 [7914]~P147(x79141,x79144,x79143)+P1(f335(x79141,x79142))+~E(x79143,f335(f335(f86(a1),f335(f335(f87(a1),x79144),x79145)),x79142))+~P1(f335(f335(f243(a1),f2(a1)),x79142))+~P1(f335(f335(f244(a1),f2(a1)),x79144))+~P1(f335(f335(f244(a1),x79142),x79144)) % 186.01/186.04 [8837]P1(f335(f335(x88371,x88372),x88373))+~P1(f335(f335(x88371,f335(f335(f42(a1),x88374),x88375)),f51(a1,x88374,x88375)))+~P1(f335(f335(f244(a1),x88375),f2(a1)))+~P1(f335(f335(f243(a1),x88373),f2(a1)))+~E(x88374,f335(f335(f86(a1),f335(f335(f87(a1),x88375),x88372)),x88373))+~P1(f335(f335(f244(a1),x88375),x88373)) % 186.01/186.04 [8846]P1(f335(f335(x88461,x88462),x88463))+~P1(f335(f335(x88461,f335(f335(f42(a1),x88464),x88465)),f51(a1,x88464,x88465)))+~E(x88464,f335(f335(f86(a1),f335(f335(f87(a1),x88465),x88462)),x88463))+~P1(f335(f335(f243(a1),f2(a1)),x88463))+~P1(f335(f335(f244(a1),f2(a1)),x88465))+~P1(f335(f335(f244(a1),x88463),x88465)) % 186.01/186.04 [9107]E(x91071,x91072)+~P57(x91073,x91075,x91074)+~P1(f335(f335(f337(x91073),x91072),x91075))+~P1(f335(f335(f337(x91073),x91071),x91075))+P1(f335(f335(f337(f933(x91073,x91073)),f335(f335(f260(x91073,x91073),x91071),x91072)),x91074))+P1(f335(f335(f337(f933(x91073,x91073)),f335(f335(f260(x91073,x91073),x91072),x91071)),x91074)) % 186.01/186.04 [9969]~P86(x99695)+~P76(x99695)+~P1(f335(f67(x99691),x99694))+P1(f335(f335(f243(x99695),f335(f335(f6(x99691,x99695),x99692),x99693)),f335(f335(f6(x99691,x99695),x99692),x99694)))+~P1(f335(f335(f243(f934(x99691,a922)),x99693),x99694))+P1(f335(f335(f337(x99691),f429(x99692,x99693,x99694,x99691,x99695)),f335(f335(f23(f934(x99691,a922)),x99694),x99693))) % 186.01/186.04 [10060]E(x100601,f195(f934(x100602,a922)))+~P1(f335(f67(x100602),x100603))+~P1(f335(f67(x100602),x100601))+P1(f335(f335(f337(f933(f934(x100602,a922),f934(x100602,a922))),f335(f335(f260(f934(x100602,a922),f934(x100602,a922)),x100603),x100601)),f327(x100602,x100604)))+~P1(f335(f335(f337(x100602),x100605),x100601))+~P1(f335(f335(f337(f933(x100602,x100602)),f335(f335(f260(x100602,x100602),f361(x100604,x100601,x100603,x100602)),x100605)),x100604)) % 186.01/186.04 [10061]E(x100611,f195(f934(x100612,a922)))+~P1(f335(f67(x100612),x100613))+~P1(f335(f67(x100612),x100611))+P1(f335(f335(f337(f933(f934(x100612,a922),f934(x100612,a922))),f335(f335(f260(f934(x100612,a922),f934(x100612,a922)),x100613),x100611)),f327(x100612,x100614)))+~P1(f335(f335(f337(x100612),x100615),x100611))+~P1(f335(f335(f337(f933(x100612,x100612)),f335(f335(f260(x100612,x100612),f610(x100614,x100611,x100613,x100612)),x100615)),x100614)) % 186.01/186.04 [10229]~P79(x102291)+~E(f335(f335(f6(x102295,x102291),x102292),x102296),x102294)+~P1(f335(f67(x102295),x102296))+P1(f335(f335(f337(x102295),f492(x102293,x102294,x102292,x102296,x102295,x102291)),x102296))+P1(f335(f335(f243(x102291),f335(x102292,x102293)),x102294))+~P1(f335(f335(f337(x102295),x102293),x102296)) % 186.01/186.04 [10276]~P79(x102761)+~E(f335(f335(f6(x102765,x102761),x102762),x102766),x102764)+~P1(f335(f67(x102765),x102766))+~P1(f335(f335(f337(x102765),x102763),x102766))+~P1(f335(f335(f243(x102761),f2(x102761)),f335(x102762,f492(x102763,x102764,x102762,x102766,x102765,x102761))))+P1(f335(f335(f243(x102761),f335(x102762,x102763)),x102764)) % 186.01/186.04 [10421]~E(x104215,x104218)+~E(x104214,x104217)+~P108(x104211)+~P76(x104212)+E(f335(f335(f6(x104211,x104212),x104213),f335(f310(x104211,x104214),x104215)),f335(f335(f6(x104211,x104212),x104216),f335(f310(x104211,x104217),x104218)))+P1(f335(f335(f243(x104211),x104214),f646(x104213,x104216,x104215,x104218,x104214,x104217,x104211,x104212))) % 186.01/186.04 [10437]~E(x104377,x104374)+~E(x104378,x104375)+~P108(x104371)+~P76(x104372)+~E(f335(x104373,f646(x104376,x104373,x104378,x104375,x104377,x104374,x104371,x104372)),f335(x104376,f646(x104376,x104373,x104378,x104375,x104377,x104374,x104371,x104372)))+E(f335(f335(f6(x104371,x104372),x104373),f335(f310(x104371,x104374),x104375)),f335(f335(f6(x104371,x104372),x104376),f335(f310(x104371,x104377),x104378))) % 186.01/186.04 [10440]~E(x104404,x104407)+~E(x104405,x104408)+~P108(x104401)+~P76(x104402)+E(f335(f335(f6(x104401,x104402),x104403),f335(f310(x104401,x104404),x104405)),f335(f335(f6(x104401,x104402),x104406),f335(f310(x104401,x104407),x104408)))+P1(f335(f335(f244(x104401),f646(x104403,x104406,x104405,x104408,x104404,x104407,x104401,x104402)),x104405)) % 186.01/186.04 [10067]~P9(x100675,x100679,x100676)+~P9(x100671,x1006710,x100673)+~P13(x100671,x100675,f934(x100672,a922),x100673,x100676,x100678)+~P1(f335(f335(f337(x100675),x100677),x100679))+~P1(f335(f335(f337(x100671),x100674),x1006710))+E(f335(f335(f45(x100671,f934(x100672,a922)),f335(f293(x100671,x100671,x100673),f335(f335(f317(x100671),x100674),f195(f934(x100671,a922))))),f335(f335(f8(f934(x100675,f934(x100672,a922)),f934(x100672,a922),x100671),f335(f45(x100675,f934(x100672,a922)),f335(f293(x100675,x100675,x100676),f335(f335(f317(x100675),x100677),f195(f934(x100675,a922)))))),x100678)),f335(f335(x100678,x100674),x100677)) % 186.01/186.04 [5835]~P109(x58353)+~P14(x58353,x58352)+~P14(x58353,x58351)+E(x58351,x58352)+~E(f335(f179(x58353),x58351),f335(f179(x58353),x58352))+~P1(f335(f144(x58353),x58352))+~P1(f335(f144(x58353),x58351)) % 186.01/186.04 [5167]~P129(x51672)+~P130(x51672)+~P144(x51672)+~P117(x51672)+~E(x51673,f2(x51672))+E(x51671,f2(a927))+E(f335(f335(f252(x51672),x51673),x51671),f2(x51672)) % 186.01/186.04 [9367]E(x93671,f2(a927))+~E(x93672,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x93673)),x93671)),f335(f264(a927,a927),x93673)))+P1(f335(f54(x93672,x93671),x93673))+~P1(f335(f335(f243(a927),f335(f264(a927,a927),x93673)),f2(a927)))+~P1(f335(f335(f243(a927),f2(a927)),f335(f264(a927,a927),x93673)))+~P1(f335(f335(f244(a927),x93671),f335(f264(a927,a927),x93673)))+~P1(f335(f335(f244(a927),f335(f264(a927,a927),x93673)),x93671)) % 186.01/186.04 [9375]~E(f335(f259(a927,a927),x93753),f2(a927))+~E(x93751,f335(f335(f86(a927),f335(f335(f87(a927),f335(f259(a927,a927),x93753)),x93752)),f335(f264(a927,a927),x93753)))+P1(f335(f54(x93751,x93752),x93753))+~P1(f335(f335(f243(a927),f335(f264(a927,a927),x93753)),f2(a927)))+~P1(f335(f335(f243(a927),f2(a927)),f335(f264(a927,a927),x93753)))+~P1(f335(f335(f244(a927),x93752),f335(f264(a927,a927),x93753)))+~P1(f335(f335(f244(a927),f335(f264(a927,a927),x93753)),x93752)) % 186.01/186.04 [8219]~P70(x82192)+E(x82191,f195(f934(x82192,a922)))+E(x82193,f195(f934(x82192,a922)))+~P1(f335(f67(x82192),x82191))+~P1(f335(f67(x82192),x82193))+~E(f335(f335(f108(f934(x82192,a922)),x82193),x82191),f195(f934(x82192,a922)))+E(f335(f335(f87(x82192),f335(f69(x82192,f87(x82192)),x82193)),f335(f69(x82192,f87(x82192)),x82191)),f335(f69(x82192,f87(x82192)),f335(f335(f117(f934(x82192,a922)),x82193),x82191))) % 186.01/186.04 [8007]E(x80071,f2(a1))+E(f335(f335(f42(a1),x80072),x80071),x80073)+~P1(f335(f335(f243(a1),x80074),f2(a1)))+~E(x80072,f335(f335(f86(a1),f335(f335(f87(a1),x80071),x80073)),x80074))+~P1(f335(f335(f243(a1),f2(a1)),x80074))+~P1(f335(f335(f244(a1),x80074),x80071))+~P1(f335(f335(f244(a1),x80071),x80074)) % 186.01/186.04 [8015]E(f51(a1,x80152,x80151),x80153)+E(x80151,f2(a1))+~P1(f335(f335(f243(a1),x80153),f2(a1)))+~E(x80152,f335(f335(f86(a1),f335(f335(f87(a1),x80151),x80154)),x80153))+~P1(f335(f335(f243(a1),f2(a1)),x80153))+~P1(f335(f335(f244(a1),x80153),x80151))+~P1(f335(f335(f244(a1),x80151),x80153)) % 186.01/186.04 [7922]~P19(x79222,x79225,x79224)+E(x79221,f195(f934(x79222,a922)))+E(x79223,f195(f934(x79222,a922)))+~P1(f335(f67(x79222),x79221))+~P1(f335(f67(x79222),x79223))+~E(f335(f335(f108(f934(x79222,a922)),x79223),x79221),f195(f934(x79222,a922)))+E(f335(x79224,f335(f335(f117(f934(x79222,a922)),x79223),x79221)),f335(f335(x79225,f335(x79224,x79223)),f335(x79224,x79221))) % 186.01/186.04 [9608]~P26(x96083,x96081,x96085,x96084)+~P26(x96081,x96083,x96086,x96082)+E(f335(f41(x96081),x96082),f335(f41(x96083),x96084))+~P1(f335(f67(x96083),x96084))+~P1(f335(f67(x96081),x96082))+~P1(f335(f335(f243(f934(x96083,a922)),f335(f318(x96081,x96083,x96086),x96082)),x96084))+~P1(f335(f335(f243(f934(x96081,a922)),f335(f318(x96083,x96081,x96085),x96084)),x96082)) % 186.01/186.04 [9552]~P1(f335(f335(f244(a1),f335(f335(f86(a1),f335(f335(f87(a1),x95525),x95521)),x95526)),f2(a1)))+~E(f335(f335(f86(a1),f335(f335(f87(a1),x95523),x95522)),x95524),f335(f335(f86(a1),f335(f335(f87(a1),x95525),x95521)),x95526))+~P1(f335(f335(f243(a1),f2(a1)),x95526))+~P1(f335(f335(f244(a1),f2(a1)),x95525))+~P1(f335(f335(f243(a1),x95525),x95523))+~P1(f335(f335(f244(a1),x95524),x95523))+P1(f335(f335(f243(a1),x95521),x95522)) % 186.01/186.04 [9318]~E(f335(f335(f86(a1),f335(f335(f87(a1),x93183),x93181)),x93184),f335(f335(f86(a1),f335(f335(f87(a1),x93185),x93182)),x93186))+~P1(f335(f335(f243(a1),f2(a1)),x93184))+~P1(f335(f335(f244(a1),f2(a1)),x93185))+~P1(f335(f335(f243(a1),x93185),x93183))+~P1(f335(f335(f244(a1),x93186),x93185))+P1(f335(f335(f243(a1),x93181),x93182))+~P1(f335(f335(f243(a1),f2(a1)),f335(f335(f86(a1),f335(f335(f87(a1),x93185),x93182)),x93186))) % 186.01/186.04 [9492]~P133(x94921)+~E(f335(f335(f86(x94921),x94922),x94924),f84(x94921))+~P1(f335(f335(f243(x94921),x94925),x94926))+~P1(f335(f335(f243(x94921),x94923),x94926))+~P1(f335(f335(f243(x94921),f2(x94921)),x94924))+~P1(f335(f335(f243(x94921),f2(x94921)),x94922))+P1(f335(f335(f243(x94921),f335(f335(f86(x94921),f335(f335(f87(x94921),x94922),x94923)),f335(f335(f87(x94921),x94924),x94925))),x94926)) % 186.01/186.04 [9493]~P134(x94931)+~E(f335(f335(f86(x94931),x94932),x94934),f84(x94931))+~P1(f335(f335(f243(x94931),f2(x94931)),x94934))+~P1(f335(f335(f243(x94931),f2(x94931)),x94932))+~P1(f335(f335(f244(x94931),x94935),x94936))+~P1(f335(f335(f244(x94931),x94933),x94936))+P1(f335(f335(f244(x94931),f335(f335(f86(x94931),f335(f335(f87(x94931),x94932),x94933)),f335(f335(f87(x94931),x94934),x94935))),x94936)) % 186.01/186.04 [10327]~P9(x103277,x103276,x103275)+E(x103271,x103272)+~P12(x103277,f934(x103274,a922),x103275,x103273)+E(f335(x103273,f799(x103271,x103272,x103273,x103274,x103275,x103276,x103277)),f335(x103273,f790(x103271,x103272,x103273,x103274,x103275,x103276,x103277)))+~E(f335(f335(f45(x103277,f934(x103274,a922)),x103271),x103273),f335(f335(f45(x103277,f934(x103274,a922)),x103272),x103273))+~P1(f335(f335(f337(f934(x103277,a922)),x103272),f335(f335(f66(x103277),x103276),x103275)))+~P1(f335(f335(f337(f934(x103277,a922)),x103271),f335(f335(f66(x103277),x103276),x103275))) % 186.01/186.04 [10372]~P9(x103723,x103727,x103726)+E(x103721,x103722)+~P12(x103723,f934(x103725,a922),x103726,x103724)+~E(f335(f335(f45(x103723,f934(x103725,a922)),x103721),x103724),f335(f335(f45(x103723,f934(x103725,a922)),x103722),x103724))+P1(f335(f335(f337(x103723),f790(x103721,x103722,x103724,x103725,x103726,x103727,x103723)),x103727))+~P1(f335(f335(f337(f934(x103723,a922)),x103722),f335(f335(f66(x103723),x103727),x103726)))+~P1(f335(f335(f337(f934(x103723,a922)),x103721),f335(f335(f66(x103723),x103727),x103726))) % 186.01/186.04 [10373]~P9(x103733,x103737,x103736)+E(x103731,x103732)+~P12(x103733,f934(x103735,a922),x103736,x103734)+~E(f335(f335(f45(x103733,f934(x103735,a922)),x103731),x103734),f335(f335(f45(x103733,f934(x103735,a922)),x103732),x103734))+P1(f335(f335(f337(x103733),f799(x103731,x103732,x103734,x103735,x103736,x103737,x103733)),x103737))+~P1(f335(f335(f337(f934(x103733,a922)),x103732),f335(f335(f66(x103733),x103737),x103736)))+~P1(f335(f335(f337(f934(x103733,a922)),x103731),f335(f335(f66(x103733),x103737),x103736))) % 186.01/186.04 [10456]E(x104561,x104562)+~P9(x104563,x104566,x104567)+~P12(x104563,f934(x104564,a922),x104567,x104565)+~E(f335(f335(f45(x104563,f934(x104564,a922)),x104561),x104565),f335(f335(f45(x104563,f934(x104564,a922)),x104562),x104565))+~P1(f335(f335(f337(f933(x104563,x104563)),f335(f335(f260(x104563,x104563),f790(x104561,x104562,x104565,x104564,x104567,x104566,x104563)),f799(x104561,x104562,x104565,x104564,x104567,x104566,x104563))),x104567))+~P1(f335(f335(f337(f934(x104563,a922)),x104562),f335(f335(f66(x104563),x104566),x104567)))+~P1(f335(f335(f337(f934(x104563,a922)),x104561),f335(f335(f66(x104563),x104566),x104567))) % 186.01/186.04 [9317]~P9(x93171,x93177,x93174)+~E(x93175,x93176)+~P1(f335(f335(f337(x93171),x93173),x93176))+~P1(f335(f335(f337(x93171),x93172),x93175))+~P1(f335(f335(f337(f934(x93171,a922)),x93176),f335(f335(f66(x93171),x93177),x93174)))+~P1(f335(f335(f337(f934(x93171,a922)),x93175),f335(f335(f66(x93171),x93177),x93174)))+P1(f335(f335(f337(f933(x93171,x93171)),f335(f335(f260(x93171,x93171),x93172),x93173)),x93174)) % 186.01/186.04 [9451]E(x94511,x94512)+~P9(x94513,x94514,x94515)+~P1(f335(f335(f337(x94513),x94516),x94512))+~P1(f335(f335(f337(x94513),x94517),x94511))+~P1(f335(f335(f337(f934(x94513,a922)),x94512),f335(f335(f66(x94513),x94514),x94515)))+~P1(f335(f335(f337(f934(x94513,a922)),x94511),f335(f335(f66(x94513),x94514),x94515)))+~P1(f335(f335(f337(f933(x94513,x94513)),f335(f335(f260(x94513,x94513),x94517),x94516)),x94515)) % 186.01/186.04 [10483]~P9(x104839,x104838,x104837)+~P9(x104831,x1048311,x1048310)+~P13(x104831,x104839,f934(x104836,a922),x1048310,x104837,x104835)+P1(f335(f335(f337(x104831),f728(x104832,x104833,x104834,x104835,x104836,x104837,x104838,x104839,x1048310,x1048311,x104831)),x1048311))+~P1(f335(f335(f337(f934(x104839,a922)),x104833),f335(f335(f66(x104839),x104838),x104837)))+~P1(f335(f335(f337(f934(x104831,a922)),x104834),f335(f335(f66(x104831),x1048311),x1048310)))+P1(f335(f335(f337(f934(x104836,a922)),f335(f335(f45(x104831,f934(x104836,a922)),x104834),f335(f335(f8(f934(x104839,f934(x104836,a922)),f934(x104836,a922),x104831),f335(f45(x104839,f934(x104836,a922)),x104833)),x104835))),x104832)) % 186.01/186.04 [10484]~P9(x1048411,x1048410,x104849)+~P9(x104841,x104848,x104847)+~P13(x1048411,x104841,f934(x104846,a922),x104849,x104847,x104845)+P1(f335(f335(f337(x104841),f742(x104842,x104843,x104844,x104845,x104846,x104847,x104848,x104841,x104849,x1048410,x1048411)),x104848))+~P1(f335(f335(f337(f934(x1048411,a922)),x104844),f335(f335(f66(x1048411),x1048410),x104849)))+~P1(f335(f335(f337(f934(x104841,a922)),x104843),f335(f335(f66(x104841),x104848),x104847)))+P1(f335(f335(f337(f934(x104846,a922)),f335(f335(f45(x1048411,f934(x104846,a922)),x104844),f335(f335(f8(f934(x104841,f934(x104846,a922)),f934(x104846,a922),x1048411),f335(f45(x104841,f934(x104846,a922)),x104843)),x104845))),x104842)) % 186.01/186.04 [10485]~P9(x104852,x104858,x104859)+~P9(x104854,x1048510,x1048511)+~P13(x104852,x104854,f934(x104851,a922),x104859,x1048511,x104856)+~P1(f335(f335(f337(f934(x104852,a922)),x104853),f335(f335(f66(x104852),x104858),x104859)))+~P1(f335(f335(f337(f934(x104854,a922)),x104855),f335(f335(f66(x104854),x1048510),x1048511)))+~P1(f335(f335(f337(f934(x104851,a922)),f335(f335(x104856,f728(x104857,x104855,x104853,x104856,x104851,x1048511,x1048510,x104854,x104859,x104858,x104852)),f742(x104857,x104855,x104853,x104856,x104851,x1048511,x1048510,x104854,x104859,x104858,x104852))),x104857))+P1(f335(f335(f337(f934(x104851,a922)),f335(f335(f45(x104852,f934(x104851,a922)),x104853),f335(f335(f8(f934(x104854,f934(x104851,a922)),f934(x104851,a922),x104852),f335(f45(x104854,f934(x104851,a922)),x104855)),x104856))),x104857)) % 186.01/186.04 [9353]E(x93531,x93532)+~P109(x93534)+~P26(x93533,x93534,x93535,f335(f335(f117(f934(x93533,a922)),f335(f179(x93533),x93531)),f335(f179(x93533),x93532)))+~E(f335(f179(x93533),x93531),f335(f179(x93533),x93532))+~P14(x93534,f335(f335(f161(x93533,x93534),x93535),x93532))+~P14(x93534,f335(f335(f161(x93533,x93534),x93535),x93531))+~P1(f335(f144(x93534),f335(f335(f161(x93533,x93534),x93535),x93532)))+~P1(f335(f144(x93534),f335(f335(f161(x93533,x93534),x93535),x93531))) % 186.01/186.04 %EqnAxiom % 186.01/186.04 [1]E(x11,x11) % 186.01/186.04 [2]E(x22,x21)+~E(x21,x22) % 186.01/186.04 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 186.01/186.04 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 186.01/186.04 [5]~E(x51,x52)+E(f107(x51),f107(x52)) % 186.01/186.04 [6]~E(x61,x62)+E(f23(x61),f23(x62)) % 186.01/186.04 [7]~E(x71,x72)+E(f195(x71),f195(x72)) % 186.01/186.04 [8]~E(x81,x82)+E(f335(x81,x83),f335(x82,x83)) % 186.01/186.04 [9]~E(x91,x92)+E(f335(x93,x91),f335(x93,x92)) % 186.01/186.04 [10]~E(x101,x102)+E(f108(x101),f108(x102)) % 186.01/186.04 [11]~E(x111,x112)+E(f241(x111),f241(x112)) % 186.01/186.04 [12]~E(x121,x122)+E(f117(x121),f117(x122)) % 186.01/186.04 [13]~E(x131,x132)+E(f242(x131),f242(x132)) % 186.01/186.04 [14]~E(x141,x142)+E(f109(x141),f109(x142)) % 186.01/186.04 [15]~E(x151,x152)+E(f25(x151),f25(x152)) % 186.01/186.04 [16]~E(x161,x162)+E(f30(x161),f30(x162)) % 186.01/186.04 [17]~E(x171,x172)+E(f6(x171,x173),f6(x172,x173)) % 186.01/186.04 [18]~E(x181,x182)+E(f6(x183,x181),f6(x183,x182)) % 186.01/186.04 [19]~E(x191,x192)+E(f90(x191),f90(x192)) % 186.01/186.04 [20]~E(x201,x202)+E(f196(x201),f196(x202)) % 186.01/186.04 [21]~E(x211,x212)+E(f161(x211,x213),f161(x212,x213)) % 186.01/186.04 [22]~E(x221,x222)+E(f161(x223,x221),f161(x223,x222)) % 186.01/186.04 [23]~E(x231,x232)+E(f742(x231,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f742(x232,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 186.01/186.04 [24]~E(x241,x242)+E(f742(x243,x241,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f742(x243,x242,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 186.01/186.04 [25]~E(x251,x252)+E(f742(x253,x254,x251,x255,x256,x257,x258,x259,x2510,x2511,x2512),f742(x253,x254,x252,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 186.01/186.04 [26]~E(x261,x262)+E(f742(x263,x264,x265,x261,x266,x267,x268,x269,x2610,x2611,x2612),f742(x263,x264,x265,x262,x266,x267,x268,x269,x2610,x2611,x2612)) % 186.01/186.04 [27]~E(x271,x272)+E(f742(x273,x274,x275,x276,x271,x277,x278,x279,x2710,x2711,x2712),f742(x273,x274,x275,x276,x272,x277,x278,x279,x2710,x2711,x2712)) % 186.01/186.04 [28]~E(x281,x282)+E(f742(x283,x284,x285,x286,x287,x281,x288,x289,x2810,x2811,x2812),f742(x283,x284,x285,x286,x287,x282,x288,x289,x2810,x2811,x2812)) % 186.01/186.04 [29]~E(x291,x292)+E(f742(x293,x294,x295,x296,x297,x298,x291,x299,x2910,x2911,x2912),f742(x293,x294,x295,x296,x297,x298,x292,x299,x2910,x2911,x2912)) % 186.01/186.04 [30]~E(x301,x302)+E(f742(x303,x304,x305,x306,x307,x308,x309,x301,x3010,x3011,x3012),f742(x303,x304,x305,x306,x307,x308,x309,x302,x3010,x3011,x3012)) % 186.01/186.04 [31]~E(x311,x312)+E(f742(x313,x314,x315,x316,x317,x318,x319,x3110,x311,x3111,x3112),f742(x313,x314,x315,x316,x317,x318,x319,x3110,x312,x3111,x3112)) % 186.01/186.04 [32]~E(x321,x322)+E(f742(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x321,x3212),f742(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x322,x3212)) % 186.01/186.04 [33]~E(x331,x332)+E(f742(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x331),f742(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x332)) % 186.01/186.04 [34]~E(x341,x342)+E(f84(x341),f84(x342)) % 186.01/186.04 [35]~E(x351,x352)+E(f87(x351),f87(x352)) % 186.01/186.04 [36]~E(x361,x362)+E(f728(x361,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f728(x362,x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 186.01/186.04 [37]~E(x371,x372)+E(f728(x373,x371,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f728(x373,x372,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 186.01/186.04 [38]~E(x381,x382)+E(f728(x383,x384,x381,x385,x386,x387,x388,x389,x3810,x3811,x3812),f728(x383,x384,x382,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 186.01/186.04 [39]~E(x391,x392)+E(f728(x393,x394,x395,x391,x396,x397,x398,x399,x3910,x3911,x3912),f728(x393,x394,x395,x392,x396,x397,x398,x399,x3910,x3911,x3912)) % 186.01/186.04 [40]~E(x401,x402)+E(f728(x403,x404,x405,x406,x401,x407,x408,x409,x4010,x4011,x4012),f728(x403,x404,x405,x406,x402,x407,x408,x409,x4010,x4011,x4012)) % 186.01/186.04 [41]~E(x411,x412)+E(f728(x413,x414,x415,x416,x417,x411,x418,x419,x4110,x4111,x4112),f728(x413,x414,x415,x416,x417,x412,x418,x419,x4110,x4111,x4112)) % 186.01/186.04 [42]~E(x421,x422)+E(f728(x423,x424,x425,x426,x427,x428,x421,x429,x4210,x4211,x4212),f728(x423,x424,x425,x426,x427,x428,x422,x429,x4210,x4211,x4212)) % 186.01/186.04 [43]~E(x431,x432)+E(f728(x433,x434,x435,x436,x437,x438,x439,x431,x4310,x4311,x4312),f728(x433,x434,x435,x436,x437,x438,x439,x432,x4310,x4311,x4312)) % 186.01/186.04 [44]~E(x441,x442)+E(f728(x443,x444,x445,x446,x447,x448,x449,x4410,x441,x4411,x4412),f728(x443,x444,x445,x446,x447,x448,x449,x4410,x442,x4411,x4412)) % 186.01/186.04 [45]~E(x451,x452)+E(f728(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x451,x4512),f728(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x452,x4512)) % 186.01/186.04 [46]~E(x461,x462)+E(f728(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x461),f728(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x4612,x462)) % 186.01/186.04 [47]~E(x471,x472)+E(f118(x471),f118(x472)) % 186.01/186.04 [48]~E(x481,x482)+E(f337(x481),f337(x482)) % 186.01/186.04 [49]~E(x491,x492)+E(f934(x491,x493),f934(x492,x493)) % 186.01/186.04 [50]~E(x501,x502)+E(f934(x503,x501),f934(x503,x502)) % 186.01/186.04 [51]~E(x511,x512)+E(f4(x511),f4(x512)) % 186.01/186.04 [52]~E(x521,x522)+E(f262(x521,x523),f262(x522,x523)) % 186.01/186.04 [53]~E(x531,x532)+E(f262(x533,x531),f262(x533,x532)) % 186.01/186.04 [54]~E(x541,x542)+E(f926(x541),f926(x542)) % 186.01/186.04 [55]~E(x551,x552)+E(f931(x551),f931(x552)) % 186.01/186.04 [56]~E(x561,x562)+E(f928(x561),f928(x562)) % 186.01/186.04 [57]~E(x571,x572)+E(f929(x571),f929(x572)) % 186.01/186.04 [58]~E(x581,x582)+E(f33(x581),f33(x582)) % 186.01/186.04 [59]~E(x591,x592)+E(f35(x591),f35(x592)) % 186.01/186.04 [60]~E(x601,x602)+E(f8(x601,x603,x604),f8(x602,x603,x604)) % 186.01/186.04 [61]~E(x611,x612)+E(f8(x613,x611,x614),f8(x613,x612,x614)) % 186.01/186.04 [62]~E(x621,x622)+E(f8(x623,x624,x621),f8(x623,x624,x622)) % 186.01/186.04 [63]~E(x631,x632)+E(f34(x631),f34(x632)) % 186.01/186.04 [64]~E(x641,x642)+E(f144(x641),f144(x642)) % 186.01/186.04 [65]~E(x651,x652)+E(f244(x651),f244(x652)) % 186.01/186.04 [66]~E(x661,x662)+E(f85(x661),f85(x662)) % 186.01/186.04 [67]~E(x671,x672)+E(f243(x671),f243(x672)) % 186.01/186.04 [68]~E(x681,x682)+E(f67(x681),f67(x682)) % 186.01/186.04 [69]~E(x691,x692)+E(f120(x691),f120(x692)) % 186.01/186.04 [70]~E(x701,x702)+E(f110(x701),f110(x702)) % 186.01/186.04 [71]~E(x711,x712)+E(f16(x711,x713),f16(x712,x713)) % 186.01/186.04 [72]~E(x721,x722)+E(f16(x723,x721),f16(x723,x722)) % 186.01/186.04 [73]~E(x731,x732)+E(f66(x731),f66(x732)) % 186.01/186.04 [74]~E(x741,x742)+E(f51(x741,x743,x744),f51(x742,x743,x744)) % 186.01/186.04 [75]~E(x751,x752)+E(f51(x753,x751,x754),f51(x753,x752,x754)) % 186.01/186.04 [76]~E(x761,x762)+E(f51(x763,x764,x761),f51(x763,x764,x762)) % 186.01/186.04 [77]~E(x771,x772)+E(f317(x771),f317(x772)) % 186.01/186.04 [78]~E(x781,x782)+E(f41(x781),f41(x782)) % 186.01/186.04 [79]~E(x791,x792)+E(f9(x791,x793),f9(x792,x793)) % 186.01/186.04 [80]~E(x801,x802)+E(f9(x803,x801),f9(x803,x802)) % 186.01/186.04 [81]~E(x811,x812)+E(f393(x811,x813,x814),f393(x812,x813,x814)) % 186.01/186.04 [82]~E(x821,x822)+E(f393(x823,x821,x824),f393(x823,x822,x824)) % 186.01/186.04 [83]~E(x831,x832)+E(f393(x833,x834,x831),f393(x833,x834,x832)) % 186.01/186.04 [84]~E(x841,x842)+E(f86(x841),f86(x842)) % 186.01/186.04 [85]~E(x851,x852)+E(f250(x851),f250(x852)) % 186.01/186.04 [86]~E(x861,x862)+E(f179(x861),f179(x862)) % 186.01/186.04 [87]~E(x871,x872)+E(f7(x871,x873,x874),f7(x872,x873,x874)) % 186.01/186.04 [88]~E(x881,x882)+E(f7(x883,x881,x884),f7(x883,x882,x884)) % 186.01/186.04 [89]~E(x891,x892)+E(f7(x893,x894,x891),f7(x893,x894,x892)) % 186.01/186.04 [90]~E(x901,x902)+E(f52(x901,x903),f52(x902,x903)) % 186.01/186.04 [91]~E(x911,x912)+E(f52(x913,x911),f52(x913,x912)) % 186.01/186.04 [92]~E(x921,x922)+E(f782(x921,x923,x924),f782(x922,x923,x924)) % 186.01/186.04 [93]~E(x931,x932)+E(f782(x933,x931,x934),f782(x933,x932,x934)) % 186.01/186.04 [94]~E(x941,x942)+E(f782(x943,x944,x941),f782(x943,x944,x942)) % 186.01/186.04 [95]~E(x951,x952)+E(f299(x951),f299(x952)) % 186.01/186.04 [96]~E(x961,x962)+E(f310(x961,x963),f310(x962,x963)) % 186.01/186.04 [97]~E(x971,x972)+E(f310(x973,x971),f310(x973,x972)) % 186.01/186.04 [98]~E(x981,x982)+E(f14(x981,x983),f14(x982,x983)) % 186.01/186.04 [99]~E(x991,x992)+E(f14(x993,x991),f14(x993,x992)) % 186.01/186.04 [100]~E(x1001,x1002)+E(f70(x1001,x1003,x1004),f70(x1002,x1003,x1004)) % 186.01/186.04 [101]~E(x1011,x1012)+E(f70(x1013,x1011,x1014),f70(x1013,x1012,x1014)) % 186.01/186.04 [102]~E(x1021,x1022)+E(f70(x1023,x1024,x1021),f70(x1023,x1024,x1022)) % 186.01/186.04 [103]~E(x1031,x1032)+E(f293(x1031,x1033,x1034),f293(x1032,x1033,x1034)) % 186.01/186.04 [104]~E(x1041,x1042)+E(f293(x1043,x1041,x1044),f293(x1043,x1042,x1044)) % 186.01/186.04 [105]~E(x1051,x1052)+E(f293(x1053,x1054,x1051),f293(x1053,x1054,x1052)) % 186.01/186.04 [106]~E(x1061,x1062)+E(f44(x1061,x1063),f44(x1062,x1063)) % 186.01/186.04 [107]~E(x1071,x1072)+E(f44(x1073,x1071),f44(x1073,x1072)) % 186.01/186.04 [108]~E(x1081,x1082)+E(f145(x1081),f145(x1082)) % 186.01/186.04 [109]~E(x1091,x1092)+E(f753(x1091,x1093),f753(x1092,x1093)) % 186.01/186.04 [110]~E(x1101,x1102)+E(f753(x1103,x1101),f753(x1103,x1102)) % 186.01/186.04 [111]~E(x1111,x1112)+E(f756(x1111,x1113,x1114,x1115,x1116,x1117,x1118,x1119),f756(x1112,x1113,x1114,x1115,x1116,x1117,x1118,x1119)) % 186.01/186.04 [112]~E(x1121,x1122)+E(f756(x1123,x1121,x1124,x1125,x1126,x1127,x1128,x1129),f756(x1123,x1122,x1124,x1125,x1126,x1127,x1128,x1129)) % 186.01/186.04 [113]~E(x1131,x1132)+E(f756(x1133,x1134,x1131,x1135,x1136,x1137,x1138,x1139),f756(x1133,x1134,x1132,x1135,x1136,x1137,x1138,x1139)) % 186.01/186.04 [114]~E(x1141,x1142)+E(f756(x1143,x1144,x1145,x1141,x1146,x1147,x1148,x1149),f756(x1143,x1144,x1145,x1142,x1146,x1147,x1148,x1149)) % 186.01/186.04 [115]~E(x1151,x1152)+E(f756(x1153,x1154,x1155,x1156,x1151,x1157,x1158,x1159),f756(x1153,x1154,x1155,x1156,x1152,x1157,x1158,x1159)) % 186.01/186.04 [116]~E(x1161,x1162)+E(f756(x1163,x1164,x1165,x1166,x1167,x1161,x1168,x1169),f756(x1163,x1164,x1165,x1166,x1167,x1162,x1168,x1169)) % 186.01/186.04 [117]~E(x1171,x1172)+E(f756(x1173,x1174,x1175,x1176,x1177,x1178,x1171,x1179),f756(x1173,x1174,x1175,x1176,x1177,x1178,x1172,x1179)) % 186.01/186.04 [118]~E(x1181,x1182)+E(f756(x1183,x1184,x1185,x1186,x1187,x1188,x1189,x1181),f756(x1183,x1184,x1185,x1186,x1187,x1188,x1189,x1182)) % 186.01/186.04 [119]~E(x1191,x1192)+E(f92(x1191,x1193),f92(x1192,x1193)) % 186.01/186.04 [120]~E(x1201,x1202)+E(f92(x1203,x1201),f92(x1203,x1202)) % 186.01/186.04 [121]~E(x1211,x1212)+E(f158(x1211),f158(x1212)) % 186.01/186.04 [122]~E(x1221,x1222)+E(f171(x1221),f171(x1222)) % 186.01/186.04 [123]~E(x1231,x1232)+E(f933(x1231,x1233),f933(x1232,x1233)) % 186.01/186.04 [124]~E(x1241,x1242)+E(f933(x1243,x1241),f933(x1243,x1242)) % 186.01/186.04 [125]~E(x1251,x1252)+E(f583(x1251,x1253,x1254),f583(x1252,x1253,x1254)) % 186.01/186.04 [126]~E(x1261,x1262)+E(f583(x1263,x1261,x1264),f583(x1263,x1262,x1264)) % 186.01/186.04 [127]~E(x1271,x1272)+E(f583(x1273,x1274,x1271),f583(x1273,x1274,x1272)) % 186.01/186.04 [128]~E(x1281,x1282)+E(f533(x1281,x1283,x1284,x1285),f533(x1282,x1283,x1284,x1285)) % 186.01/186.04 [129]~E(x1291,x1292)+E(f533(x1293,x1291,x1294,x1295),f533(x1293,x1292,x1294,x1295)) % 186.01/186.04 [130]~E(x1301,x1302)+E(f533(x1303,x1304,x1301,x1305),f533(x1303,x1304,x1302,x1305)) % 186.01/186.04 [131]~E(x1311,x1312)+E(f533(x1313,x1314,x1315,x1311),f533(x1313,x1314,x1315,x1312)) % 186.01/186.04 [132]~E(x1321,x1322)+E(f55(x1321,x1323),f55(x1322,x1323)) % 186.01/186.04 [133]~E(x1331,x1332)+E(f55(x1333,x1331),f55(x1333,x1332)) % 186.01/186.04 [134]~E(x1341,x1342)+E(f403(x1341,x1343,x1344,x1345,x1346,x1347),f403(x1342,x1343,x1344,x1345,x1346,x1347)) % 186.01/186.04 [135]~E(x1351,x1352)+E(f403(x1353,x1351,x1354,x1355,x1356,x1357),f403(x1353,x1352,x1354,x1355,x1356,x1357)) % 186.01/186.04 [136]~E(x1361,x1362)+E(f403(x1363,x1364,x1361,x1365,x1366,x1367),f403(x1363,x1364,x1362,x1365,x1366,x1367)) % 186.01/186.04 [137]~E(x1371,x1372)+E(f403(x1373,x1374,x1375,x1371,x1376,x1377),f403(x1373,x1374,x1375,x1372,x1376,x1377)) % 186.01/186.04 [138]~E(x1381,x1382)+E(f403(x1383,x1384,x1385,x1386,x1381,x1387),f403(x1383,x1384,x1385,x1386,x1382,x1387)) % 186.01/186.04 [139]~E(x1391,x1392)+E(f403(x1393,x1394,x1395,x1396,x1397,x1391),f403(x1393,x1394,x1395,x1396,x1397,x1392)) % 186.01/186.04 [140]~E(x1401,x1402)+E(f46(x1401,x1403),f46(x1402,x1403)) % 186.01/186.04 [141]~E(x1411,x1412)+E(f46(x1413,x1411),f46(x1413,x1412)) % 186.01/186.04 [142]~E(x1421,x1422)+E(f43(x1421,x1423),f43(x1422,x1423)) % 186.01/186.04 [143]~E(x1431,x1432)+E(f43(x1433,x1431),f43(x1433,x1432)) % 186.01/186.04 [144]~E(x1441,x1442)+E(f166(x1441,x1443),f166(x1442,x1443)) % 186.01/186.04 [145]~E(x1451,x1452)+E(f166(x1453,x1451),f166(x1453,x1452)) % 186.01/186.04 [146]~E(x1461,x1462)+E(f364(x1461,x1463,x1464),f364(x1462,x1463,x1464)) % 186.01/186.04 [147]~E(x1471,x1472)+E(f364(x1473,x1471,x1474),f364(x1473,x1472,x1474)) % 186.01/186.04 [148]~E(x1481,x1482)+E(f364(x1483,x1484,x1481),f364(x1483,x1484,x1482)) % 186.01/186.04 [149]~E(x1491,x1492)+E(f45(x1491,x1493),f45(x1492,x1493)) % 186.01/186.04 [150]~E(x1501,x1502)+E(f45(x1503,x1501),f45(x1503,x1502)) % 186.01/186.04 [151]~E(x1511,x1512)+E(f11(x1511,x1513,x1514),f11(x1512,x1513,x1514)) % 186.01/186.04 [152]~E(x1521,x1522)+E(f11(x1523,x1521,x1524),f11(x1523,x1522,x1524)) % 186.01/186.04 [153]~E(x1531,x1532)+E(f11(x1533,x1534,x1531),f11(x1533,x1534,x1532)) % 186.01/186.04 [154]~E(x1541,x1542)+E(f175(x1541),f175(x1542)) % 186.01/186.04 [155]~E(x1551,x1552)+E(f251(x1551,x1553,x1554),f251(x1552,x1553,x1554)) % 186.01/186.04 [156]~E(x1561,x1562)+E(f251(x1563,x1561,x1564),f251(x1563,x1562,x1564)) % 186.01/186.04 [157]~E(x1571,x1572)+E(f251(x1573,x1574,x1571),f251(x1573,x1574,x1572)) % 186.01/186.04 [158]~E(x1581,x1582)+E(f259(x1581,x1583),f259(x1582,x1583)) % 186.01/186.04 [159]~E(x1591,x1592)+E(f259(x1593,x1591),f259(x1593,x1592)) % 186.01/186.04 [160]~E(x1601,x1602)+E(f265(x1601,x1603,x1604),f265(x1602,x1603,x1604)) % 186.01/186.04 [161]~E(x1611,x1612)+E(f265(x1613,x1611,x1614),f265(x1613,x1612,x1614)) % 186.01/186.04 [162]~E(x1621,x1622)+E(f265(x1623,x1624,x1621),f265(x1623,x1624,x1622)) % 186.01/186.04 [163]~E(x1631,x1632)+E(f112(x1631),f112(x1632)) % 186.01/186.04 [164]~E(x1641,x1642)+E(f114(x1641),f114(x1642)) % 186.01/186.04 [165]~E(x1651,x1652)+E(f336(x1651),f336(x1652)) % 186.01/186.04 [166]~E(x1661,x1662)+E(f71(x1661,x1663,x1664),f71(x1662,x1663,x1664)) % 186.01/186.04 [167]~E(x1671,x1672)+E(f71(x1673,x1671,x1674),f71(x1673,x1672,x1674)) % 186.01/186.04 [168]~E(x1681,x1682)+E(f71(x1683,x1684,x1681),f71(x1683,x1684,x1682)) % 186.01/186.04 [169]~E(x1691,x1692)+E(f573(x1691),f573(x1692)) % 186.01/186.04 [170]~E(x1701,x1702)+E(f260(x1701,x1703),f260(x1702,x1703)) % 186.01/186.04 [171]~E(x1711,x1712)+E(f260(x1713,x1711),f260(x1713,x1712)) % 186.01/186.04 [172]~E(x1721,x1722)+E(f256(x1721,x1723),f256(x1722,x1723)) % 186.01/186.04 [173]~E(x1731,x1732)+E(f256(x1733,x1731),f256(x1733,x1732)) % 186.01/186.04 [174]~E(x1741,x1742)+E(f249(x1741,x1743),f249(x1742,x1743)) % 186.01/186.04 [175]~E(x1751,x1752)+E(f249(x1753,x1751),f249(x1753,x1752)) % 186.01/186.04 [176]~E(x1761,x1762)+E(f168(x1761,x1763),f168(x1762,x1763)) % 186.01/186.04 [177]~E(x1771,x1772)+E(f168(x1773,x1771),f168(x1773,x1772)) % 186.01/186.04 [178]~E(x1781,x1782)+E(f163(x1781,x1783,x1784,x1785),f163(x1782,x1783,x1784,x1785)) % 186.01/186.04 [179]~E(x1791,x1792)+E(f163(x1793,x1791,x1794,x1795),f163(x1793,x1792,x1794,x1795)) % 186.01/186.04 [180]~E(x1801,x1802)+E(f163(x1803,x1804,x1801,x1805),f163(x1803,x1804,x1802,x1805)) % 186.01/186.04 [181]~E(x1811,x1812)+E(f163(x1813,x1814,x1815,x1811),f163(x1813,x1814,x1815,x1812)) % 186.01/186.04 [182]~E(x1821,x1822)+E(f313(x1821,x1823,x1824),f313(x1822,x1823,x1824)) % 186.01/186.04 [183]~E(x1831,x1832)+E(f313(x1833,x1831,x1834),f313(x1833,x1832,x1834)) % 186.01/186.04 [184]~E(x1841,x1842)+E(f313(x1843,x1844,x1841),f313(x1843,x1844,x1842)) % 186.01/186.04 [185]~E(x1851,x1852)+E(f311(x1851,x1853,x1854),f311(x1852,x1853,x1854)) % 186.01/186.04 [186]~E(x1861,x1862)+E(f311(x1863,x1861,x1864),f311(x1863,x1862,x1864)) % 186.01/186.04 [187]~E(x1871,x1872)+E(f311(x1873,x1874,x1871),f311(x1873,x1874,x1872)) % 186.01/186.04 [188]~E(x1881,x1882)+E(f270(x1881),f270(x1882)) % 186.01/186.04 [189]~E(x1891,x1892)+E(f869(x1891,x1893,x1894),f869(x1892,x1893,x1894)) % 186.01/186.04 [190]~E(x1901,x1902)+E(f869(x1903,x1901,x1904),f869(x1903,x1902,x1904)) % 186.01/186.04 [191]~E(x1911,x1912)+E(f869(x1913,x1914,x1911),f869(x1913,x1914,x1912)) % 186.01/186.04 [192]~E(x1921,x1922)+E(f5(x1921),f5(x1922)) % 186.01/186.04 [193]~E(x1931,x1932)+E(f873(x1931,x1933,x1934),f873(x1932,x1933,x1934)) % 186.01/186.04 [194]~E(x1941,x1942)+E(f873(x1943,x1941,x1944),f873(x1943,x1942,x1944)) % 186.01/186.04 [195]~E(x1951,x1952)+E(f873(x1953,x1954,x1951),f873(x1953,x1954,x1952)) % 186.01/186.04 [196]~E(x1961,x1962)+E(f42(x1961),f42(x1962)) % 186.01/186.04 [197]~E(x1971,x1972)+E(f883(x1971,x1973,x1974,x1975),f883(x1972,x1973,x1974,x1975)) % 186.01/186.04 [198]~E(x1981,x1982)+E(f883(x1983,x1981,x1984,x1985),f883(x1983,x1982,x1984,x1985)) % 186.01/186.04 [199]~E(x1991,x1992)+E(f883(x1993,x1994,x1991,x1995),f883(x1993,x1994,x1992,x1995)) % 186.01/186.04 [200]~E(x2001,x2002)+E(f883(x2003,x2004,x2005,x2001),f883(x2003,x2004,x2005,x2002)) % 186.01/186.04 [201]~E(x2011,x2012)+E(f188(x2011,x2013),f188(x2012,x2013)) % 186.01/186.04 [202]~E(x2021,x2022)+E(f188(x2023,x2021),f188(x2023,x2022)) % 186.01/186.04 [203]~E(x2031,x2032)+E(f372(x2031,x2033),f372(x2032,x2033)) % 186.01/186.04 [204]~E(x2041,x2042)+E(f372(x2043,x2041),f372(x2043,x2042)) % 186.01/186.04 [205]~E(x2051,x2052)+E(f315(x2051,x2053),f315(x2052,x2053)) % 186.01/186.04 [206]~E(x2061,x2062)+E(f315(x2063,x2061),f315(x2063,x2062)) % 186.01/186.04 [207]~E(x2071,x2072)+E(f682(x2071,x2073,x2074),f682(x2072,x2073,x2074)) % 186.01/186.04 [208]~E(x2081,x2082)+E(f682(x2083,x2081,x2084),f682(x2083,x2082,x2084)) % 186.01/186.04 [209]~E(x2091,x2092)+E(f682(x2093,x2094,x2091),f682(x2093,x2094,x2092)) % 186.01/186.04 [210]~E(x2101,x2102)+E(f141(x2101),f141(x2102)) % 186.01/186.04 [211]~E(x2111,x2112)+E(f177(x2111,x2113,x2114),f177(x2112,x2113,x2114)) % 186.01/186.04 [212]~E(x2121,x2122)+E(f177(x2123,x2121,x2124),f177(x2123,x2122,x2124)) % 186.01/186.04 [213]~E(x2131,x2132)+E(f177(x2133,x2134,x2131),f177(x2133,x2134,x2132)) % 186.01/186.04 [214]~E(x2141,x2142)+E(f165(x2141,x2143),f165(x2142,x2143)) % 186.01/186.04 [215]~E(x2151,x2152)+E(f165(x2153,x2151),f165(x2153,x2152)) % 186.01/186.04 [216]~E(x2161,x2162)+E(f143(x2161,x2163),f143(x2162,x2163)) % 186.01/186.04 [217]~E(x2171,x2172)+E(f143(x2173,x2171),f143(x2173,x2172)) % 186.01/186.04 [218]~E(x2181,x2182)+E(f318(x2181,x2183,x2184),f318(x2182,x2183,x2184)) % 186.01/186.04 [219]~E(x2191,x2192)+E(f318(x2193,x2191,x2194),f318(x2193,x2192,x2194)) % 186.01/186.04 [220]~E(x2201,x2202)+E(f318(x2203,x2204,x2201),f318(x2203,x2204,x2202)) % 186.01/186.04 [221]~E(x2211,x2212)+E(f542(x2211,x2213,x2214,x2215,x2216),f542(x2212,x2213,x2214,x2215,x2216)) % 186.01/186.04 [222]~E(x2221,x2222)+E(f542(x2223,x2221,x2224,x2225,x2226),f542(x2223,x2222,x2224,x2225,x2226)) % 186.01/186.04 [223]~E(x2231,x2232)+E(f542(x2233,x2234,x2231,x2235,x2236),f542(x2233,x2234,x2232,x2235,x2236)) % 186.01/186.04 [224]~E(x2241,x2242)+E(f542(x2243,x2244,x2245,x2241,x2246),f542(x2243,x2244,x2245,x2242,x2246)) % 186.01/186.04 [225]~E(x2251,x2252)+E(f542(x2253,x2254,x2255,x2256,x2251),f542(x2253,x2254,x2255,x2256,x2252)) % 186.01/186.04 [226]~E(x2261,x2262)+E(f266(x2261,x2263,x2264,x2265,x2266,x2267),f266(x2262,x2263,x2264,x2265,x2266,x2267)) % 186.01/186.04 [227]~E(x2271,x2272)+E(f266(x2273,x2271,x2274,x2275,x2276,x2277),f266(x2273,x2272,x2274,x2275,x2276,x2277)) % 186.01/186.04 [228]~E(x2281,x2282)+E(f266(x2283,x2284,x2281,x2285,x2286,x2287),f266(x2283,x2284,x2282,x2285,x2286,x2287)) % 186.01/186.04 [229]~E(x2291,x2292)+E(f266(x2293,x2294,x2295,x2291,x2296,x2297),f266(x2293,x2294,x2295,x2292,x2296,x2297)) % 186.01/186.04 [230]~E(x2301,x2302)+E(f266(x2303,x2304,x2305,x2306,x2301,x2307),f266(x2303,x2304,x2305,x2306,x2302,x2307)) % 186.01/186.04 [231]~E(x2311,x2312)+E(f266(x2313,x2314,x2315,x2316,x2317,x2311),f266(x2313,x2314,x2315,x2316,x2317,x2312)) % 186.01/186.04 [232]~E(x2321,x2322)+E(f674(x2321,x2323,x2324,x2325),f674(x2322,x2323,x2324,x2325)) % 186.01/186.04 [233]~E(x2331,x2332)+E(f674(x2333,x2331,x2334,x2335),f674(x2333,x2332,x2334,x2335)) % 186.01/186.04 [234]~E(x2341,x2342)+E(f674(x2343,x2344,x2341,x2345),f674(x2343,x2344,x2342,x2345)) % 186.01/186.04 [235]~E(x2351,x2352)+E(f674(x2353,x2354,x2355,x2351),f674(x2353,x2354,x2355,x2352)) % 186.01/186.04 [236]~E(x2361,x2362)+E(f540(x2361,x2363,x2364,x2365,x2366,x2367,x2368,x2369),f540(x2362,x2363,x2364,x2365,x2366,x2367,x2368,x2369)) % 186.01/186.04 [237]~E(x2371,x2372)+E(f540(x2373,x2371,x2374,x2375,x2376,x2377,x2378,x2379),f540(x2373,x2372,x2374,x2375,x2376,x2377,x2378,x2379)) % 186.01/186.04 [238]~E(x2381,x2382)+E(f540(x2383,x2384,x2381,x2385,x2386,x2387,x2388,x2389),f540(x2383,x2384,x2382,x2385,x2386,x2387,x2388,x2389)) % 186.01/186.04 [239]~E(x2391,x2392)+E(f540(x2393,x2394,x2395,x2391,x2396,x2397,x2398,x2399),f540(x2393,x2394,x2395,x2392,x2396,x2397,x2398,x2399)) % 186.01/186.04 [240]~E(x2401,x2402)+E(f540(x2403,x2404,x2405,x2406,x2401,x2407,x2408,x2409),f540(x2403,x2404,x2405,x2406,x2402,x2407,x2408,x2409)) % 186.01/186.04 [241]~E(x2411,x2412)+E(f540(x2413,x2414,x2415,x2416,x2417,x2411,x2418,x2419),f540(x2413,x2414,x2415,x2416,x2417,x2412,x2418,x2419)) % 186.01/186.04 [242]~E(x2421,x2422)+E(f540(x2423,x2424,x2425,x2426,x2427,x2428,x2421,x2429),f540(x2423,x2424,x2425,x2426,x2427,x2428,x2422,x2429)) % 186.01/186.04 [243]~E(x2431,x2432)+E(f540(x2433,x2434,x2435,x2436,x2437,x2438,x2439,x2431),f540(x2433,x2434,x2435,x2436,x2437,x2438,x2439,x2432)) % 186.01/186.04 [244]~E(x2441,x2442)+E(f752(x2441,x2443),f752(x2442,x2443)) % 186.01/186.04 [245]~E(x2451,x2452)+E(f752(x2453,x2451),f752(x2453,x2452)) % 186.01/186.04 [246]~E(x2461,x2462)+E(f62(x2461),f62(x2462)) % 186.01/186.04 [247]~E(x2471,x2472)+E(f622(x2471,x2473,x2474,x2475,x2476),f622(x2472,x2473,x2474,x2475,x2476)) % 186.01/186.04 [248]~E(x2481,x2482)+E(f622(x2483,x2481,x2484,x2485,x2486),f622(x2483,x2482,x2484,x2485,x2486)) % 186.01/186.04 [249]~E(x2491,x2492)+E(f622(x2493,x2494,x2491,x2495,x2496),f622(x2493,x2494,x2492,x2495,x2496)) % 186.01/186.04 [250]~E(x2501,x2502)+E(f622(x2503,x2504,x2505,x2501,x2506),f622(x2503,x2504,x2505,x2502,x2506)) % 186.01/186.04 [251]~E(x2511,x2512)+E(f622(x2513,x2514,x2515,x2516,x2511),f622(x2513,x2514,x2515,x2516,x2512)) % 186.01/186.04 [252]~E(x2521,x2522)+E(f186(x2521,x2523),f186(x2522,x2523)) % 186.01/186.04 [253]~E(x2531,x2532)+E(f186(x2533,x2531),f186(x2533,x2532)) % 186.01/186.04 [254]~E(x2541,x2542)+E(f319(x2541,x2543,x2544),f319(x2542,x2543,x2544)) % 186.01/186.04 [255]~E(x2551,x2552)+E(f319(x2553,x2551,x2554),f319(x2553,x2552,x2554)) % 186.01/186.04 [256]~E(x2561,x2562)+E(f319(x2563,x2564,x2561),f319(x2563,x2564,x2562)) % 186.01/186.04 [257]~E(x2571,x2572)+E(f146(x2571,x2573),f146(x2572,x2573)) % 186.01/186.04 [258]~E(x2581,x2582)+E(f146(x2583,x2581),f146(x2583,x2582)) % 186.01/186.04 [259]~E(x2591,x2592)+E(f402(x2591,x2593,x2594),f402(x2592,x2593,x2594)) % 186.01/186.04 [260]~E(x2601,x2602)+E(f402(x2603,x2601,x2604),f402(x2603,x2602,x2604)) % 186.01/186.04 [261]~E(x2611,x2612)+E(f402(x2613,x2614,x2611),f402(x2613,x2614,x2612)) % 186.01/186.04 [262]~E(x2621,x2622)+E(f18(x2621,x2623,x2624),f18(x2622,x2623,x2624)) % 186.01/186.04 [263]~E(x2631,x2632)+E(f18(x2633,x2631,x2634),f18(x2633,x2632,x2634)) % 186.01/186.04 [264]~E(x2641,x2642)+E(f18(x2643,x2644,x2641),f18(x2643,x2644,x2642)) % 186.01/186.04 [265]~E(x2651,x2652)+E(f643(x2651,x2653,x2654,x2655,x2656),f643(x2652,x2653,x2654,x2655,x2656)) % 186.01/186.04 [266]~E(x2661,x2662)+E(f643(x2663,x2661,x2664,x2665,x2666),f643(x2663,x2662,x2664,x2665,x2666)) % 186.01/186.04 [267]~E(x2671,x2672)+E(f643(x2673,x2674,x2671,x2675,x2676),f643(x2673,x2674,x2672,x2675,x2676)) % 186.01/186.04 [268]~E(x2681,x2682)+E(f643(x2683,x2684,x2685,x2681,x2686),f643(x2683,x2684,x2685,x2682,x2686)) % 186.01/186.04 [269]~E(x2691,x2692)+E(f643(x2693,x2694,x2695,x2696,x2691),f643(x2693,x2694,x2695,x2696,x2692)) % 186.01/186.04 [270]~E(x2701,x2702)+E(f13(x2701,x2703),f13(x2702,x2703)) % 186.01/186.04 [271]~E(x2711,x2712)+E(f13(x2713,x2711),f13(x2713,x2712)) % 186.01/186.04 [272]~E(x2721,x2722)+E(f788(x2721,x2723,x2724),f788(x2722,x2723,x2724)) % 186.01/186.04 [273]~E(x2731,x2732)+E(f788(x2733,x2731,x2734),f788(x2733,x2732,x2734)) % 186.01/186.04 [274]~E(x2741,x2742)+E(f788(x2743,x2744,x2741),f788(x2743,x2744,x2742)) % 186.01/186.04 [275]~E(x2751,x2752)+E(f661(x2751,x2753,x2754,x2755),f661(x2752,x2753,x2754,x2755)) % 186.01/186.04 [276]~E(x2761,x2762)+E(f661(x2763,x2761,x2764,x2765),f661(x2763,x2762,x2764,x2765)) % 186.01/186.04 [277]~E(x2771,x2772)+E(f661(x2773,x2774,x2771,x2775),f661(x2773,x2774,x2772,x2775)) % 186.01/186.04 [278]~E(x2781,x2782)+E(f661(x2783,x2784,x2785,x2781),f661(x2783,x2784,x2785,x2782)) % 186.01/186.04 [279]~E(x2791,x2792)+E(f297(x2791,x2793,x2794),f297(x2792,x2793,x2794)) % 186.01/186.04 [280]~E(x2801,x2802)+E(f297(x2803,x2801,x2804),f297(x2803,x2802,x2804)) % 186.01/186.04 [281]~E(x2811,x2812)+E(f297(x2813,x2814,x2811),f297(x2813,x2814,x2812)) % 186.01/186.04 [282]~E(x2821,x2822)+E(f327(x2821,x2823),f327(x2822,x2823)) % 186.01/186.04 [283]~E(x2831,x2832)+E(f327(x2833,x2831),f327(x2833,x2832)) % 186.01/186.04 [284]~E(x2841,x2842)+E(f10(x2841,x2843),f10(x2842,x2843)) % 186.01/186.04 [285]~E(x2851,x2852)+E(f10(x2853,x2851),f10(x2853,x2852)) % 186.01/186.04 [286]~E(x2861,x2862)+E(f323(x2861,x2863),f323(x2862,x2863)) % 186.01/186.04 [287]~E(x2871,x2872)+E(f323(x2873,x2871),f323(x2873,x2872)) % 186.01/186.04 [288]~E(x2881,x2882)+E(f672(x2881,x2883,x2884,x2885),f672(x2882,x2883,x2884,x2885)) % 186.01/186.04 [289]~E(x2891,x2892)+E(f672(x2893,x2891,x2894,x2895),f672(x2893,x2892,x2894,x2895)) % 186.01/186.04 [290]~E(x2901,x2902)+E(f672(x2903,x2904,x2901,x2905),f672(x2903,x2904,x2902,x2905)) % 186.01/186.04 [291]~E(x2911,x2912)+E(f672(x2913,x2914,x2915,x2911),f672(x2913,x2914,x2915,x2912)) % 186.01/186.04 [292]~E(x2921,x2922)+E(f224(x2921,x2923),f224(x2922,x2923)) % 186.01/186.04 [293]~E(x2931,x2932)+E(f224(x2933,x2931),f224(x2933,x2932)) % 186.01/186.04 [294]~E(x2941,x2942)+E(f121(x2941,x2943),f121(x2942,x2943)) % 186.01/186.04 [295]~E(x2951,x2952)+E(f121(x2953,x2951),f121(x2953,x2952)) % 186.01/186.04 [296]~E(x2961,x2962)+E(f328(x2961,x2963,x2964,x2965),f328(x2962,x2963,x2964,x2965)) % 186.01/186.04 [297]~E(x2971,x2972)+E(f328(x2973,x2971,x2974,x2975),f328(x2973,x2972,x2974,x2975)) % 186.01/186.04 [298]~E(x2981,x2982)+E(f328(x2983,x2984,x2981,x2985),f328(x2983,x2984,x2982,x2985)) % 186.01/186.04 [299]~E(x2991,x2992)+E(f328(x2993,x2994,x2995,x2991),f328(x2993,x2994,x2995,x2992)) % 186.01/186.04 [300]~E(x3001,x3002)+E(f53(x3001,x3003),f53(x3002,x3003)) % 186.01/186.04 [301]~E(x3011,x3012)+E(f53(x3013,x3011),f53(x3013,x3012)) % 186.01/186.04 [302]~E(x3021,x3022)+E(f159(x3021,x3023),f159(x3022,x3023)) % 186.01/186.04 [303]~E(x3031,x3032)+E(f159(x3033,x3031),f159(x3033,x3032)) % 186.01/186.04 [304]~E(x3041,x3042)+E(f81(x3041),f81(x3042)) % 186.01/186.04 [305]~E(x3051,x3052)+E(f198(x3051),f198(x3052)) % 186.01/186.04 [306]~E(x3061,x3062)+E(f190(x3061,x3063),f190(x3062,x3063)) % 186.01/186.04 [307]~E(x3071,x3072)+E(f190(x3073,x3071),f190(x3073,x3072)) % 186.01/186.04 [308]~E(x3081,x3082)+E(f122(x3081),f122(x3082)) % 186.01/186.04 [309]~E(x3091,x3092)+E(f93(x3091),f93(x3092)) % 186.01/186.04 [310]~E(x3101,x3102)+E(f707(x3101,x3103,x3104,x3105,x3106),f707(x3102,x3103,x3104,x3105,x3106)) % 186.01/186.04 [311]~E(x3111,x3112)+E(f707(x3113,x3111,x3114,x3115,x3116),f707(x3113,x3112,x3114,x3115,x3116)) % 186.01/186.04 [312]~E(x3121,x3122)+E(f707(x3123,x3124,x3121,x3125,x3126),f707(x3123,x3124,x3122,x3125,x3126)) % 186.01/186.04 [313]~E(x3131,x3132)+E(f707(x3133,x3134,x3135,x3131,x3136),f707(x3133,x3134,x3135,x3132,x3136)) % 186.01/186.04 [314]~E(x3141,x3142)+E(f707(x3143,x3144,x3145,x3146,x3141),f707(x3143,x3144,x3145,x3146,x3142)) % 186.01/186.04 [315]~E(x3151,x3152)+E(f264(x3151,x3153),f264(x3152,x3153)) % 186.01/186.04 [316]~E(x3161,x3162)+E(f264(x3163,x3161),f264(x3163,x3162)) % 186.01/186.04 [317]~E(x3171,x3172)+E(f15(x3171,x3173),f15(x3172,x3173)) % 186.01/186.04 [318]~E(x3181,x3182)+E(f15(x3183,x3181),f15(x3183,x3182)) % 186.01/186.04 [319]~E(x3191,x3192)+E(f172(x3191),f172(x3192)) % 186.01/186.04 [320]~E(x3201,x3202)+E(f295(x3201),f295(x3202)) % 186.01/186.04 [321]~E(x3211,x3212)+E(f301(x3211,x3213),f301(x3212,x3213)) % 186.01/186.04 [322]~E(x3221,x3222)+E(f301(x3223,x3221),f301(x3223,x3222)) % 186.01/186.04 [323]~E(x3231,x3232)+E(f99(x3231,x3233,x3234),f99(x3232,x3233,x3234)) % 186.01/186.04 [324]~E(x3241,x3242)+E(f99(x3243,x3241,x3244),f99(x3243,x3242,x3244)) % 186.01/186.04 [325]~E(x3251,x3252)+E(f99(x3253,x3254,x3251),f99(x3253,x3254,x3252)) % 186.01/186.04 [326]~E(x3261,x3262)+E(f861(x3261,x3263,x3264,x3265,x3266,x3267,x3268,x3269),f861(x3262,x3263,x3264,x3265,x3266,x3267,x3268,x3269)) % 186.01/186.04 [327]~E(x3271,x3272)+E(f861(x3273,x3271,x3274,x3275,x3276,x3277,x3278,x3279),f861(x3273,x3272,x3274,x3275,x3276,x3277,x3278,x3279)) % 186.01/186.04 [328]~E(x3281,x3282)+E(f861(x3283,x3284,x3281,x3285,x3286,x3287,x3288,x3289),f861(x3283,x3284,x3282,x3285,x3286,x3287,x3288,x3289)) % 186.01/186.04 [329]~E(x3291,x3292)+E(f861(x3293,x3294,x3295,x3291,x3296,x3297,x3298,x3299),f861(x3293,x3294,x3295,x3292,x3296,x3297,x3298,x3299)) % 186.01/186.04 [330]~E(x3301,x3302)+E(f861(x3303,x3304,x3305,x3306,x3301,x3307,x3308,x3309),f861(x3303,x3304,x3305,x3306,x3302,x3307,x3308,x3309)) % 186.01/186.04 [331]~E(x3311,x3312)+E(f861(x3313,x3314,x3315,x3316,x3317,x3311,x3318,x3319),f861(x3313,x3314,x3315,x3316,x3317,x3312,x3318,x3319)) % 186.01/186.04 [332]~E(x3321,x3322)+E(f861(x3323,x3324,x3325,x3326,x3327,x3328,x3321,x3329),f861(x3323,x3324,x3325,x3326,x3327,x3328,x3322,x3329)) % 186.01/186.04 [333]~E(x3331,x3332)+E(f861(x3333,x3334,x3335,x3336,x3337,x3338,x3339,x3331),f861(x3333,x3334,x3335,x3336,x3337,x3338,x3339,x3332)) % 186.01/186.04 [334]~E(x3341,x3342)+E(f935(x3341,x3343),f935(x3342,x3343)) % 186.01/186.04 [335]~E(x3351,x3352)+E(f935(x3353,x3351),f935(x3353,x3352)) % 186.01/186.04 [336]~E(x3361,x3362)+E(f932(x3361,x3363),f932(x3362,x3363)) % 186.01/186.04 [337]~E(x3371,x3372)+E(f932(x3373,x3371),f932(x3373,x3372)) % 186.01/186.04 [338]~E(x3381,x3382)+E(f174(x3381),f174(x3382)) % 186.01/186.04 [339]~E(x3391,x3392)+E(f294(x3391,x3393),f294(x3392,x3393)) % 186.01/186.04 [340]~E(x3401,x3402)+E(f294(x3403,x3401),f294(x3403,x3402)) % 186.01/186.04 [341]~E(x3411,x3412)+E(f565(x3411,x3413,x3414),f565(x3412,x3413,x3414)) % 186.01/186.04 [342]~E(x3421,x3422)+E(f565(x3423,x3421,x3424),f565(x3423,x3422,x3424)) % 186.01/186.04 [343]~E(x3431,x3432)+E(f565(x3433,x3434,x3431),f565(x3433,x3434,x3432)) % 186.01/186.04 [344]~E(x3441,x3442)+E(f69(x3441,x3443),f69(x3442,x3443)) % 186.01/186.04 [345]~E(x3451,x3452)+E(f69(x3453,x3451),f69(x3453,x3452)) % 186.01/186.04 [346]~E(x3461,x3462)+E(f178(x3461),f178(x3462)) % 186.01/186.04 [347]~E(x3471,x3472)+E(f258(x3471,x3473,x3474),f258(x3472,x3473,x3474)) % 186.01/186.04 [348]~E(x3481,x3482)+E(f258(x3483,x3481,x3484),f258(x3483,x3482,x3484)) % 186.01/186.04 [349]~E(x3491,x3492)+E(f258(x3493,x3494,x3491),f258(x3493,x3494,x3492)) % 186.01/186.04 [350]~E(x3501,x3502)+E(f61(x3501,x3503,x3504),f61(x3502,x3503,x3504)) % 186.01/186.04 [351]~E(x3511,x3512)+E(f61(x3513,x3511,x3514),f61(x3513,x3512,x3514)) % 186.01/186.04 [352]~E(x3521,x3522)+E(f61(x3523,x3524,x3521),f61(x3523,x3524,x3522)) % 186.01/186.04 [353]~E(x3531,x3532)+E(f706(x3531,x3533,x3534,x3535,x3536),f706(x3532,x3533,x3534,x3535,x3536)) % 186.01/186.04 [354]~E(x3541,x3542)+E(f706(x3543,x3541,x3544,x3545,x3546),f706(x3543,x3542,x3544,x3545,x3546)) % 186.01/186.04 [355]~E(x3551,x3552)+E(f706(x3553,x3554,x3551,x3555,x3556),f706(x3553,x3554,x3552,x3555,x3556)) % 186.01/186.04 [356]~E(x3561,x3562)+E(f706(x3563,x3564,x3565,x3561,x3566),f706(x3563,x3564,x3565,x3562,x3566)) % 186.01/186.04 [357]~E(x3571,x3572)+E(f706(x3573,x3574,x3575,x3576,x3571),f706(x3573,x3574,x3575,x3576,x3572)) % 186.01/186.04 [358]~E(x3581,x3582)+E(f103(x3581),f103(x3582)) % 186.01/186.04 [359]~E(x3591,x3592)+E(f74(x3591,x3593,x3594),f74(x3592,x3593,x3594)) % 186.01/186.04 [360]~E(x3601,x3602)+E(f74(x3603,x3601,x3604),f74(x3603,x3602,x3604)) % 186.01/186.04 [361]~E(x3611,x3612)+E(f74(x3613,x3614,x3611),f74(x3613,x3614,x3612)) % 186.01/186.04 [362]~E(x3621,x3622)+E(f78(x3621,x3623,x3624,x3625),f78(x3622,x3623,x3624,x3625)) % 186.01/186.04 [363]~E(x3631,x3632)+E(f78(x3633,x3631,x3634,x3635),f78(x3633,x3632,x3634,x3635)) % 186.01/186.04 [364]~E(x3641,x3642)+E(f78(x3643,x3644,x3641,x3645),f78(x3643,x3644,x3642,x3645)) % 186.01/186.04 [365]~E(x3651,x3652)+E(f78(x3653,x3654,x3655,x3651),f78(x3653,x3654,x3655,x3652)) % 186.01/186.04 [366]~E(x3661,x3662)+E(f185(x3661,x3663),f185(x3662,x3663)) % 186.01/186.04 [367]~E(x3671,x3672)+E(f185(x3673,x3671),f185(x3673,x3672)) % 186.01/186.04 [368]~E(x3681,x3682)+E(f478(x3681,x3683,x3684),f478(x3682,x3683,x3684)) % 186.01/186.04 [369]~E(x3691,x3692)+E(f478(x3693,x3691,x3694),f478(x3693,x3692,x3694)) % 186.01/186.04 [370]~E(x3701,x3702)+E(f478(x3703,x3704,x3701),f478(x3703,x3704,x3702)) % 186.01/186.04 [371]~E(x3711,x3712)+E(f252(x3711),f252(x3712)) % 186.01/186.04 [372]~E(x3721,x3722)+E(f229(x3721,x3723,x3724,x3725),f229(x3722,x3723,x3724,x3725)) % 186.01/186.04 [373]~E(x3731,x3732)+E(f229(x3733,x3731,x3734,x3735),f229(x3733,x3732,x3734,x3735)) % 186.01/186.04 [374]~E(x3741,x3742)+E(f229(x3743,x3744,x3741,x3745),f229(x3743,x3744,x3742,x3745)) % 186.01/186.04 [375]~E(x3751,x3752)+E(f229(x3753,x3754,x3755,x3751),f229(x3753,x3754,x3755,x3752)) % 186.01/186.04 [376]~E(x3761,x3762)+E(f182(x3761),f182(x3762)) % 186.01/186.04 [377]~E(x3771,x3772)+E(f27(x3771,x3773),f27(x3772,x3773)) % 186.01/186.04 [378]~E(x3781,x3782)+E(f27(x3783,x3781),f27(x3783,x3782)) % 186.01/186.04 [379]~E(x3791,x3792)+E(f312(x3791),f312(x3792)) % 186.01/186.04 [380]~E(x3801,x3802)+E(f72(x3801,x3803,x3804,x3805,x3806),f72(x3802,x3803,x3804,x3805,x3806)) % 186.01/186.04 [381]~E(x3811,x3812)+E(f72(x3813,x3811,x3814,x3815,x3816),f72(x3813,x3812,x3814,x3815,x3816)) % 186.01/186.04 [382]~E(x3821,x3822)+E(f72(x3823,x3824,x3821,x3825,x3826),f72(x3823,x3824,x3822,x3825,x3826)) % 186.01/186.04 [383]~E(x3831,x3832)+E(f72(x3833,x3834,x3835,x3831,x3836),f72(x3833,x3834,x3835,x3832,x3836)) % 186.01/186.04 [384]~E(x3841,x3842)+E(f72(x3843,x3844,x3845,x3846,x3841),f72(x3843,x3844,x3845,x3846,x3842)) % 186.01/186.04 [385]~E(x3851,x3852)+E(f789(x3851,x3853,x3854,x3855,x3856,x3857),f789(x3852,x3853,x3854,x3855,x3856,x3857)) % 186.01/186.04 [386]~E(x3861,x3862)+E(f789(x3863,x3861,x3864,x3865,x3866,x3867),f789(x3863,x3862,x3864,x3865,x3866,x3867)) % 186.01/186.04 [387]~E(x3871,x3872)+E(f789(x3873,x3874,x3871,x3875,x3876,x3877),f789(x3873,x3874,x3872,x3875,x3876,x3877)) % 186.01/186.04 [388]~E(x3881,x3882)+E(f789(x3883,x3884,x3885,x3881,x3886,x3887),f789(x3883,x3884,x3885,x3882,x3886,x3887)) % 186.01/186.04 [389]~E(x3891,x3892)+E(f789(x3893,x3894,x3895,x3896,x3891,x3897),f789(x3893,x3894,x3895,x3896,x3892,x3897)) % 186.01/186.04 [390]~E(x3901,x3902)+E(f789(x3903,x3904,x3905,x3906,x3907,x3901),f789(x3903,x3904,x3905,x3906,x3907,x3902)) % 186.01/186.04 [391]~E(x3911,x3912)+E(f326(x3911,x3913),f326(x3912,x3913)) % 186.01/186.04 [392]~E(x3921,x3922)+E(f326(x3923,x3921),f326(x3923,x3922)) % 186.01/186.04 [393]~E(x3931,x3932)+E(f80(x3931,x3933,x3934,x3935,x3936),f80(x3932,x3933,x3934,x3935,x3936)) % 186.01/186.04 [394]~E(x3941,x3942)+E(f80(x3943,x3941,x3944,x3945,x3946),f80(x3943,x3942,x3944,x3945,x3946)) % 186.01/186.04 [395]~E(x3951,x3952)+E(f80(x3953,x3954,x3951,x3955,x3956),f80(x3953,x3954,x3952,x3955,x3956)) % 186.01/186.04 [396]~E(x3961,x3962)+E(f80(x3963,x3964,x3965,x3961,x3966),f80(x3963,x3964,x3965,x3962,x3966)) % 186.01/186.04 [397]~E(x3971,x3972)+E(f80(x3973,x3974,x3975,x3976,x3971),f80(x3973,x3974,x3975,x3976,x3972)) % 186.01/186.04 [398]~E(x3981,x3982)+E(f167(x3981,x3983),f167(x3982,x3983)) % 186.01/186.04 [399]~E(x3991,x3992)+E(f167(x3993,x3991),f167(x3993,x3992)) % 186.01/186.04 [400]~E(x4001,x4002)+E(f91(x4001,x4003),f91(x4002,x4003)) % 186.01/186.04 [401]~E(x4011,x4012)+E(f91(x4013,x4011),f91(x4013,x4012)) % 186.01/186.04 [402]~E(x4021,x4022)+E(f149(x4021,x4023,x4024,x4025),f149(x4022,x4023,x4024,x4025)) % 186.01/186.04 [403]~E(x4031,x4032)+E(f149(x4033,x4031,x4034,x4035),f149(x4033,x4032,x4034,x4035)) % 186.01/186.04 [404]~E(x4041,x4042)+E(f149(x4043,x4044,x4041,x4045),f149(x4043,x4044,x4042,x4045)) % 186.01/186.04 [405]~E(x4051,x4052)+E(f149(x4053,x4054,x4055,x4051),f149(x4053,x4054,x4055,x4052)) % 186.01/186.04 [406]~E(x4061,x4062)+E(f860(x4061,x4063,x4064,x4065,x4066,x4067,x4068),f860(x4062,x4063,x4064,x4065,x4066,x4067,x4068)) % 186.01/186.04 [407]~E(x4071,x4072)+E(f860(x4073,x4071,x4074,x4075,x4076,x4077,x4078),f860(x4073,x4072,x4074,x4075,x4076,x4077,x4078)) % 186.01/186.04 [408]~E(x4081,x4082)+E(f860(x4083,x4084,x4081,x4085,x4086,x4087,x4088),f860(x4083,x4084,x4082,x4085,x4086,x4087,x4088)) % 186.01/186.04 [409]~E(x4091,x4092)+E(f860(x4093,x4094,x4095,x4091,x4096,x4097,x4098),f860(x4093,x4094,x4095,x4092,x4096,x4097,x4098)) % 186.01/186.04 [410]~E(x4101,x4102)+E(f860(x4103,x4104,x4105,x4106,x4101,x4107,x4108),f860(x4103,x4104,x4105,x4106,x4102,x4107,x4108)) % 186.01/186.04 [411]~E(x4111,x4112)+E(f860(x4113,x4114,x4115,x4116,x4117,x4111,x4118),f860(x4113,x4114,x4115,x4116,x4117,x4112,x4118)) % 186.01/186.04 [412]~E(x4121,x4122)+E(f860(x4123,x4124,x4125,x4126,x4127,x4128,x4121),f860(x4123,x4124,x4125,x4126,x4127,x4128,x4122)) % 186.01/186.04 [413]~E(x4131,x4132)+E(f809(x4131,x4133,x4134,x4135),f809(x4132,x4133,x4134,x4135)) % 186.01/186.04 [414]~E(x4141,x4142)+E(f809(x4143,x4141,x4144,x4145),f809(x4143,x4142,x4144,x4145)) % 186.01/186.04 [415]~E(x4151,x4152)+E(f809(x4153,x4154,x4151,x4155),f809(x4153,x4154,x4152,x4155)) % 186.01/186.04 [416]~E(x4161,x4162)+E(f809(x4163,x4164,x4165,x4161),f809(x4163,x4164,x4165,x4162)) % 186.01/186.04 [417]~E(x4171,x4172)+E(f874(x4171,x4173,x4174),f874(x4172,x4173,x4174)) % 186.01/186.04 [418]~E(x4181,x4182)+E(f874(x4183,x4181,x4184),f874(x4183,x4182,x4184)) % 186.01/186.04 [419]~E(x4191,x4192)+E(f874(x4193,x4194,x4191),f874(x4193,x4194,x4192)) % 186.01/186.04 [420]~E(x4201,x4202)+E(f123(x4201,x4203,x4204),f123(x4202,x4203,x4204)) % 186.01/186.04 [421]~E(x4211,x4212)+E(f123(x4213,x4211,x4214),f123(x4213,x4212,x4214)) % 186.01/186.04 [422]~E(x4221,x4222)+E(f123(x4223,x4224,x4221),f123(x4223,x4224,x4222)) % 186.01/186.04 [423]~E(x4231,x4232)+E(f710(x4231,x4233,x4234,x4235),f710(x4232,x4233,x4234,x4235)) % 186.01/186.04 [424]~E(x4241,x4242)+E(f710(x4243,x4241,x4244,x4245),f710(x4243,x4242,x4244,x4245)) % 186.01/186.04 [425]~E(x4251,x4252)+E(f710(x4253,x4254,x4251,x4255),f710(x4253,x4254,x4252,x4255)) % 186.01/186.04 [426]~E(x4261,x4262)+E(f710(x4263,x4264,x4265,x4261),f710(x4263,x4264,x4265,x4262)) % 186.01/186.04 [427]~E(x4271,x4272)+E(f275(x4271),f275(x4272)) % 186.01/186.04 [428]~E(x4281,x4282)+E(f133(x4281,x4283,x4284),f133(x4282,x4283,x4284)) % 186.01/186.04 [429]~E(x4291,x4292)+E(f133(x4293,x4291,x4294),f133(x4293,x4292,x4294)) % 186.01/186.04 [430]~E(x4301,x4302)+E(f133(x4303,x4304,x4301),f133(x4303,x4304,x4302)) % 186.01/186.04 [431]~E(x4311,x4312)+E(f754(x4311,x4313),f754(x4312,x4313)) % 186.01/186.04 [432]~E(x4321,x4322)+E(f754(x4323,x4321),f754(x4323,x4322)) % 186.01/186.04 [433]~E(x4331,x4332)+E(f594(x4331,x4333,x4334,x4335),f594(x4332,x4333,x4334,x4335)) % 186.01/186.04 [434]~E(x4341,x4342)+E(f594(x4343,x4341,x4344,x4345),f594(x4343,x4342,x4344,x4345)) % 186.01/186.04 [435]~E(x4351,x4352)+E(f594(x4353,x4354,x4351,x4355),f594(x4353,x4354,x4352,x4355)) % 186.01/186.04 [436]~E(x4361,x4362)+E(f594(x4363,x4364,x4365,x4361),f594(x4363,x4364,x4365,x4362)) % 186.01/186.04 [437]~E(x4371,x4372)+E(f309(x4371),f309(x4372)) % 186.01/186.04 [438]~E(x4381,x4382)+E(f277(x4381,x4383),f277(x4382,x4383)) % 186.01/186.04 [439]~E(x4391,x4392)+E(f277(x4393,x4391),f277(x4393,x4392)) % 186.01/186.04 [440]~E(x4401,x4402)+E(f290(x4401),f290(x4402)) % 186.01/186.04 [441]~E(x4411,x4412)+E(f126(x4411),f126(x4412)) % 186.01/186.04 [442]~E(x4421,x4422)+E(f127(x4421,x4423),f127(x4422,x4423)) % 186.01/186.04 [443]~E(x4431,x4432)+E(f127(x4433,x4431),f127(x4433,x4432)) % 186.01/186.04 [444]~E(x4441,x4442)+E(f810(x4441,x4443,x4444,x4445),f810(x4442,x4443,x4444,x4445)) % 186.01/186.04 [445]~E(x4451,x4452)+E(f810(x4453,x4451,x4454,x4455),f810(x4453,x4452,x4454,x4455)) % 186.01/186.04 [446]~E(x4461,x4462)+E(f810(x4463,x4464,x4461,x4465),f810(x4463,x4464,x4462,x4465)) % 186.01/186.04 [447]~E(x4471,x4472)+E(f810(x4473,x4474,x4475,x4471),f810(x4473,x4474,x4475,x4472)) % 186.01/186.04 [448]~E(x4481,x4482)+E(f257(x4481,x4483,x4484),f257(x4482,x4483,x4484)) % 186.01/186.04 [449]~E(x4491,x4492)+E(f257(x4493,x4491,x4494),f257(x4493,x4492,x4494)) % 186.01/186.04 [450]~E(x4501,x4502)+E(f257(x4503,x4504,x4501),f257(x4503,x4504,x4502)) % 186.01/186.04 [451]~E(x4511,x4512)+E(f316(x4511),f316(x4512)) % 186.01/186.04 [452]~E(x4521,x4522)+E(f655(x4521,x4523,x4524,x4525,x4526),f655(x4522,x4523,x4524,x4525,x4526)) % 186.01/186.04 [453]~E(x4531,x4532)+E(f655(x4533,x4531,x4534,x4535,x4536),f655(x4533,x4532,x4534,x4535,x4536)) % 186.01/186.04 [454]~E(x4541,x4542)+E(f655(x4543,x4544,x4541,x4545,x4546),f655(x4543,x4544,x4542,x4545,x4546)) % 186.01/186.04 [455]~E(x4551,x4552)+E(f655(x4553,x4554,x4555,x4551,x4556),f655(x4553,x4554,x4555,x4552,x4556)) % 186.01/186.04 [456]~E(x4561,x4562)+E(f655(x4563,x4564,x4565,x4566,x4561),f655(x4563,x4564,x4565,x4566,x4562)) % 186.01/186.04 [457]~E(x4571,x4572)+E(f32(x4571,x4573),f32(x4572,x4573)) % 186.01/186.04 [458]~E(x4581,x4582)+E(f32(x4583,x4581),f32(x4583,x4582)) % 186.01/186.04 [459]~E(x4591,x4592)+E(f411(x4591,x4593),f411(x4592,x4593)) % 186.01/186.04 [460]~E(x4601,x4602)+E(f411(x4603,x4601),f411(x4603,x4602)) % 186.01/186.04 [461]~E(x4611,x4612)+E(f96(x4611,x4613),f96(x4612,x4613)) % 186.01/186.04 [462]~E(x4621,x4622)+E(f96(x4623,x4621),f96(x4623,x4622)) % 186.01/186.04 [463]~E(x4631,x4632)+E(f154(x4631,x4633),f154(x4632,x4633)) % 186.01/186.04 [464]~E(x4641,x4642)+E(f154(x4643,x4641),f154(x4643,x4642)) % 186.01/186.04 [465]~E(x4651,x4652)+E(f160(x4651,x4653),f160(x4652,x4653)) % 186.01/186.04 [466]~E(x4661,x4662)+E(f160(x4663,x4661),f160(x4663,x4662)) % 186.01/186.04 [467]~E(x4671,x4672)+E(f271(x4671,x4673),f271(x4672,x4673)) % 186.01/186.04 [468]~E(x4681,x4682)+E(f271(x4683,x4681),f271(x4683,x4682)) % 186.01/186.04 [469]~E(x4691,x4692)+E(f88(x4691,x4693),f88(x4692,x4693)) % 186.01/186.04 [470]~E(x4701,x4702)+E(f88(x4703,x4701),f88(x4703,x4702)) % 186.01/186.04 [471]~E(x4711,x4712)+E(f184(x4711,x4713,x4714),f184(x4712,x4713,x4714)) % 186.01/186.04 [472]~E(x4721,x4722)+E(f184(x4723,x4721,x4724),f184(x4723,x4722,x4724)) % 186.01/186.04 [473]~E(x4731,x4732)+E(f184(x4733,x4734,x4731),f184(x4733,x4734,x4732)) % 186.01/186.04 [474]~E(x4741,x4742)+E(f885(x4741,x4743,x4744,x4745),f885(x4742,x4743,x4744,x4745)) % 186.01/186.04 [475]~E(x4751,x4752)+E(f885(x4753,x4751,x4754,x4755),f885(x4753,x4752,x4754,x4755)) % 186.01/186.04 [476]~E(x4761,x4762)+E(f885(x4763,x4764,x4761,x4765),f885(x4763,x4764,x4762,x4765)) % 186.01/186.04 [477]~E(x4771,x4772)+E(f885(x4773,x4774,x4775,x4771),f885(x4773,x4774,x4775,x4772)) % 186.01/186.04 [478]~E(x4781,x4782)+E(f56(x4781,x4783),f56(x4782,x4783)) % 186.01/186.04 [479]~E(x4791,x4792)+E(f56(x4793,x4791),f56(x4793,x4792)) % 186.01/186.04 [480]~E(x4801,x4802)+E(f232(x4801,x4803,x4804,x4805,x4806),f232(x4802,x4803,x4804,x4805,x4806)) % 186.01/186.04 [481]~E(x4811,x4812)+E(f232(x4813,x4811,x4814,x4815,x4816),f232(x4813,x4812,x4814,x4815,x4816)) % 186.01/186.04 [482]~E(x4821,x4822)+E(f232(x4823,x4824,x4821,x4825,x4826),f232(x4823,x4824,x4822,x4825,x4826)) % 186.01/186.04 [483]~E(x4831,x4832)+E(f232(x4833,x4834,x4835,x4831,x4836),f232(x4833,x4834,x4835,x4832,x4836)) % 186.01/186.04 [484]~E(x4841,x4842)+E(f232(x4843,x4844,x4845,x4846,x4841),f232(x4843,x4844,x4845,x4846,x4842)) % 186.01/186.04 [485]~E(x4851,x4852)+E(f464(x4851),f464(x4852)) % 186.01/186.04 [486]~E(x4861,x4862)+E(f915(x4861,x4863,x4864,x4865),f915(x4862,x4863,x4864,x4865)) % 186.01/186.04 [487]~E(x4871,x4872)+E(f915(x4873,x4871,x4874,x4875),f915(x4873,x4872,x4874,x4875)) % 186.01/186.04 [488]~E(x4881,x4882)+E(f915(x4883,x4884,x4881,x4885),f915(x4883,x4884,x4882,x4885)) % 186.01/186.04 [489]~E(x4891,x4892)+E(f915(x4893,x4894,x4895,x4891),f915(x4893,x4894,x4895,x4892)) % 186.01/186.04 [490]~E(x4901,x4902)+E(f544(x4901,x4903),f544(x4902,x4903)) % 186.01/186.04 [491]~E(x4911,x4912)+E(f544(x4913,x4911),f544(x4913,x4912)) % 186.01/186.04 [492]~E(x4921,x4922)+E(f63(x4921),f63(x4922)) % 186.01/186.04 [493]~E(x4931,x4932)+E(f586(x4931,x4933,x4934),f586(x4932,x4933,x4934)) % 186.01/186.04 [494]~E(x4941,x4942)+E(f586(x4943,x4941,x4944),f586(x4943,x4942,x4944)) % 186.01/186.04 [495]~E(x4951,x4952)+E(f586(x4953,x4954,x4951),f586(x4953,x4954,x4952)) % 186.01/186.04 [496]~E(x4961,x4962)+E(f834(x4961,x4963,x4964,x4965,x4966,x4967),f834(x4962,x4963,x4964,x4965,x4966,x4967)) % 186.01/186.04 [497]~E(x4971,x4972)+E(f834(x4973,x4971,x4974,x4975,x4976,x4977),f834(x4973,x4972,x4974,x4975,x4976,x4977)) % 186.01/186.04 [498]~E(x4981,x4982)+E(f834(x4983,x4984,x4981,x4985,x4986,x4987),f834(x4983,x4984,x4982,x4985,x4986,x4987)) % 186.01/186.04 [499]~E(x4991,x4992)+E(f834(x4993,x4994,x4995,x4991,x4996,x4997),f834(x4993,x4994,x4995,x4992,x4996,x4997)) % 186.01/186.04 [500]~E(x5001,x5002)+E(f834(x5003,x5004,x5005,x5006,x5001,x5007),f834(x5003,x5004,x5005,x5006,x5002,x5007)) % 186.01/186.04 [501]~E(x5011,x5012)+E(f834(x5013,x5014,x5015,x5016,x5017,x5011),f834(x5013,x5014,x5015,x5016,x5017,x5012)) % 186.01/186.04 [502]~E(x5021,x5022)+E(f887(x5021,x5023,x5024,x5025),f887(x5022,x5023,x5024,x5025)) % 186.01/186.04 [503]~E(x5031,x5032)+E(f887(x5033,x5031,x5034,x5035),f887(x5033,x5032,x5034,x5035)) % 186.01/186.04 [504]~E(x5041,x5042)+E(f887(x5043,x5044,x5041,x5045),f887(x5043,x5044,x5042,x5045)) % 186.01/186.04 [505]~E(x5051,x5052)+E(f887(x5053,x5054,x5055,x5051),f887(x5053,x5054,x5055,x5052)) % 186.01/186.04 [506]~E(x5061,x5062)+E(f614(x5061,x5063,x5064),f614(x5062,x5063,x5064)) % 186.01/186.04 [507]~E(x5071,x5072)+E(f614(x5073,x5071,x5074),f614(x5073,x5072,x5074)) % 186.01/186.04 [508]~E(x5081,x5082)+E(f614(x5083,x5084,x5081),f614(x5083,x5084,x5082)) % 186.01/186.04 [509]~E(x5091,x5092)+E(f623(x5091,x5093,x5094,x5095,x5096),f623(x5092,x5093,x5094,x5095,x5096)) % 186.01/186.04 [510]~E(x5101,x5102)+E(f623(x5103,x5101,x5104,x5105,x5106),f623(x5103,x5102,x5104,x5105,x5106)) % 186.01/186.04 [511]~E(x5111,x5112)+E(f623(x5113,x5114,x5111,x5115,x5116),f623(x5113,x5114,x5112,x5115,x5116)) % 186.01/186.04 [512]~E(x5121,x5122)+E(f623(x5123,x5124,x5125,x5121,x5126),f623(x5123,x5124,x5125,x5122,x5126)) % 186.01/186.04 [513]~E(x5131,x5132)+E(f623(x5133,x5134,x5135,x5136,x5131),f623(x5133,x5134,x5135,x5136,x5132)) % 186.01/186.04 [514]~E(x5141,x5142)+E(f684(x5141,x5143,x5144,x5145),f684(x5142,x5143,x5144,x5145)) % 186.01/186.04 [515]~E(x5151,x5152)+E(f684(x5153,x5151,x5154,x5155),f684(x5153,x5152,x5154,x5155)) % 186.01/186.04 [516]~E(x5161,x5162)+E(f684(x5163,x5164,x5161,x5165),f684(x5163,x5164,x5162,x5165)) % 186.01/186.04 [517]~E(x5171,x5172)+E(f684(x5173,x5174,x5175,x5171),f684(x5173,x5174,x5175,x5172)) % 186.01/186.04 [518]~E(x5181,x5182)+E(f521(x5181,x5183),f521(x5182,x5183)) % 186.01/186.04 [519]~E(x5191,x5192)+E(f521(x5193,x5191),f521(x5193,x5192)) % 186.01/186.04 [520]~E(x5201,x5202)+E(f397(x5201,x5203,x5204),f397(x5202,x5203,x5204)) % 186.01/186.04 [521]~E(x5211,x5212)+E(f397(x5213,x5211,x5214),f397(x5213,x5212,x5214)) % 186.01/186.04 [522]~E(x5221,x5222)+E(f397(x5223,x5224,x5221),f397(x5223,x5224,x5222)) % 186.01/186.04 [523]~E(x5231,x5232)+E(f392(x5231,x5233,x5234),f392(x5232,x5233,x5234)) % 186.01/186.04 [524]~E(x5241,x5242)+E(f392(x5243,x5241,x5244),f392(x5243,x5242,x5244)) % 186.01/186.04 [525]~E(x5251,x5252)+E(f392(x5253,x5254,x5251),f392(x5253,x5254,x5252)) % 186.01/186.04 [526]~E(x5261,x5262)+E(f183(x5261,x5263,x5264),f183(x5262,x5263,x5264)) % 186.01/186.04 [527]~E(x5271,x5272)+E(f183(x5273,x5271,x5274),f183(x5273,x5272,x5274)) % 186.01/186.04 [528]~E(x5281,x5282)+E(f183(x5283,x5284,x5281),f183(x5283,x5284,x5282)) % 186.01/186.04 [529]~E(x5291,x5292)+E(f484(x5291,x5293,x5294,x5295,x5296),f484(x5292,x5293,x5294,x5295,x5296)) % 186.01/186.04 [530]~E(x5301,x5302)+E(f484(x5303,x5301,x5304,x5305,x5306),f484(x5303,x5302,x5304,x5305,x5306)) % 186.01/186.04 [531]~E(x5311,x5312)+E(f484(x5313,x5314,x5311,x5315,x5316),f484(x5313,x5314,x5312,x5315,x5316)) % 186.01/186.04 [532]~E(x5321,x5322)+E(f484(x5323,x5324,x5325,x5321,x5326),f484(x5323,x5324,x5325,x5322,x5326)) % 186.01/186.04 [533]~E(x5331,x5332)+E(f484(x5333,x5334,x5335,x5336,x5331),f484(x5333,x5334,x5335,x5336,x5332)) % 186.01/186.04 [534]~E(x5341,x5342)+E(f292(x5341,x5343),f292(x5342,x5343)) % 186.01/186.04 [535]~E(x5351,x5352)+E(f292(x5353,x5351),f292(x5353,x5352)) % 186.01/186.04 [536]~E(x5361,x5362)+E(f49(x5361),f49(x5362)) % 186.01/186.04 [537]~E(x5371,x5372)+E(f322(x5371),f322(x5372)) % 186.01/186.04 [538]~E(x5381,x5382)+E(f155(x5381,x5383,x5384),f155(x5382,x5383,x5384)) % 186.01/186.04 [539]~E(x5391,x5392)+E(f155(x5393,x5391,x5394),f155(x5393,x5392,x5394)) % 186.01/186.04 [540]~E(x5401,x5402)+E(f155(x5403,x5404,x5401),f155(x5403,x5404,x5402)) % 186.01/186.04 [541]~E(x5411,x5412)+E(f267(x5411,x5413,x5414,x5415),f267(x5412,x5413,x5414,x5415)) % 186.01/186.04 [542]~E(x5421,x5422)+E(f267(x5423,x5421,x5424,x5425),f267(x5423,x5422,x5424,x5425)) % 186.01/186.04 [543]~E(x5431,x5432)+E(f267(x5433,x5434,x5431,x5435),f267(x5433,x5434,x5432,x5435)) % 186.01/186.04 [544]~E(x5441,x5442)+E(f267(x5443,x5444,x5445,x5441),f267(x5443,x5444,x5445,x5442)) % 186.01/186.04 [545]~E(x5451,x5452)+E(f324(x5451,x5453),f324(x5452,x5453)) % 186.01/186.04 [546]~E(x5461,x5462)+E(f324(x5463,x5461),f324(x5463,x5462)) % 186.01/186.04 [547]~E(x5471,x5472)+E(f785(x5471,x5473,x5474),f785(x5472,x5473,x5474)) % 186.01/186.04 [548]~E(x5481,x5482)+E(f785(x5483,x5481,x5484),f785(x5483,x5482,x5484)) % 186.01/186.04 [549]~E(x5491,x5492)+E(f785(x5493,x5494,x5491),f785(x5493,x5494,x5492)) % 186.01/186.04 [550]~E(x5501,x5502)+E(f437(x5501),f437(x5502)) % 186.01/186.04 [551]~E(x5511,x5512)+E(f365(x5511,x5513,x5514,x5515),f365(x5512,x5513,x5514,x5515)) % 186.01/186.04 [552]~E(x5521,x5522)+E(f365(x5523,x5521,x5524,x5525),f365(x5523,x5522,x5524,x5525)) % 186.01/186.04 [553]~E(x5531,x5532)+E(f365(x5533,x5534,x5531,x5535),f365(x5533,x5534,x5532,x5535)) % 186.01/186.04 [554]~E(x5541,x5542)+E(f365(x5543,x5544,x5545,x5541),f365(x5543,x5544,x5545,x5542)) % 186.01/186.04 [555]~E(x5551,x5552)+E(f851(x5551,x5553,x5554,x5555,x5556),f851(x5552,x5553,x5554,x5555,x5556)) % 186.01/186.04 [556]~E(x5561,x5562)+E(f851(x5563,x5561,x5564,x5565,x5566),f851(x5563,x5562,x5564,x5565,x5566)) % 186.01/186.04 [557]~E(x5571,x5572)+E(f851(x5573,x5574,x5571,x5575,x5576),f851(x5573,x5574,x5572,x5575,x5576)) % 186.01/186.04 [558]~E(x5581,x5582)+E(f851(x5583,x5584,x5585,x5581,x5586),f851(x5583,x5584,x5585,x5582,x5586)) % 186.01/186.04 [559]~E(x5591,x5592)+E(f851(x5593,x5594,x5595,x5596,x5591),f851(x5593,x5594,x5595,x5596,x5592)) % 186.01/186.04 [560]~E(x5601,x5602)+E(f305(x5601,x5603,x5604,x5605,x5606),f305(x5602,x5603,x5604,x5605,x5606)) % 186.01/186.04 [561]~E(x5611,x5612)+E(f305(x5613,x5611,x5614,x5615,x5616),f305(x5613,x5612,x5614,x5615,x5616)) % 186.01/186.04 [562]~E(x5621,x5622)+E(f305(x5623,x5624,x5621,x5625,x5626),f305(x5623,x5624,x5622,x5625,x5626)) % 186.01/186.04 [563]~E(x5631,x5632)+E(f305(x5633,x5634,x5635,x5631,x5636),f305(x5633,x5634,x5635,x5632,x5636)) % 186.01/186.04 [564]~E(x5641,x5642)+E(f305(x5643,x5644,x5645,x5646,x5641),f305(x5643,x5644,x5645,x5646,x5642)) % 186.01/186.04 [565]~E(x5651,x5652)+E(f525(x5651,x5653,x5654,x5655),f525(x5652,x5653,x5654,x5655)) % 186.01/186.04 [566]~E(x5661,x5662)+E(f525(x5663,x5661,x5664,x5665),f525(x5663,x5662,x5664,x5665)) % 186.01/186.04 [567]~E(x5671,x5672)+E(f525(x5673,x5674,x5671,x5675),f525(x5673,x5674,x5672,x5675)) % 186.01/186.04 [568]~E(x5681,x5682)+E(f525(x5683,x5684,x5685,x5681),f525(x5683,x5684,x5685,x5682)) % 186.01/186.04 [569]~E(x5691,x5692)+E(f717(x5691,x5693,x5694,x5695,x5696),f717(x5692,x5693,x5694,x5695,x5696)) % 186.01/186.04 [570]~E(x5701,x5702)+E(f717(x5703,x5701,x5704,x5705,x5706),f717(x5703,x5702,x5704,x5705,x5706)) % 186.01/186.04 [571]~E(x5711,x5712)+E(f717(x5713,x5714,x5711,x5715,x5716),f717(x5713,x5714,x5712,x5715,x5716)) % 186.01/186.04 [572]~E(x5721,x5722)+E(f717(x5723,x5724,x5725,x5721,x5726),f717(x5723,x5724,x5725,x5722,x5726)) % 186.01/186.04 [573]~E(x5731,x5732)+E(f717(x5733,x5734,x5735,x5736,x5731),f717(x5733,x5734,x5735,x5736,x5732)) % 186.01/186.04 [574]~E(x5741,x5742)+E(f97(x5741,x5743,x5744,x5745),f97(x5742,x5743,x5744,x5745)) % 186.01/186.04 [575]~E(x5751,x5752)+E(f97(x5753,x5751,x5754,x5755),f97(x5753,x5752,x5754,x5755)) % 186.01/186.04 [576]~E(x5761,x5762)+E(f97(x5763,x5764,x5761,x5765),f97(x5763,x5764,x5762,x5765)) % 186.01/186.04 [577]~E(x5771,x5772)+E(f97(x5773,x5774,x5775,x5771),f97(x5773,x5774,x5775,x5772)) % 186.01/186.04 [578]~E(x5781,x5782)+E(f12(x5781,x5783,x5784),f12(x5782,x5783,x5784)) % 186.01/186.04 [579]~E(x5791,x5792)+E(f12(x5793,x5791,x5794),f12(x5793,x5792,x5794)) % 186.01/186.04 [580]~E(x5801,x5802)+E(f12(x5803,x5804,x5801),f12(x5803,x5804,x5802)) % 186.01/186.04 [581]~E(x5811,x5812)+E(f551(x5811,x5813,x5814,x5815,x5816),f551(x5812,x5813,x5814,x5815,x5816)) % 186.01/186.04 [582]~E(x5821,x5822)+E(f551(x5823,x5821,x5824,x5825,x5826),f551(x5823,x5822,x5824,x5825,x5826)) % 186.01/186.04 [583]~E(x5831,x5832)+E(f551(x5833,x5834,x5831,x5835,x5836),f551(x5833,x5834,x5832,x5835,x5836)) % 186.01/186.04 [584]~E(x5841,x5842)+E(f551(x5843,x5844,x5845,x5841,x5846),f551(x5843,x5844,x5845,x5842,x5846)) % 186.01/186.04 [585]~E(x5851,x5852)+E(f551(x5853,x5854,x5855,x5856,x5851),f551(x5853,x5854,x5855,x5856,x5852)) % 186.01/186.04 [586]~E(x5861,x5862)+E(f845(x5861,x5863,x5864),f845(x5862,x5863,x5864)) % 186.01/186.04 [587]~E(x5871,x5872)+E(f845(x5873,x5871,x5874),f845(x5873,x5872,x5874)) % 186.01/186.04 [588]~E(x5881,x5882)+E(f845(x5883,x5884,x5881),f845(x5883,x5884,x5882)) % 186.01/186.04 [589]~E(x5891,x5892)+E(f274(x5891,x5893),f274(x5892,x5893)) % 186.01/186.04 [590]~E(x5901,x5902)+E(f274(x5903,x5901),f274(x5903,x5902)) % 186.01/186.04 [591]~E(x5911,x5912)+E(f176(x5911,x5913,x5914),f176(x5912,x5913,x5914)) % 186.01/186.04 [592]~E(x5921,x5922)+E(f176(x5923,x5921,x5924),f176(x5923,x5922,x5924)) % 186.01/186.04 [593]~E(x5931,x5932)+E(f176(x5933,x5934,x5931),f176(x5933,x5934,x5932)) % 186.01/186.04 [594]~E(x5941,x5942)+E(f59(x5941,x5943),f59(x5942,x5943)) % 186.01/186.04 [595]~E(x5951,x5952)+E(f59(x5953,x5951),f59(x5953,x5952)) % 186.01/186.04 [596]~E(x5961,x5962)+E(f489(x5961,x5963,x5964),f489(x5962,x5963,x5964)) % 186.01/186.04 [597]~E(x5971,x5972)+E(f489(x5973,x5971,x5974),f489(x5973,x5972,x5974)) % 186.01/186.04 [598]~E(x5981,x5982)+E(f489(x5983,x5984,x5981),f489(x5983,x5984,x5982)) % 186.01/186.04 [599]~E(x5991,x5992)+E(f272(x5991,x5993),f272(x5992,x5993)) % 186.01/186.04 [600]~E(x6001,x6002)+E(f272(x6003,x6001),f272(x6003,x6002)) % 186.01/186.04 [601]~E(x6011,x6012)+E(f291(x6011),f291(x6012)) % 186.01/186.04 [602]~E(x6021,x6022)+E(f151(x6021,x6023),f151(x6022,x6023)) % 186.01/186.04 [603]~E(x6031,x6032)+E(f151(x6033,x6031),f151(x6033,x6032)) % 186.01/186.04 [604]~E(x6041,x6042)+E(f429(x6041,x6043,x6044,x6045,x6046),f429(x6042,x6043,x6044,x6045,x6046)) % 186.01/186.04 [605]~E(x6051,x6052)+E(f429(x6053,x6051,x6054,x6055,x6056),f429(x6053,x6052,x6054,x6055,x6056)) % 186.01/186.04 [606]~E(x6061,x6062)+E(f429(x6063,x6064,x6061,x6065,x6066),f429(x6063,x6064,x6062,x6065,x6066)) % 186.01/186.04 [607]~E(x6071,x6072)+E(f429(x6073,x6074,x6075,x6071,x6076),f429(x6073,x6074,x6075,x6072,x6076)) % 186.01/186.04 [608]~E(x6081,x6082)+E(f429(x6083,x6084,x6085,x6086,x6081),f429(x6083,x6084,x6085,x6086,x6082)) % 186.01/186.04 [609]~E(x6091,x6092)+E(f54(x6091,x6093),f54(x6092,x6093)) % 186.01/186.04 [610]~E(x6101,x6102)+E(f54(x6103,x6101),f54(x6103,x6102)) % 186.01/186.04 [611]~E(x6111,x6112)+E(f703(x6111,x6113,x6114),f703(x6112,x6113,x6114)) % 186.01/186.04 [612]~E(x6121,x6122)+E(f703(x6123,x6121,x6124),f703(x6123,x6122,x6124)) % 186.01/186.04 [613]~E(x6131,x6132)+E(f703(x6133,x6134,x6131),f703(x6133,x6134,x6132)) % 186.01/186.04 [614]~E(x6141,x6142)+E(f602(x6141,x6143),f602(x6142,x6143)) % 186.01/186.04 [615]~E(x6151,x6152)+E(f602(x6153,x6151),f602(x6153,x6152)) % 186.01/186.04 [616]~E(x6161,x6162)+E(f289(x6161),f289(x6162)) % 186.01/186.04 [617]~E(x6171,x6172)+E(f401(x6171,x6173,x6174),f401(x6172,x6173,x6174)) % 186.01/186.04 [618]~E(x6181,x6182)+E(f401(x6183,x6181,x6184),f401(x6183,x6182,x6184)) % 186.01/186.04 [619]~E(x6191,x6192)+E(f401(x6193,x6194,x6191),f401(x6193,x6194,x6192)) % 186.01/186.04 [620]~E(x6201,x6202)+E(f750(x6201,x6203),f750(x6202,x6203)) % 186.01/186.04 [621]~E(x6211,x6212)+E(f750(x6213,x6211),f750(x6213,x6212)) % 186.01/186.04 [622]~E(x6221,x6222)+E(f639(x6221,x6223,x6224,x6225,x6226),f639(x6222,x6223,x6224,x6225,x6226)) % 186.01/186.04 [623]~E(x6231,x6232)+E(f639(x6233,x6231,x6234,x6235,x6236),f639(x6233,x6232,x6234,x6235,x6236)) % 186.01/186.04 [624]~E(x6241,x6242)+E(f639(x6243,x6244,x6241,x6245,x6246),f639(x6243,x6244,x6242,x6245,x6246)) % 186.01/186.04 [625]~E(x6251,x6252)+E(f639(x6253,x6254,x6255,x6251,x6256),f639(x6253,x6254,x6255,x6252,x6256)) % 186.01/186.04 [626]~E(x6261,x6262)+E(f639(x6263,x6264,x6265,x6266,x6261),f639(x6263,x6264,x6265,x6266,x6262)) % 186.01/186.04 [627]~E(x6271,x6272)+E(f94(x6271),f94(x6272)) % 186.01/186.04 [628]~E(x6281,x6282)+E(f286(x6281),f286(x6282)) % 186.01/186.04 [629]~E(x6291,x6292)+E(f148(x6291),f148(x6292)) % 186.01/186.04 [630]~E(x6301,x6302)+E(f765(x6301,x6303,x6304,x6305,x6306),f765(x6302,x6303,x6304,x6305,x6306)) % 186.01/186.04 [631]~E(x6311,x6312)+E(f765(x6313,x6311,x6314,x6315,x6316),f765(x6313,x6312,x6314,x6315,x6316)) % 186.01/186.04 [632]~E(x6321,x6322)+E(f765(x6323,x6324,x6321,x6325,x6326),f765(x6323,x6324,x6322,x6325,x6326)) % 186.01/186.04 [633]~E(x6331,x6332)+E(f765(x6333,x6334,x6335,x6331,x6336),f765(x6333,x6334,x6335,x6332,x6336)) % 186.01/186.04 [634]~E(x6341,x6342)+E(f765(x6343,x6344,x6345,x6346,x6341),f765(x6343,x6344,x6345,x6346,x6342)) % 186.01/186.04 [635]~E(x6351,x6352)+E(f21(x6351,x6353),f21(x6352,x6353)) % 186.01/186.04 [636]~E(x6361,x6362)+E(f21(x6363,x6361),f21(x6363,x6362)) % 186.01/186.04 [637]~E(x6371,x6372)+E(f650(x6371,x6373,x6374,x6375),f650(x6372,x6373,x6374,x6375)) % 186.01/186.04 [638]~E(x6381,x6382)+E(f650(x6383,x6381,x6384,x6385),f650(x6383,x6382,x6384,x6385)) % 186.01/186.04 [639]~E(x6391,x6392)+E(f650(x6393,x6394,x6391,x6395),f650(x6393,x6394,x6392,x6395)) % 186.01/186.04 [640]~E(x6401,x6402)+E(f650(x6403,x6404,x6405,x6401),f650(x6403,x6404,x6405,x6402)) % 186.01/186.04 [641]~E(x6411,x6412)+E(f686(x6411,x6413,x6414,x6415,x6416),f686(x6412,x6413,x6414,x6415,x6416)) % 186.01/186.04 [642]~E(x6421,x6422)+E(f686(x6423,x6421,x6424,x6425,x6426),f686(x6423,x6422,x6424,x6425,x6426)) % 186.01/186.04 [643]~E(x6431,x6432)+E(f686(x6433,x6434,x6431,x6435,x6436),f686(x6433,x6434,x6432,x6435,x6436)) % 186.01/186.04 [644]~E(x6441,x6442)+E(f686(x6443,x6444,x6445,x6441,x6446),f686(x6443,x6444,x6445,x6442,x6446)) % 186.01/186.04 [645]~E(x6451,x6452)+E(f686(x6453,x6454,x6455,x6456,x6451),f686(x6453,x6454,x6455,x6456,x6452)) % 186.01/186.04 [646]~E(x6461,x6462)+E(f680(x6461,x6463,x6464,x6465,x6466),f680(x6462,x6463,x6464,x6465,x6466)) % 186.01/186.04 [647]~E(x6471,x6472)+E(f680(x6473,x6471,x6474,x6475,x6476),f680(x6473,x6472,x6474,x6475,x6476)) % 186.01/186.04 [648]~E(x6481,x6482)+E(f680(x6483,x6484,x6481,x6485,x6486),f680(x6483,x6484,x6482,x6485,x6486)) % 186.01/186.04 [649]~E(x6491,x6492)+E(f680(x6493,x6494,x6495,x6491,x6496),f680(x6493,x6494,x6495,x6492,x6496)) % 186.01/186.04 [650]~E(x6501,x6502)+E(f680(x6503,x6504,x6505,x6506,x6501),f680(x6503,x6504,x6505,x6506,x6502)) % 186.01/186.04 [651]~E(x6511,x6512)+E(f132(x6511,x6513),f132(x6512,x6513)) % 186.01/186.04 [652]~E(x6521,x6522)+E(f132(x6523,x6521),f132(x6523,x6522)) % 186.01/186.04 [653]~E(x6531,x6532)+E(f867(x6531,x6533,x6534),f867(x6532,x6533,x6534)) % 186.01/186.04 [654]~E(x6541,x6542)+E(f867(x6543,x6541,x6544),f867(x6543,x6542,x6544)) % 186.01/186.04 [655]~E(x6551,x6552)+E(f867(x6553,x6554,x6551),f867(x6553,x6554,x6552)) % 186.01/186.04 [656]~E(x6561,x6562)+E(f607(x6561,x6563,x6564,x6565),f607(x6562,x6563,x6564,x6565)) % 186.01/186.04 [657]~E(x6571,x6572)+E(f607(x6573,x6571,x6574,x6575),f607(x6573,x6572,x6574,x6575)) % 186.01/186.04 [658]~E(x6581,x6582)+E(f607(x6583,x6584,x6581,x6585),f607(x6583,x6584,x6582,x6585)) % 186.01/186.04 [659]~E(x6591,x6592)+E(f607(x6593,x6594,x6595,x6591),f607(x6593,x6594,x6595,x6592)) % 186.01/186.04 [660]~E(x6601,x6602)+E(f848(x6601,x6603,x6604),f848(x6602,x6603,x6604)) % 186.01/186.04 [661]~E(x6611,x6612)+E(f848(x6613,x6611,x6614),f848(x6613,x6612,x6614)) % 186.01/186.04 [662]~E(x6621,x6622)+E(f848(x6623,x6624,x6621),f848(x6623,x6624,x6622)) % 186.01/186.04 [663]~E(x6631,x6632)+E(f531(x6631,x6633),f531(x6632,x6633)) % 186.01/186.04 [664]~E(x6641,x6642)+E(f531(x6643,x6641),f531(x6643,x6642)) % 186.01/186.04 [665]~E(x6651,x6652)+E(f804(x6651),f804(x6652)) % 186.01/186.04 [666]~E(x6661,x6662)+E(f585(x6661,x6663,x6664),f585(x6662,x6663,x6664)) % 186.01/186.04 [667]~E(x6671,x6672)+E(f585(x6673,x6671,x6674),f585(x6673,x6672,x6674)) % 186.01/186.04 [668]~E(x6681,x6682)+E(f585(x6683,x6684,x6681),f585(x6683,x6684,x6682)) % 186.01/186.04 [669]~E(x6691,x6692)+E(f441(x6691),f441(x6692)) % 186.01/186.04 [670]~E(x6701,x6702)+E(f164(x6701,x6703),f164(x6702,x6703)) % 186.01/186.04 [671]~E(x6711,x6712)+E(f164(x6713,x6711),f164(x6713,x6712)) % 186.01/186.04 [672]~E(x6721,x6722)+E(f173(x6721,x6723,x6724),f173(x6722,x6723,x6724)) % 186.01/186.04 [673]~E(x6731,x6732)+E(f173(x6733,x6731,x6734),f173(x6733,x6732,x6734)) % 186.01/186.04 [674]~E(x6741,x6742)+E(f173(x6743,x6744,x6741),f173(x6743,x6744,x6742)) % 186.01/186.04 [675]~E(x6751,x6752)+E(f629(x6751,x6753,x6754),f629(x6752,x6753,x6754)) % 186.01/186.04 [676]~E(x6761,x6762)+E(f629(x6763,x6761,x6764),f629(x6763,x6762,x6764)) % 186.01/186.04 [677]~E(x6771,x6772)+E(f629(x6773,x6774,x6771),f629(x6773,x6774,x6772)) % 186.01/186.04 [678]~E(x6781,x6782)+E(f649(x6781,x6783,x6784,x6785),f649(x6782,x6783,x6784,x6785)) % 186.01/186.04 [679]~E(x6791,x6792)+E(f649(x6793,x6791,x6794,x6795),f649(x6793,x6792,x6794,x6795)) % 186.01/186.04 [680]~E(x6801,x6802)+E(f649(x6803,x6804,x6801,x6805),f649(x6803,x6804,x6802,x6805)) % 186.01/186.04 [681]~E(x6811,x6812)+E(f649(x6813,x6814,x6815,x6811),f649(x6813,x6814,x6815,x6812)) % 186.01/186.04 [682]~E(x6821,x6822)+E(f746(x6821,x6823,x6824,x6825),f746(x6822,x6823,x6824,x6825)) % 186.01/186.04 [683]~E(x6831,x6832)+E(f746(x6833,x6831,x6834,x6835),f746(x6833,x6832,x6834,x6835)) % 186.01/186.04 [684]~E(x6841,x6842)+E(f746(x6843,x6844,x6841,x6845),f746(x6843,x6844,x6842,x6845)) % 186.01/186.04 [685]~E(x6851,x6852)+E(f746(x6853,x6854,x6855,x6851),f746(x6853,x6854,x6855,x6852)) % 186.01/186.04 [686]~E(x6861,x6862)+E(f157(x6861,x6863,x6864,x6865),f157(x6862,x6863,x6864,x6865)) % 186.01/186.04 [687]~E(x6871,x6872)+E(f157(x6873,x6871,x6874,x6875),f157(x6873,x6872,x6874,x6875)) % 186.01/186.04 [688]~E(x6881,x6882)+E(f157(x6883,x6884,x6881,x6885),f157(x6883,x6884,x6882,x6885)) % 186.01/186.04 [689]~E(x6891,x6892)+E(f157(x6893,x6894,x6895,x6891),f157(x6893,x6894,x6895,x6892)) % 186.01/186.04 [690]~E(x6901,x6902)+E(f98(x6901,x6903,x6904,x6905),f98(x6902,x6903,x6904,x6905)) % 186.01/186.04 [691]~E(x6911,x6912)+E(f98(x6913,x6911,x6914,x6915),f98(x6913,x6912,x6914,x6915)) % 186.01/186.04 [692]~E(x6921,x6922)+E(f98(x6923,x6924,x6921,x6925),f98(x6923,x6924,x6922,x6925)) % 186.01/186.04 [693]~E(x6931,x6932)+E(f98(x6933,x6934,x6935,x6931),f98(x6933,x6934,x6935,x6932)) % 186.01/186.04 [694]~E(x6941,x6942)+E(f597(x6941,x6943,x6944,x6945,x6946,x6947),f597(x6942,x6943,x6944,x6945,x6946,x6947)) % 186.01/186.04 [695]~E(x6951,x6952)+E(f597(x6953,x6951,x6954,x6955,x6956,x6957),f597(x6953,x6952,x6954,x6955,x6956,x6957)) % 186.01/186.04 [696]~E(x6961,x6962)+E(f597(x6963,x6964,x6961,x6965,x6966,x6967),f597(x6963,x6964,x6962,x6965,x6966,x6967)) % 186.01/186.04 [697]~E(x6971,x6972)+E(f597(x6973,x6974,x6975,x6971,x6976,x6977),f597(x6973,x6974,x6975,x6972,x6976,x6977)) % 186.01/186.04 [698]~E(x6981,x6982)+E(f597(x6983,x6984,x6985,x6986,x6981,x6987),f597(x6983,x6984,x6985,x6986,x6982,x6987)) % 186.01/186.04 [699]~E(x6991,x6992)+E(f597(x6993,x6994,x6995,x6996,x6997,x6991),f597(x6993,x6994,x6995,x6996,x6997,x6992)) % 186.01/186.04 [700]~E(x7001,x7002)+E(f747(x7001,x7003,x7004,x7005),f747(x7002,x7003,x7004,x7005)) % 186.01/186.04 [701]~E(x7011,x7012)+E(f747(x7013,x7011,x7014,x7015),f747(x7013,x7012,x7014,x7015)) % 186.01/186.04 [702]~E(x7021,x7022)+E(f747(x7023,x7024,x7021,x7025),f747(x7023,x7024,x7022,x7025)) % 186.01/186.04 [703]~E(x7031,x7032)+E(f747(x7033,x7034,x7035,x7031),f747(x7033,x7034,x7035,x7032)) % 186.01/186.04 [704]~E(x7041,x7042)+E(f28(x7041,x7043,x7044),f28(x7042,x7043,x7044)) % 186.01/186.04 [705]~E(x7051,x7052)+E(f28(x7053,x7051,x7054),f28(x7053,x7052,x7054)) % 186.01/186.04 [706]~E(x7061,x7062)+E(f28(x7063,x7064,x7061),f28(x7063,x7064,x7062)) % 186.01/186.04 [707]~E(x7071,x7072)+E(f31(x7071,x7073),f31(x7072,x7073)) % 186.01/186.04 [708]~E(x7081,x7082)+E(f31(x7083,x7081),f31(x7083,x7082)) % 186.01/186.04 [709]~E(x7091,x7092)+E(f73(x7091,x7093,x7094),f73(x7092,x7093,x7094)) % 186.01/186.04 [710]~E(x7101,x7102)+E(f73(x7103,x7101,x7104),f73(x7103,x7102,x7104)) % 186.01/186.04 [711]~E(x7111,x7112)+E(f73(x7113,x7114,x7111),f73(x7113,x7114,x7112)) % 186.01/186.04 [712]~E(x7121,x7122)+E(f850(x7121,x7123,x7124,x7125),f850(x7122,x7123,x7124,x7125)) % 186.01/186.04 [713]~E(x7131,x7132)+E(f850(x7133,x7131,x7134,x7135),f850(x7133,x7132,x7134,x7135)) % 186.01/186.04 [714]~E(x7141,x7142)+E(f850(x7143,x7144,x7141,x7145),f850(x7143,x7144,x7142,x7145)) % 186.01/186.04 [715]~E(x7151,x7152)+E(f850(x7153,x7154,x7155,x7151),f850(x7153,x7154,x7155,x7152)) % 186.01/186.04 [716]~E(x7161,x7162)+E(f814(x7161,x7163,x7164,x7165,x7166,x7167,x7168),f814(x7162,x7163,x7164,x7165,x7166,x7167,x7168)) % 186.01/186.05 [717]~E(x7171,x7172)+E(f814(x7173,x7171,x7174,x7175,x7176,x7177,x7178),f814(x7173,x7172,x7174,x7175,x7176,x7177,x7178)) % 186.01/186.05 [718]~E(x7181,x7182)+E(f814(x7183,x7184,x7181,x7185,x7186,x7187,x7188),f814(x7183,x7184,x7182,x7185,x7186,x7187,x7188)) % 186.01/186.05 [719]~E(x7191,x7192)+E(f814(x7193,x7194,x7195,x7191,x7196,x7197,x7198),f814(x7193,x7194,x7195,x7192,x7196,x7197,x7198)) % 186.01/186.05 [720]~E(x7201,x7202)+E(f814(x7203,x7204,x7205,x7206,x7201,x7207,x7208),f814(x7203,x7204,x7205,x7206,x7202,x7207,x7208)) % 186.01/186.05 [721]~E(x7211,x7212)+E(f814(x7213,x7214,x7215,x7216,x7217,x7211,x7218),f814(x7213,x7214,x7215,x7216,x7217,x7212,x7218)) % 186.01/186.05 [722]~E(x7221,x7222)+E(f814(x7223,x7224,x7225,x7226,x7227,x7228,x7221),f814(x7223,x7224,x7225,x7226,x7227,x7228,x7222)) % 186.01/186.05 [723]~E(x7231,x7232)+E(f253(x7231,x7233,x7234),f253(x7232,x7233,x7234)) % 186.01/186.05 [724]~E(x7241,x7242)+E(f253(x7243,x7241,x7244),f253(x7243,x7242,x7244)) % 186.01/186.05 [725]~E(x7251,x7252)+E(f253(x7253,x7254,x7251),f253(x7253,x7254,x7252)) % 186.01/186.05 [726]~E(x7261,x7262)+E(f529(x7261,x7263),f529(x7262,x7263)) % 186.01/186.05 [727]~E(x7271,x7272)+E(f529(x7273,x7271),f529(x7273,x7272)) % 186.01/186.05 [728]~E(x7281,x7282)+E(f653(x7281,x7283,x7284,x7285,x7286),f653(x7282,x7283,x7284,x7285,x7286)) % 186.01/186.05 [729]~E(x7291,x7292)+E(f653(x7293,x7291,x7294,x7295,x7296),f653(x7293,x7292,x7294,x7295,x7296)) % 186.01/186.05 [730]~E(x7301,x7302)+E(f653(x7303,x7304,x7301,x7305,x7306),f653(x7303,x7304,x7302,x7305,x7306)) % 186.01/186.05 [731]~E(x7311,x7312)+E(f653(x7313,x7314,x7315,x7311,x7316),f653(x7313,x7314,x7315,x7312,x7316)) % 186.01/186.05 [732]~E(x7321,x7322)+E(f653(x7323,x7324,x7325,x7326,x7321),f653(x7323,x7324,x7325,x7326,x7322)) % 186.01/186.05 [733]~E(x7331,x7332)+E(f280(x7331,x7333),f280(x7332,x7333)) % 186.01/186.05 [734]~E(x7341,x7342)+E(f280(x7343,x7341),f280(x7343,x7342)) % 186.01/186.05 [735]~E(x7351,x7352)+E(f449(x7351,x7353,x7354,x7355),f449(x7352,x7353,x7354,x7355)) % 186.01/186.05 [736]~E(x7361,x7362)+E(f449(x7363,x7361,x7364,x7365),f449(x7363,x7362,x7364,x7365)) % 186.01/186.05 [737]~E(x7371,x7372)+E(f449(x7373,x7374,x7371,x7375),f449(x7373,x7374,x7372,x7375)) % 186.01/186.05 [738]~E(x7381,x7382)+E(f449(x7383,x7384,x7385,x7381),f449(x7383,x7384,x7385,x7382)) % 186.01/186.05 [739]~E(x7391,x7392)+E(f679(x7391,x7393,x7394,x7395,x7396),f679(x7392,x7393,x7394,x7395,x7396)) % 186.01/186.05 [740]~E(x7401,x7402)+E(f679(x7403,x7401,x7404,x7405,x7406),f679(x7403,x7402,x7404,x7405,x7406)) % 186.01/186.05 [741]~E(x7411,x7412)+E(f679(x7413,x7414,x7411,x7415,x7416),f679(x7413,x7414,x7412,x7415,x7416)) % 186.01/186.05 [742]~E(x7421,x7422)+E(f679(x7423,x7424,x7425,x7421,x7426),f679(x7423,x7424,x7425,x7422,x7426)) % 186.01/186.05 [743]~E(x7431,x7432)+E(f679(x7433,x7434,x7435,x7436,x7431),f679(x7433,x7434,x7435,x7436,x7432)) % 186.01/186.05 [744]~E(x7441,x7442)+E(f116(x7441),f116(x7442)) % 186.01/186.05 [745]~E(x7451,x7452)+E(f273(x7451,x7453,x7454),f273(x7452,x7453,x7454)) % 186.01/186.05 [746]~E(x7461,x7462)+E(f273(x7463,x7461,x7464),f273(x7463,x7462,x7464)) % 186.01/186.05 [747]~E(x7471,x7472)+E(f273(x7473,x7474,x7471),f273(x7473,x7474,x7472)) % 186.01/186.05 [748]~E(x7481,x7482)+E(f79(x7481,x7483),f79(x7482,x7483)) % 186.01/186.05 [749]~E(x7491,x7492)+E(f79(x7493,x7491),f79(x7493,x7492)) % 186.01/186.05 [750]~E(x7501,x7502)+E(f557(x7501,x7503,x7504),f557(x7502,x7503,x7504)) % 186.01/186.05 [751]~E(x7511,x7512)+E(f557(x7513,x7511,x7514),f557(x7513,x7512,x7514)) % 186.01/186.05 [752]~E(x7521,x7522)+E(f557(x7523,x7524,x7521),f557(x7523,x7524,x7522)) % 186.01/186.05 [753]~E(x7531,x7532)+E(f221(x7531),f221(x7532)) % 186.01/186.05 [754]~E(x7541,x7542)+E(f580(x7541,x7543,x7544),f580(x7542,x7543,x7544)) % 186.01/186.05 [755]~E(x7551,x7552)+E(f580(x7553,x7551,x7554),f580(x7553,x7552,x7554)) % 186.01/186.05 [756]~E(x7561,x7562)+E(f580(x7563,x7564,x7561),f580(x7563,x7564,x7562)) % 186.01/186.05 [757]~E(x7571,x7572)+E(f152(x7571,x7573),f152(x7572,x7573)) % 186.01/186.05 [758]~E(x7581,x7582)+E(f152(x7583,x7581),f152(x7583,x7582)) % 186.01/186.05 [759]~E(x7591,x7592)+E(f735(x7591,x7593,x7594),f735(x7592,x7593,x7594)) % 186.01/186.05 [760]~E(x7601,x7602)+E(f735(x7603,x7601,x7604),f735(x7603,x7602,x7604)) % 186.01/186.05 [761]~E(x7611,x7612)+E(f735(x7613,x7614,x7611),f735(x7613,x7614,x7612)) % 186.01/186.05 [762]~E(x7621,x7622)+E(f374(x7621,x7623),f374(x7622,x7623)) % 186.01/186.05 [763]~E(x7631,x7632)+E(f374(x7633,x7631),f374(x7633,x7632)) % 186.01/186.05 [764]~E(x7641,x7642)+E(f783(x7641,x7643,x7644),f783(x7642,x7643,x7644)) % 186.01/186.05 [765]~E(x7651,x7652)+E(f783(x7653,x7651,x7654),f783(x7653,x7652,x7654)) % 186.01/186.05 [766]~E(x7661,x7662)+E(f783(x7663,x7664,x7661),f783(x7663,x7664,x7662)) % 186.01/186.05 [767]~E(x7671,x7672)+E(f866(x7671,x7673,x7674,x7675,x7676,x7677,x7678,x7679),f866(x7672,x7673,x7674,x7675,x7676,x7677,x7678,x7679)) % 186.01/186.05 [768]~E(x7681,x7682)+E(f866(x7683,x7681,x7684,x7685,x7686,x7687,x7688,x7689),f866(x7683,x7682,x7684,x7685,x7686,x7687,x7688,x7689)) % 186.01/186.05 [769]~E(x7691,x7692)+E(f866(x7693,x7694,x7691,x7695,x7696,x7697,x7698,x7699),f866(x7693,x7694,x7692,x7695,x7696,x7697,x7698,x7699)) % 186.01/186.05 [770]~E(x7701,x7702)+E(f866(x7703,x7704,x7705,x7701,x7706,x7707,x7708,x7709),f866(x7703,x7704,x7705,x7702,x7706,x7707,x7708,x7709)) % 186.01/186.05 [771]~E(x7711,x7712)+E(f866(x7713,x7714,x7715,x7716,x7711,x7717,x7718,x7719),f866(x7713,x7714,x7715,x7716,x7712,x7717,x7718,x7719)) % 186.01/186.05 [772]~E(x7721,x7722)+E(f866(x7723,x7724,x7725,x7726,x7727,x7721,x7728,x7729),f866(x7723,x7724,x7725,x7726,x7727,x7722,x7728,x7729)) % 186.01/186.05 [773]~E(x7731,x7732)+E(f866(x7733,x7734,x7735,x7736,x7737,x7738,x7731,x7739),f866(x7733,x7734,x7735,x7736,x7737,x7738,x7732,x7739)) % 186.01/186.05 [774]~E(x7741,x7742)+E(f866(x7743,x7744,x7745,x7746,x7747,x7748,x7749,x7741),f866(x7743,x7744,x7745,x7746,x7747,x7748,x7749,x7742)) % 186.01/186.05 [775]~E(x7751,x7752)+E(f432(x7751),f432(x7752)) % 186.01/186.05 [776]~E(x7761,x7762)+E(f627(x7761,x7763,x7764,x7765,x7766),f627(x7762,x7763,x7764,x7765,x7766)) % 186.01/186.05 [777]~E(x7771,x7772)+E(f627(x7773,x7771,x7774,x7775,x7776),f627(x7773,x7772,x7774,x7775,x7776)) % 186.01/186.05 [778]~E(x7781,x7782)+E(f627(x7783,x7784,x7781,x7785,x7786),f627(x7783,x7784,x7782,x7785,x7786)) % 186.01/186.05 [779]~E(x7791,x7792)+E(f627(x7793,x7794,x7795,x7791,x7796),f627(x7793,x7794,x7795,x7792,x7796)) % 186.01/186.05 [780]~E(x7801,x7802)+E(f627(x7803,x7804,x7805,x7806,x7801),f627(x7803,x7804,x7805,x7806,x7802)) % 186.01/186.05 [781]~E(x7811,x7812)+E(f321(x7811,x7813,x7814,x7815),f321(x7812,x7813,x7814,x7815)) % 186.01/186.05 [782]~E(x7821,x7822)+E(f321(x7823,x7821,x7824,x7825),f321(x7823,x7822,x7824,x7825)) % 186.01/186.05 [783]~E(x7831,x7832)+E(f321(x7833,x7834,x7831,x7835),f321(x7833,x7834,x7832,x7835)) % 186.01/186.05 [784]~E(x7841,x7842)+E(f321(x7843,x7844,x7845,x7841),f321(x7843,x7844,x7845,x7842)) % 186.01/186.05 [785]~E(x7851,x7852)+E(f881(x7851,x7853,x7854,x7855,x7856,x7857),f881(x7852,x7853,x7854,x7855,x7856,x7857)) % 186.01/186.05 [786]~E(x7861,x7862)+E(f881(x7863,x7861,x7864,x7865,x7866,x7867),f881(x7863,x7862,x7864,x7865,x7866,x7867)) % 186.01/186.05 [787]~E(x7871,x7872)+E(f881(x7873,x7874,x7871,x7875,x7876,x7877),f881(x7873,x7874,x7872,x7875,x7876,x7877)) % 186.01/186.05 [788]~E(x7881,x7882)+E(f881(x7883,x7884,x7885,x7881,x7886,x7887),f881(x7883,x7884,x7885,x7882,x7886,x7887)) % 186.01/186.05 [789]~E(x7891,x7892)+E(f881(x7893,x7894,x7895,x7896,x7891,x7897),f881(x7893,x7894,x7895,x7896,x7892,x7897)) % 186.01/186.05 [790]~E(x7901,x7902)+E(f881(x7903,x7904,x7905,x7906,x7907,x7901),f881(x7903,x7904,x7905,x7906,x7907,x7902)) % 186.01/186.05 [791]~E(x7911,x7912)+E(f445(x7911,x7913),f445(x7912,x7913)) % 186.01/186.05 [792]~E(x7921,x7922)+E(f445(x7923,x7921),f445(x7923,x7922)) % 186.01/186.05 [793]~E(x7931,x7932)+E(f832(x7931),f832(x7932)) % 186.01/186.05 [794]~E(x7941,x7942)+E(f748(x7941,x7943),f748(x7942,x7943)) % 186.01/186.05 [795]~E(x7951,x7952)+E(f748(x7953,x7951),f748(x7953,x7952)) % 186.01/186.05 [796]~E(x7961,x7962)+E(f823(x7961,x7963,x7964,x7965),f823(x7962,x7963,x7964,x7965)) % 186.01/186.05 [797]~E(x7971,x7972)+E(f823(x7973,x7971,x7974,x7975),f823(x7973,x7972,x7974,x7975)) % 186.01/186.05 [798]~E(x7981,x7982)+E(f823(x7983,x7984,x7981,x7985),f823(x7983,x7984,x7982,x7985)) % 186.01/186.05 [799]~E(x7991,x7992)+E(f823(x7993,x7994,x7995,x7991),f823(x7993,x7994,x7995,x7992)) % 186.01/186.05 [800]~E(x8001,x8002)+E(f296(x8001,x8003),f296(x8002,x8003)) % 186.01/186.05 [801]~E(x8011,x8012)+E(f296(x8013,x8011),f296(x8013,x8012)) % 186.01/186.05 [802]~E(x8021,x8022)+E(f829(x8021,x8023),f829(x8022,x8023)) % 186.01/186.05 [803]~E(x8031,x8032)+E(f829(x8033,x8031),f829(x8033,x8032)) % 186.01/186.05 [804]~E(x8041,x8042)+E(f733(x8041,x8043),f733(x8042,x8043)) % 186.01/186.05 [805]~E(x8051,x8052)+E(f733(x8053,x8051),f733(x8053,x8052)) % 186.01/186.05 [806]~E(x8061,x8062)+E(f409(x8061,x8063,x8064,x8065),f409(x8062,x8063,x8064,x8065)) % 186.01/186.05 [807]~E(x8071,x8072)+E(f409(x8073,x8071,x8074,x8075),f409(x8073,x8072,x8074,x8075)) % 186.01/186.05 [808]~E(x8081,x8082)+E(f409(x8083,x8084,x8081,x8085),f409(x8083,x8084,x8082,x8085)) % 186.01/186.05 [809]~E(x8091,x8092)+E(f409(x8093,x8094,x8095,x8091),f409(x8093,x8094,x8095,x8092)) % 186.01/186.05 [810]~E(x8101,x8102)+E(f571(x8101,x8103,x8104,x8105,x8106,x8107,x8108),f571(x8102,x8103,x8104,x8105,x8106,x8107,x8108)) % 186.01/186.05 [811]~E(x8111,x8112)+E(f571(x8113,x8111,x8114,x8115,x8116,x8117,x8118),f571(x8113,x8112,x8114,x8115,x8116,x8117,x8118)) % 186.01/186.05 [812]~E(x8121,x8122)+E(f571(x8123,x8124,x8121,x8125,x8126,x8127,x8128),f571(x8123,x8124,x8122,x8125,x8126,x8127,x8128)) % 186.01/186.05 [813]~E(x8131,x8132)+E(f571(x8133,x8134,x8135,x8131,x8136,x8137,x8138),f571(x8133,x8134,x8135,x8132,x8136,x8137,x8138)) % 186.01/186.05 [814]~E(x8141,x8142)+E(f571(x8143,x8144,x8145,x8146,x8141,x8147,x8148),f571(x8143,x8144,x8145,x8146,x8142,x8147,x8148)) % 186.01/186.05 [815]~E(x8151,x8152)+E(f571(x8153,x8154,x8155,x8156,x8157,x8151,x8158),f571(x8153,x8154,x8155,x8156,x8157,x8152,x8158)) % 186.01/186.05 [816]~E(x8161,x8162)+E(f571(x8163,x8164,x8165,x8166,x8167,x8168,x8161),f571(x8163,x8164,x8165,x8166,x8167,x8168,x8162)) % 186.01/186.05 [817]~E(x8171,x8172)+E(f584(x8171,x8173,x8174),f584(x8172,x8173,x8174)) % 186.01/186.05 [818]~E(x8181,x8182)+E(f584(x8183,x8181,x8184),f584(x8183,x8182,x8184)) % 186.01/186.05 [819]~E(x8191,x8192)+E(f584(x8193,x8194,x8191),f584(x8193,x8194,x8192)) % 186.01/186.05 [820]~E(x8201,x8202)+E(f29(x8201,x8203,x8204),f29(x8202,x8203,x8204)) % 186.01/186.05 [821]~E(x8211,x8212)+E(f29(x8213,x8211,x8214),f29(x8213,x8212,x8214)) % 186.01/186.05 [822]~E(x8221,x8222)+E(f29(x8223,x8224,x8221),f29(x8223,x8224,x8222)) % 186.01/186.05 [823]~E(x8231,x8232)+E(f363(x8231,x8233,x8234),f363(x8232,x8233,x8234)) % 186.01/186.05 [824]~E(x8241,x8242)+E(f363(x8243,x8241,x8244),f363(x8243,x8242,x8244)) % 186.01/186.05 [825]~E(x8251,x8252)+E(f363(x8253,x8254,x8251),f363(x8253,x8254,x8252)) % 186.01/186.05 [826]~E(x8261,x8262)+E(f526(x8261,x8263,x8264,x8265),f526(x8262,x8263,x8264,x8265)) % 186.01/186.05 [827]~E(x8271,x8272)+E(f526(x8273,x8271,x8274,x8275),f526(x8273,x8272,x8274,x8275)) % 186.01/186.05 [828]~E(x8281,x8282)+E(f526(x8283,x8284,x8281,x8285),f526(x8283,x8284,x8282,x8285)) % 186.01/186.05 [829]~E(x8291,x8292)+E(f526(x8293,x8294,x8295,x8291),f526(x8293,x8294,x8295,x8292)) % 186.01/186.05 [830]~E(x8301,x8302)+E(f683(x8301,x8303,x8304),f683(x8302,x8303,x8304)) % 186.01/186.05 [831]~E(x8311,x8312)+E(f683(x8313,x8311,x8314),f683(x8313,x8312,x8314)) % 186.01/186.05 [832]~E(x8321,x8322)+E(f683(x8323,x8324,x8321),f683(x8323,x8324,x8322)) % 186.01/186.05 [833]~E(x8331,x8332)+E(f214(x8331,x8333,x8334,x8335),f214(x8332,x8333,x8334,x8335)) % 186.01/186.05 [834]~E(x8341,x8342)+E(f214(x8343,x8341,x8344,x8345),f214(x8343,x8342,x8344,x8345)) % 186.01/186.05 [835]~E(x8351,x8352)+E(f214(x8353,x8354,x8351,x8355),f214(x8353,x8354,x8352,x8355)) % 186.01/186.05 [836]~E(x8361,x8362)+E(f214(x8363,x8364,x8365,x8361),f214(x8363,x8364,x8365,x8362)) % 186.01/186.05 [837]~E(x8371,x8372)+E(f767(x8371,x8373,x8374,x8375,x8376),f767(x8372,x8373,x8374,x8375,x8376)) % 186.01/186.05 [838]~E(x8381,x8382)+E(f767(x8383,x8381,x8384,x8385,x8386),f767(x8383,x8382,x8384,x8385,x8386)) % 186.01/186.05 [839]~E(x8391,x8392)+E(f767(x8393,x8394,x8391,x8395,x8396),f767(x8393,x8394,x8392,x8395,x8396)) % 186.01/186.05 [840]~E(x8401,x8402)+E(f767(x8403,x8404,x8405,x8401,x8406),f767(x8403,x8404,x8405,x8402,x8406)) % 186.01/186.05 [841]~E(x8411,x8412)+E(f767(x8413,x8414,x8415,x8416,x8411),f767(x8413,x8414,x8415,x8416,x8412)) % 186.01/186.05 [842]~E(x8421,x8422)+E(f308(x8421,x8423,x8424,x8425,x8426),f308(x8422,x8423,x8424,x8425,x8426)) % 186.01/186.05 [843]~E(x8431,x8432)+E(f308(x8433,x8431,x8434,x8435,x8436),f308(x8433,x8432,x8434,x8435,x8436)) % 186.01/186.05 [844]~E(x8441,x8442)+E(f308(x8443,x8444,x8441,x8445,x8446),f308(x8443,x8444,x8442,x8445,x8446)) % 186.01/186.05 [845]~E(x8451,x8452)+E(f308(x8453,x8454,x8455,x8451,x8456),f308(x8453,x8454,x8455,x8452,x8456)) % 186.01/186.05 [846]~E(x8461,x8462)+E(f308(x8463,x8464,x8465,x8466,x8461),f308(x8463,x8464,x8465,x8466,x8462)) % 186.01/186.05 [847]~E(x8471,x8472)+E(f492(x8471,x8473,x8474,x8475,x8476,x8477),f492(x8472,x8473,x8474,x8475,x8476,x8477)) % 186.01/186.05 [848]~E(x8481,x8482)+E(f492(x8483,x8481,x8484,x8485,x8486,x8487),f492(x8483,x8482,x8484,x8485,x8486,x8487)) % 186.01/186.05 [849]~E(x8491,x8492)+E(f492(x8493,x8494,x8491,x8495,x8496,x8497),f492(x8493,x8494,x8492,x8495,x8496,x8497)) % 186.01/186.05 [850]~E(x8501,x8502)+E(f492(x8503,x8504,x8505,x8501,x8506,x8507),f492(x8503,x8504,x8505,x8502,x8506,x8507)) % 186.01/186.05 [851]~E(x8511,x8512)+E(f492(x8513,x8514,x8515,x8516,x8511,x8517),f492(x8513,x8514,x8515,x8516,x8512,x8517)) % 186.01/186.05 [852]~E(x8521,x8522)+E(f492(x8523,x8524,x8525,x8526,x8527,x8521),f492(x8523,x8524,x8525,x8526,x8527,x8522)) % 186.01/186.05 [853]~E(x8531,x8532)+E(f535(x8531,x8533,x8534,x8535),f535(x8532,x8533,x8534,x8535)) % 186.01/186.05 [854]~E(x8541,x8542)+E(f535(x8543,x8541,x8544,x8545),f535(x8543,x8542,x8544,x8545)) % 186.01/186.05 [855]~E(x8551,x8552)+E(f535(x8553,x8554,x8551,x8555),f535(x8553,x8554,x8552,x8555)) % 186.01/186.05 [856]~E(x8561,x8562)+E(f535(x8563,x8564,x8565,x8561),f535(x8563,x8564,x8565,x8562)) % 186.01/186.05 [857]~E(x8571,x8572)+E(f302(x8571,x8573,x8574),f302(x8572,x8573,x8574)) % 186.01/186.05 [858]~E(x8581,x8582)+E(f302(x8583,x8581,x8584),f302(x8583,x8582,x8584)) % 186.01/186.05 [859]~E(x8591,x8592)+E(f302(x8593,x8594,x8591),f302(x8593,x8594,x8592)) % 186.01/186.05 [860]~E(x8601,x8602)+E(f868(x8601,x8603,x8604),f868(x8602,x8603,x8604)) % 186.01/186.05 [861]~E(x8611,x8612)+E(f868(x8613,x8611,x8614),f868(x8613,x8612,x8614)) % 186.01/186.05 [862]~E(x8621,x8622)+E(f868(x8623,x8624,x8621),f868(x8623,x8624,x8622)) % 186.01/186.05 [863]~E(x8631,x8632)+E(f654(x8631,x8633,x8634,x8635,x8636),f654(x8632,x8633,x8634,x8635,x8636)) % 186.01/186.05 [864]~E(x8641,x8642)+E(f654(x8643,x8641,x8644,x8645,x8646),f654(x8643,x8642,x8644,x8645,x8646)) % 186.01/186.05 [865]~E(x8651,x8652)+E(f654(x8653,x8654,x8651,x8655,x8656),f654(x8653,x8654,x8652,x8655,x8656)) % 186.01/186.05 [866]~E(x8661,x8662)+E(f654(x8663,x8664,x8665,x8661,x8666),f654(x8663,x8664,x8665,x8662,x8666)) % 186.01/186.05 [867]~E(x8671,x8672)+E(f654(x8673,x8674,x8675,x8676,x8671),f654(x8673,x8674,x8675,x8676,x8672)) % 186.01/186.05 [868]~E(x8681,x8682)+E(f191(x8681,x8683,x8684),f191(x8682,x8683,x8684)) % 186.01/186.05 [869]~E(x8691,x8692)+E(f191(x8693,x8691,x8694),f191(x8693,x8692,x8694)) % 186.01/186.05 [870]~E(x8701,x8702)+E(f191(x8703,x8704,x8701),f191(x8703,x8704,x8702)) % 186.01/186.05 [871]~E(x8711,x8712)+E(f314(x8711,x8713,x8714),f314(x8712,x8713,x8714)) % 186.01/186.05 [872]~E(x8721,x8722)+E(f314(x8723,x8721,x8724),f314(x8723,x8722,x8724)) % 186.01/186.05 [873]~E(x8731,x8732)+E(f314(x8733,x8734,x8731),f314(x8733,x8734,x8732)) % 186.01/186.05 [874]~E(x8741,x8742)+E(f727(x8741,x8743,x8744),f727(x8742,x8743,x8744)) % 186.01/186.05 [875]~E(x8751,x8752)+E(f727(x8753,x8751,x8754),f727(x8753,x8752,x8754)) % 186.01/186.05 [876]~E(x8761,x8762)+E(f727(x8763,x8764,x8761),f727(x8763,x8764,x8762)) % 186.01/186.05 [877]~E(x8771,x8772)+E(f634(x8771,x8773,x8774,x8775),f634(x8772,x8773,x8774,x8775)) % 186.01/186.05 [878]~E(x8781,x8782)+E(f634(x8783,x8781,x8784,x8785),f634(x8783,x8782,x8784,x8785)) % 186.01/186.05 [879]~E(x8791,x8792)+E(f634(x8793,x8794,x8791,x8795),f634(x8793,x8794,x8792,x8795)) % 186.01/186.05 [880]~E(x8801,x8802)+E(f634(x8803,x8804,x8805,x8801),f634(x8803,x8804,x8805,x8802)) % 186.01/186.05 [881]~E(x8811,x8812)+E(f193(x8811),f193(x8812)) % 186.01/186.05 [882]~E(x8821,x8822)+E(f125(x8821,x8823,x8824),f125(x8822,x8823,x8824)) % 186.01/186.05 [883]~E(x8831,x8832)+E(f125(x8833,x8831,x8834),f125(x8833,x8832,x8834)) % 186.01/186.05 [884]~E(x8841,x8842)+E(f125(x8843,x8844,x8841),f125(x8843,x8844,x8842)) % 186.01/186.05 [885]~E(x8851,x8852)+E(f726(x8851,x8853,x8854),f726(x8852,x8853,x8854)) % 186.01/186.05 [886]~E(x8861,x8862)+E(f726(x8863,x8861,x8864),f726(x8863,x8862,x8864)) % 186.01/186.05 [887]~E(x8871,x8872)+E(f726(x8873,x8874,x8871),f726(x8873,x8874,x8872)) % 186.01/186.05 [888]~E(x8881,x8882)+E(f422(x8881,x8883,x8884,x8885,x8886),f422(x8882,x8883,x8884,x8885,x8886)) % 186.01/186.05 [889]~E(x8891,x8892)+E(f422(x8893,x8891,x8894,x8895,x8896),f422(x8893,x8892,x8894,x8895,x8896)) % 186.01/186.05 [890]~E(x8901,x8902)+E(f422(x8903,x8904,x8901,x8905,x8906),f422(x8903,x8904,x8902,x8905,x8906)) % 186.01/186.05 [891]~E(x8911,x8912)+E(f422(x8913,x8914,x8915,x8911,x8916),f422(x8913,x8914,x8915,x8912,x8916)) % 186.01/186.05 [892]~E(x8921,x8922)+E(f422(x8923,x8924,x8925,x8926,x8921),f422(x8923,x8924,x8925,x8926,x8922)) % 186.01/186.05 [893]~E(x8931,x8932)+E(f657(x8931,x8933,x8934,x8935,x8936,x8937,x8938),f657(x8932,x8933,x8934,x8935,x8936,x8937,x8938)) % 186.01/186.05 [894]~E(x8941,x8942)+E(f657(x8943,x8941,x8944,x8945,x8946,x8947,x8948),f657(x8943,x8942,x8944,x8945,x8946,x8947,x8948)) % 186.01/186.05 [895]~E(x8951,x8952)+E(f657(x8953,x8954,x8951,x8955,x8956,x8957,x8958),f657(x8953,x8954,x8952,x8955,x8956,x8957,x8958)) % 186.01/186.05 [896]~E(x8961,x8962)+E(f657(x8963,x8964,x8965,x8961,x8966,x8967,x8968),f657(x8963,x8964,x8965,x8962,x8966,x8967,x8968)) % 186.01/186.05 [897]~E(x8971,x8972)+E(f657(x8973,x8974,x8975,x8976,x8971,x8977,x8978),f657(x8973,x8974,x8975,x8976,x8972,x8977,x8978)) % 186.01/186.05 [898]~E(x8981,x8982)+E(f657(x8983,x8984,x8985,x8986,x8987,x8981,x8988),f657(x8983,x8984,x8985,x8986,x8987,x8982,x8988)) % 186.01/186.05 [899]~E(x8991,x8992)+E(f657(x8993,x8994,x8995,x8996,x8997,x8998,x8991),f657(x8993,x8994,x8995,x8996,x8997,x8998,x8992)) % 186.01/186.05 [900]~E(x9001,x9002)+E(f520(x9001,x9003,x9004,x9005,x9006,x9007,x9008),f520(x9002,x9003,x9004,x9005,x9006,x9007,x9008)) % 186.01/186.05 [901]~E(x9011,x9012)+E(f520(x9013,x9011,x9014,x9015,x9016,x9017,x9018),f520(x9013,x9012,x9014,x9015,x9016,x9017,x9018)) % 186.01/186.05 [902]~E(x9021,x9022)+E(f520(x9023,x9024,x9021,x9025,x9026,x9027,x9028),f520(x9023,x9024,x9022,x9025,x9026,x9027,x9028)) % 186.01/186.05 [903]~E(x9031,x9032)+E(f520(x9033,x9034,x9035,x9031,x9036,x9037,x9038),f520(x9033,x9034,x9035,x9032,x9036,x9037,x9038)) % 186.01/186.05 [904]~E(x9041,x9042)+E(f520(x9043,x9044,x9045,x9046,x9041,x9047,x9048),f520(x9043,x9044,x9045,x9046,x9042,x9047,x9048)) % 186.01/186.05 [905]~E(x9051,x9052)+E(f520(x9053,x9054,x9055,x9056,x9057,x9051,x9058),f520(x9053,x9054,x9055,x9056,x9057,x9052,x9058)) % 186.01/186.05 [906]~E(x9061,x9062)+E(f520(x9063,x9064,x9065,x9066,x9067,x9068,x9061),f520(x9063,x9064,x9065,x9066,x9067,x9068,x9062)) % 186.01/186.05 [907]~E(x9071,x9072)+E(f872(x9071,x9073,x9074),f872(x9072,x9073,x9074)) % 186.01/186.05 [908]~E(x9081,x9082)+E(f872(x9083,x9081,x9084),f872(x9083,x9082,x9084)) % 186.01/186.05 [909]~E(x9091,x9092)+E(f872(x9093,x9094,x9091),f872(x9093,x9094,x9092)) % 186.01/186.05 [910]~E(x9101,x9102)+E(f261(x9101,x9103,x9104,x9105,x9106),f261(x9102,x9103,x9104,x9105,x9106)) % 186.01/186.05 [911]~E(x9111,x9112)+E(f261(x9113,x9111,x9114,x9115,x9116),f261(x9113,x9112,x9114,x9115,x9116)) % 186.01/186.05 [912]~E(x9121,x9122)+E(f261(x9123,x9124,x9121,x9125,x9126),f261(x9123,x9124,x9122,x9125,x9126)) % 186.01/186.05 [913]~E(x9131,x9132)+E(f261(x9133,x9134,x9135,x9131,x9136),f261(x9133,x9134,x9135,x9132,x9136)) % 186.01/186.05 [914]~E(x9141,x9142)+E(f261(x9143,x9144,x9145,x9146,x9141),f261(x9143,x9144,x9145,x9146,x9142)) % 186.01/186.05 [915]~E(x9151,x9152)+E(f278(x9151,x9153),f278(x9152,x9153)) % 186.01/186.05 [916]~E(x9161,x9162)+E(f278(x9163,x9161),f278(x9163,x9162)) % 186.01/186.05 [917]~E(x9171,x9172)+E(f758(x9171,x9173,x9174,x9175),f758(x9172,x9173,x9174,x9175)) % 186.01/186.05 [918]~E(x9181,x9182)+E(f758(x9183,x9181,x9184,x9185),f758(x9183,x9182,x9184,x9185)) % 186.01/186.05 [919]~E(x9191,x9192)+E(f758(x9193,x9194,x9191,x9195),f758(x9193,x9194,x9192,x9195)) % 186.01/186.05 [920]~E(x9201,x9202)+E(f758(x9203,x9204,x9205,x9201),f758(x9203,x9204,x9205,x9202)) % 186.01/186.05 [921]~E(x9211,x9212)+E(f797(x9211,x9213,x9214,x9215),f797(x9212,x9213,x9214,x9215)) % 186.01/186.05 [922]~E(x9221,x9222)+E(f797(x9223,x9221,x9224,x9225),f797(x9223,x9222,x9224,x9225)) % 186.01/186.05 [923]~E(x9231,x9232)+E(f797(x9233,x9234,x9231,x9235),f797(x9233,x9234,x9232,x9235)) % 186.01/186.05 [924]~E(x9241,x9242)+E(f797(x9243,x9244,x9245,x9241),f797(x9243,x9244,x9245,x9242)) % 186.01/186.05 [925]~E(x9251,x9252)+E(f414(x9251,x9253,x9254,x9255,x9256,x9257),f414(x9252,x9253,x9254,x9255,x9256,x9257)) % 186.01/186.05 [926]~E(x9261,x9262)+E(f414(x9263,x9261,x9264,x9265,x9266,x9267),f414(x9263,x9262,x9264,x9265,x9266,x9267)) % 186.01/186.05 [927]~E(x9271,x9272)+E(f414(x9273,x9274,x9271,x9275,x9276,x9277),f414(x9273,x9274,x9272,x9275,x9276,x9277)) % 186.01/186.05 [928]~E(x9281,x9282)+E(f414(x9283,x9284,x9285,x9281,x9286,x9287),f414(x9283,x9284,x9285,x9282,x9286,x9287)) % 186.01/186.05 [929]~E(x9291,x9292)+E(f414(x9293,x9294,x9295,x9296,x9291,x9297),f414(x9293,x9294,x9295,x9296,x9292,x9297)) % 186.01/186.05 [930]~E(x9301,x9302)+E(f414(x9303,x9304,x9305,x9306,x9307,x9301),f414(x9303,x9304,x9305,x9306,x9307,x9302)) % 186.01/186.05 [931]~E(x9311,x9312)+E(f282(x9311,x9313,x9314),f282(x9312,x9313,x9314)) % 186.01/186.05 [932]~E(x9321,x9322)+E(f282(x9323,x9321,x9324),f282(x9323,x9322,x9324)) % 186.01/186.05 [933]~E(x9331,x9332)+E(f282(x9333,x9334,x9331),f282(x9333,x9334,x9332)) % 186.01/186.05 [934]~E(x9341,x9342)+E(f784(x9341,x9343,x9344),f784(x9342,x9343,x9344)) % 186.01/186.05 [935]~E(x9351,x9352)+E(f784(x9353,x9351,x9354),f784(x9353,x9352,x9354)) % 186.01/186.05 [936]~E(x9361,x9362)+E(f784(x9363,x9364,x9361),f784(x9363,x9364,x9362)) % 186.01/186.05 [937]~E(x9371,x9372)+E(f761(x9371,x9373,x9374),f761(x9372,x9373,x9374)) % 186.01/186.05 [938]~E(x9381,x9382)+E(f761(x9383,x9381,x9384),f761(x9383,x9382,x9384)) % 186.01/186.05 [939]~E(x9391,x9392)+E(f761(x9393,x9394,x9391),f761(x9393,x9394,x9392)) % 186.01/186.05 [940]~E(x9401,x9402)+E(f849(x9401,x9403,x9404,x9405),f849(x9402,x9403,x9404,x9405)) % 186.01/186.05 [941]~E(x9411,x9412)+E(f849(x9413,x9411,x9414,x9415),f849(x9413,x9412,x9414,x9415)) % 186.01/186.05 [942]~E(x9421,x9422)+E(f849(x9423,x9424,x9421,x9425),f849(x9423,x9424,x9422,x9425)) % 186.01/186.05 [943]~E(x9431,x9432)+E(f849(x9433,x9434,x9435,x9431),f849(x9433,x9434,x9435,x9432)) % 186.01/186.05 [944]~E(x9441,x9442)+E(f36(x9441,x9443,x9444,x9445),f36(x9442,x9443,x9444,x9445)) % 186.01/186.05 [945]~E(x9451,x9452)+E(f36(x9453,x9451,x9454,x9455),f36(x9453,x9452,x9454,x9455)) % 186.01/186.05 [946]~E(x9461,x9462)+E(f36(x9463,x9464,x9461,x9465),f36(x9463,x9464,x9462,x9465)) % 186.01/186.05 [947]~E(x9471,x9472)+E(f36(x9473,x9474,x9475,x9471),f36(x9473,x9474,x9475,x9472)) % 186.01/186.05 [948]~E(x9481,x9482)+E(f352(x9481,x9483,x9484),f352(x9482,x9483,x9484)) % 186.01/186.05 [949]~E(x9491,x9492)+E(f352(x9493,x9491,x9494),f352(x9493,x9492,x9494)) % 186.01/186.05 [950]~E(x9501,x9502)+E(f352(x9503,x9504,x9501),f352(x9503,x9504,x9502)) % 186.01/186.05 [951]~E(x9511,x9512)+E(f563(x9511,x9513,x9514,x9515,x9516,x9517),f563(x9512,x9513,x9514,x9515,x9516,x9517)) % 186.01/186.05 [952]~E(x9521,x9522)+E(f563(x9523,x9521,x9524,x9525,x9526,x9527),f563(x9523,x9522,x9524,x9525,x9526,x9527)) % 186.01/186.05 [953]~E(x9531,x9532)+E(f563(x9533,x9534,x9531,x9535,x9536,x9537),f563(x9533,x9534,x9532,x9535,x9536,x9537)) % 186.01/186.05 [954]~E(x9541,x9542)+E(f563(x9543,x9544,x9545,x9541,x9546,x9547),f563(x9543,x9544,x9545,x9542,x9546,x9547)) % 186.01/186.05 [955]~E(x9551,x9552)+E(f563(x9553,x9554,x9555,x9556,x9551,x9557),f563(x9553,x9554,x9555,x9556,x9552,x9557)) % 186.01/186.05 [956]~E(x9561,x9562)+E(f563(x9563,x9564,x9565,x9566,x9567,x9561),f563(x9563,x9564,x9565,x9566,x9567,x9562)) % 186.01/186.05 [957]~E(x9571,x9572)+E(f439(x9571,x9573,x9574,x9575,x9576),f439(x9572,x9573,x9574,x9575,x9576)) % 186.01/186.05 [958]~E(x9581,x9582)+E(f439(x9583,x9581,x9584,x9585,x9586),f439(x9583,x9582,x9584,x9585,x9586)) % 186.01/186.05 [959]~E(x9591,x9592)+E(f439(x9593,x9594,x9591,x9595,x9596),f439(x9593,x9594,x9592,x9595,x9596)) % 186.01/186.05 [960]~E(x9601,x9602)+E(f439(x9603,x9604,x9605,x9601,x9606),f439(x9603,x9604,x9605,x9602,x9606)) % 186.01/186.05 [961]~E(x9611,x9612)+E(f439(x9613,x9614,x9615,x9616,x9611),f439(x9613,x9614,x9615,x9616,x9612)) % 186.01/186.05 [962]~E(x9621,x9622)+E(f896(x9621,x9623,x9624,x9625,x9626,x9627,x9628),f896(x9622,x9623,x9624,x9625,x9626,x9627,x9628)) % 186.01/186.05 [963]~E(x9631,x9632)+E(f896(x9633,x9631,x9634,x9635,x9636,x9637,x9638),f896(x9633,x9632,x9634,x9635,x9636,x9637,x9638)) % 186.01/186.05 [964]~E(x9641,x9642)+E(f896(x9643,x9644,x9641,x9645,x9646,x9647,x9648),f896(x9643,x9644,x9642,x9645,x9646,x9647,x9648)) % 186.01/186.05 [965]~E(x9651,x9652)+E(f896(x9653,x9654,x9655,x9651,x9656,x9657,x9658),f896(x9653,x9654,x9655,x9652,x9656,x9657,x9658)) % 186.01/186.05 [966]~E(x9661,x9662)+E(f896(x9663,x9664,x9665,x9666,x9661,x9667,x9668),f896(x9663,x9664,x9665,x9666,x9662,x9667,x9668)) % 186.01/186.05 [967]~E(x9671,x9672)+E(f896(x9673,x9674,x9675,x9676,x9677,x9671,x9678),f896(x9673,x9674,x9675,x9676,x9677,x9672,x9678)) % 186.01/186.05 [968]~E(x9681,x9682)+E(f896(x9683,x9684,x9685,x9686,x9687,x9688,x9681),f896(x9683,x9684,x9685,x9686,x9687,x9688,x9682)) % 186.01/186.05 [969]~E(x9691,x9692)+E(f696(x9691,x9693,x9694),f696(x9692,x9693,x9694)) % 186.01/186.05 [970]~E(x9701,x9702)+E(f696(x9703,x9701,x9704),f696(x9703,x9702,x9704)) % 186.01/186.05 [971]~E(x9711,x9712)+E(f696(x9713,x9714,x9711),f696(x9713,x9714,x9712)) % 186.01/186.05 [972]~E(x9721,x9722)+E(f455(x9721,x9723,x9724),f455(x9722,x9723,x9724)) % 186.01/186.05 [973]~E(x9731,x9732)+E(f455(x9733,x9731,x9734),f455(x9733,x9732,x9734)) % 186.01/186.05 [974]~E(x9741,x9742)+E(f455(x9743,x9744,x9741),f455(x9743,x9744,x9742)) % 186.01/186.05 [975]~E(x9751,x9752)+E(f508(x9751,x9753,x9754),f508(x9752,x9753,x9754)) % 186.01/186.05 [976]~E(x9761,x9762)+E(f508(x9763,x9761,x9764),f508(x9763,x9762,x9764)) % 186.01/186.05 [977]~E(x9771,x9772)+E(f508(x9773,x9774,x9771),f508(x9773,x9774,x9772)) % 186.01/186.05 [978]~E(x9781,x9782)+E(f719(x9781,x9783,x9784,x9785,x9786),f719(x9782,x9783,x9784,x9785,x9786)) % 186.01/186.05 [979]~E(x9791,x9792)+E(f719(x9793,x9791,x9794,x9795,x9796),f719(x9793,x9792,x9794,x9795,x9796)) % 186.01/186.05 [980]~E(x9801,x9802)+E(f719(x9803,x9804,x9801,x9805,x9806),f719(x9803,x9804,x9802,x9805,x9806)) % 186.01/186.05 [981]~E(x9811,x9812)+E(f719(x9813,x9814,x9815,x9811,x9816),f719(x9813,x9814,x9815,x9812,x9816)) % 186.01/186.05 [982]~E(x9821,x9822)+E(f719(x9823,x9824,x9825,x9826,x9821),f719(x9823,x9824,x9825,x9826,x9822)) % 186.01/186.05 [983]~E(x9831,x9832)+E(f852(x9831,x9833,x9834,x9835,x9836),f852(x9832,x9833,x9834,x9835,x9836)) % 186.01/186.05 [984]~E(x9841,x9842)+E(f852(x9843,x9841,x9844,x9845,x9846),f852(x9843,x9842,x9844,x9845,x9846)) % 186.01/186.05 [985]~E(x9851,x9852)+E(f852(x9853,x9854,x9851,x9855,x9856),f852(x9853,x9854,x9852,x9855,x9856)) % 186.01/186.05 [986]~E(x9861,x9862)+E(f852(x9863,x9864,x9865,x9861,x9866),f852(x9863,x9864,x9865,x9862,x9866)) % 186.01/186.05 [987]~E(x9871,x9872)+E(f852(x9873,x9874,x9875,x9876,x9871),f852(x9873,x9874,x9875,x9876,x9872)) % 186.01/186.05 [988]~E(x9881,x9882)+E(f82(x9881,x9883,x9884,x9885,x9886),f82(x9882,x9883,x9884,x9885,x9886)) % 186.01/186.05 [989]~E(x9891,x9892)+E(f82(x9893,x9891,x9894,x9895,x9896),f82(x9893,x9892,x9894,x9895,x9896)) % 186.01/186.05 [990]~E(x9901,x9902)+E(f82(x9903,x9904,x9901,x9905,x9906),f82(x9903,x9904,x9902,x9905,x9906)) % 186.01/186.05 [991]~E(x9911,x9912)+E(f82(x9913,x9914,x9915,x9911,x9916),f82(x9913,x9914,x9915,x9912,x9916)) % 186.01/186.05 [992]~E(x9921,x9922)+E(f82(x9923,x9924,x9925,x9926,x9921),f82(x9923,x9924,x9925,x9926,x9922)) % 186.01/186.05 [993]~E(x9931,x9932)+E(f473(x9931,x9933,x9934),f473(x9932,x9933,x9934)) % 186.01/186.05 [994]~E(x9941,x9942)+E(f473(x9943,x9941,x9944),f473(x9943,x9942,x9944)) % 186.01/186.05 [995]~E(x9951,x9952)+E(f473(x9953,x9954,x9951),f473(x9953,x9954,x9952)) % 186.01/186.05 [996]~E(x9961,x9962)+E(f624(x9961,x9963,x9964,x9965,x9966),f624(x9962,x9963,x9964,x9965,x9966)) % 186.01/186.05 [997]~E(x9971,x9972)+E(f624(x9973,x9971,x9974,x9975,x9976),f624(x9973,x9972,x9974,x9975,x9976)) % 186.01/186.05 [998]~E(x9981,x9982)+E(f624(x9983,x9984,x9981,x9985,x9986),f624(x9983,x9984,x9982,x9985,x9986)) % 186.01/186.05 [999]~E(x9991,x9992)+E(f624(x9993,x9994,x9995,x9991,x9996),f624(x9993,x9994,x9995,x9992,x9996)) % 186.01/186.05 [1000]~E(x10001,x10002)+E(f624(x10003,x10004,x10005,x10006,x10001),f624(x10003,x10004,x10005,x10006,x10002)) % 186.01/186.05 [1001]~E(x10011,x10012)+E(f199(x10011,x10013),f199(x10012,x10013)) % 186.01/186.05 [1002]~E(x10021,x10022)+E(f199(x10023,x10021),f199(x10023,x10022)) % 186.01/186.05 [1003]~E(x10031,x10032)+E(f841(x10031,x10033),f841(x10032,x10033)) % 186.01/186.05 [1004]~E(x10041,x10042)+E(f841(x10043,x10041),f841(x10043,x10042)) % 186.01/186.05 [1005]~E(x10051,x10052)+E(f128(x10051,x10053),f128(x10052,x10053)) % 186.01/186.05 [1006]~E(x10061,x10062)+E(f128(x10063,x10061),f128(x10063,x10062)) % 186.01/186.05 [1007]~E(x10071,x10072)+E(f239(x10071,x10073,x10074),f239(x10072,x10073,x10074)) % 186.01/186.05 [1008]~E(x10081,x10082)+E(f239(x10083,x10081,x10084),f239(x10083,x10082,x10084)) % 186.01/186.05 [1009]~E(x10091,x10092)+E(f239(x10093,x10094,x10091),f239(x10093,x10094,x10092)) % 186.01/186.05 [1010]~E(x10101,x10102)+E(f37(x10101,x10103,x10104,x10105),f37(x10102,x10103,x10104,x10105)) % 186.01/186.05 [1011]~E(x10111,x10112)+E(f37(x10113,x10111,x10114,x10115),f37(x10113,x10112,x10114,x10115)) % 186.01/186.05 [1012]~E(x10121,x10122)+E(f37(x10123,x10124,x10121,x10125),f37(x10123,x10124,x10122,x10125)) % 186.01/186.05 [1013]~E(x10131,x10132)+E(f37(x10133,x10134,x10135,x10131),f37(x10133,x10134,x10135,x10132)) % 186.01/186.05 [1014]~E(x10141,x10142)+E(f715(x10141,x10143,x10144),f715(x10142,x10143,x10144)) % 186.01/186.05 [1015]~E(x10151,x10152)+E(f715(x10153,x10151,x10154),f715(x10153,x10152,x10154)) % 186.01/186.05 [1016]~E(x10161,x10162)+E(f715(x10163,x10164,x10161),f715(x10163,x10164,x10162)) % 186.01/186.05 [1017]~E(x10171,x10172)+E(f875(x10171,x10173,x10174),f875(x10172,x10173,x10174)) % 186.01/186.05 [1018]~E(x10181,x10182)+E(f875(x10183,x10181,x10184),f875(x10183,x10182,x10184)) % 186.01/186.05 [1019]~E(x10191,x10192)+E(f875(x10193,x10194,x10191),f875(x10193,x10194,x10192)) % 186.01/186.05 [1020]~E(x10201,x10202)+E(f137(x10201,x10203,x10204,x10205),f137(x10202,x10203,x10204,x10205)) % 186.01/186.05 [1021]~E(x10211,x10212)+E(f137(x10213,x10211,x10214,x10215),f137(x10213,x10212,x10214,x10215)) % 186.01/186.05 [1022]~E(x10221,x10222)+E(f137(x10223,x10224,x10221,x10225),f137(x10223,x10224,x10222,x10225)) % 186.01/186.05 [1023]~E(x10231,x10232)+E(f137(x10233,x10234,x10235,x10231),f137(x10233,x10234,x10235,x10232)) % 186.01/186.05 [1024]~E(x10241,x10242)+E(f636(x10241,x10243,x10244,x10245),f636(x10242,x10243,x10244,x10245)) % 186.01/186.05 [1025]~E(x10251,x10252)+E(f636(x10253,x10251,x10254,x10255),f636(x10253,x10252,x10254,x10255)) % 186.01/186.05 [1026]~E(x10261,x10262)+E(f636(x10263,x10264,x10261,x10265),f636(x10263,x10264,x10262,x10265)) % 186.01/186.05 [1027]~E(x10271,x10272)+E(f636(x10273,x10274,x10275,x10271),f636(x10273,x10274,x10275,x10272)) % 186.01/186.05 [1028]~E(x10281,x10282)+E(f818(x10281,x10283,x10284,x10285,x10286,x10287,x10288),f818(x10282,x10283,x10284,x10285,x10286,x10287,x10288)) % 186.01/186.05 [1029]~E(x10291,x10292)+E(f818(x10293,x10291,x10294,x10295,x10296,x10297,x10298),f818(x10293,x10292,x10294,x10295,x10296,x10297,x10298)) % 186.01/186.05 [1030]~E(x10301,x10302)+E(f818(x10303,x10304,x10301,x10305,x10306,x10307,x10308),f818(x10303,x10304,x10302,x10305,x10306,x10307,x10308)) % 186.01/186.05 [1031]~E(x10311,x10312)+E(f818(x10313,x10314,x10315,x10311,x10316,x10317,x10318),f818(x10313,x10314,x10315,x10312,x10316,x10317,x10318)) % 186.01/186.05 [1032]~E(x10321,x10322)+E(f818(x10323,x10324,x10325,x10326,x10321,x10327,x10328),f818(x10323,x10324,x10325,x10326,x10322,x10327,x10328)) % 186.01/186.05 [1033]~E(x10331,x10332)+E(f818(x10333,x10334,x10335,x10336,x10337,x10331,x10338),f818(x10333,x10334,x10335,x10336,x10337,x10332,x10338)) % 186.01/186.05 [1034]~E(x10341,x10342)+E(f818(x10343,x10344,x10345,x10346,x10347,x10348,x10341),f818(x10343,x10344,x10345,x10346,x10347,x10348,x10342)) % 186.01/186.05 [1035]~E(x10351,x10352)+E(f751(x10351,x10353,x10354,x10355),f751(x10352,x10353,x10354,x10355)) % 186.01/186.05 [1036]~E(x10361,x10362)+E(f751(x10363,x10361,x10364,x10365),f751(x10363,x10362,x10364,x10365)) % 186.01/186.05 [1037]~E(x10371,x10372)+E(f751(x10373,x10374,x10371,x10375),f751(x10373,x10374,x10372,x10375)) % 186.01/186.05 [1038]~E(x10381,x10382)+E(f751(x10383,x10384,x10385,x10381),f751(x10383,x10384,x10385,x10382)) % 186.01/186.05 [1039]~E(x10391,x10392)+E(f596(x10391,x10393,x10394,x10395,x10396,x10397),f596(x10392,x10393,x10394,x10395,x10396,x10397)) % 186.01/186.05 [1040]~E(x10401,x10402)+E(f596(x10403,x10401,x10404,x10405,x10406,x10407),f596(x10403,x10402,x10404,x10405,x10406,x10407)) % 186.01/186.05 [1041]~E(x10411,x10412)+E(f596(x10413,x10414,x10411,x10415,x10416,x10417),f596(x10413,x10414,x10412,x10415,x10416,x10417)) % 186.01/186.05 [1042]~E(x10421,x10422)+E(f596(x10423,x10424,x10425,x10421,x10426,x10427),f596(x10423,x10424,x10425,x10422,x10426,x10427)) % 186.01/186.05 [1043]~E(x10431,x10432)+E(f596(x10433,x10434,x10435,x10436,x10431,x10437),f596(x10433,x10434,x10435,x10436,x10432,x10437)) % 186.01/186.05 [1044]~E(x10441,x10442)+E(f596(x10443,x10444,x10445,x10446,x10447,x10441),f596(x10443,x10444,x10445,x10446,x10447,x10442)) % 186.01/186.05 [1045]~E(x10451,x10452)+E(f505(x10451,x10453,x10454,x10455),f505(x10452,x10453,x10454,x10455)) % 186.01/186.05 [1046]~E(x10461,x10462)+E(f505(x10463,x10461,x10464,x10465),f505(x10463,x10462,x10464,x10465)) % 186.01/186.05 [1047]~E(x10471,x10472)+E(f505(x10473,x10474,x10471,x10475),f505(x10473,x10474,x10472,x10475)) % 186.01/186.05 [1048]~E(x10481,x10482)+E(f505(x10483,x10484,x10485,x10481),f505(x10483,x10484,x10485,x10482)) % 186.01/186.05 [1049]~E(x10491,x10492)+E(f206(x10491,x10493,x10494,x10495),f206(x10492,x10493,x10494,x10495)) % 186.01/186.05 [1050]~E(x10501,x10502)+E(f206(x10503,x10501,x10504,x10505),f206(x10503,x10502,x10504,x10505)) % 186.01/186.05 [1051]~E(x10511,x10512)+E(f206(x10513,x10514,x10511,x10515),f206(x10513,x10514,x10512,x10515)) % 186.01/186.05 [1052]~E(x10521,x10522)+E(f206(x10523,x10524,x10525,x10521),f206(x10523,x10524,x10525,x10522)) % 186.01/186.05 [1053]~E(x10531,x10532)+E(f741(x10531,x10533,x10534),f741(x10532,x10533,x10534)) % 186.01/186.05 [1054]~E(x10541,x10542)+E(f741(x10543,x10541,x10544),f741(x10543,x10542,x10544)) % 186.01/186.05 [1055]~E(x10551,x10552)+E(f741(x10553,x10554,x10551),f741(x10553,x10554,x10552)) % 186.01/186.05 [1056]~E(x10561,x10562)+E(f701(x10561,x10563,x10564),f701(x10562,x10563,x10564)) % 186.01/186.05 [1057]~E(x10571,x10572)+E(f701(x10573,x10571,x10574),f701(x10573,x10572,x10574)) % 186.01/186.05 [1058]~E(x10581,x10582)+E(f701(x10583,x10584,x10581),f701(x10583,x10584,x10582)) % 186.01/186.05 [1059]~E(x10591,x10592)+E(f853(x10591,x10593,x10594),f853(x10592,x10593,x10594)) % 186.01/186.05 [1060]~E(x10601,x10602)+E(f853(x10603,x10601,x10604),f853(x10603,x10602,x10604)) % 186.01/186.05 [1061]~E(x10611,x10612)+E(f853(x10613,x10614,x10611),f853(x10613,x10614,x10612)) % 186.01/186.05 [1062]~E(x10621,x10622)+E(f19(x10621,x10623,x10624,x10625),f19(x10622,x10623,x10624,x10625)) % 186.01/186.05 [1063]~E(x10631,x10632)+E(f19(x10633,x10631,x10634,x10635),f19(x10633,x10632,x10634,x10635)) % 186.01/186.05 [1064]~E(x10641,x10642)+E(f19(x10643,x10644,x10641,x10645),f19(x10643,x10644,x10642,x10645)) % 186.01/186.05 [1065]~E(x10651,x10652)+E(f19(x10653,x10654,x10655,x10651),f19(x10653,x10654,x10655,x10652)) % 186.01/186.05 [1066]~E(x10661,x10662)+E(f773(x10661,x10663,x10664),f773(x10662,x10663,x10664)) % 186.01/186.05 [1067]~E(x10671,x10672)+E(f773(x10673,x10671,x10674),f773(x10673,x10672,x10674)) % 186.01/186.05 [1068]~E(x10681,x10682)+E(f773(x10683,x10684,x10681),f773(x10683,x10684,x10682)) % 186.01/186.05 [1069]~E(x10691,x10692)+E(f854(x10691,x10693,x10694,x10695,x10696),f854(x10692,x10693,x10694,x10695,x10696)) % 186.01/186.05 [1070]~E(x10701,x10702)+E(f854(x10703,x10701,x10704,x10705,x10706),f854(x10703,x10702,x10704,x10705,x10706)) % 186.01/186.05 [1071]~E(x10711,x10712)+E(f854(x10713,x10714,x10711,x10715,x10716),f854(x10713,x10714,x10712,x10715,x10716)) % 186.01/186.05 [1072]~E(x10721,x10722)+E(f854(x10723,x10724,x10725,x10721,x10726),f854(x10723,x10724,x10725,x10722,x10726)) % 186.01/186.05 [1073]~E(x10731,x10732)+E(f854(x10733,x10734,x10735,x10736,x10731),f854(x10733,x10734,x10735,x10736,x10732)) % 186.01/186.05 [1074]~E(x10741,x10742)+E(f812(x10741,x10743,x10744,x10745,x10746,x10747,x10748),f812(x10742,x10743,x10744,x10745,x10746,x10747,x10748)) % 186.01/186.05 [1075]~E(x10751,x10752)+E(f812(x10753,x10751,x10754,x10755,x10756,x10757,x10758),f812(x10753,x10752,x10754,x10755,x10756,x10757,x10758)) % 186.01/186.05 [1076]~E(x10761,x10762)+E(f812(x10763,x10764,x10761,x10765,x10766,x10767,x10768),f812(x10763,x10764,x10762,x10765,x10766,x10767,x10768)) % 186.01/186.05 [1077]~E(x10771,x10772)+E(f812(x10773,x10774,x10775,x10771,x10776,x10777,x10778),f812(x10773,x10774,x10775,x10772,x10776,x10777,x10778)) % 186.01/186.05 [1078]~E(x10781,x10782)+E(f812(x10783,x10784,x10785,x10786,x10781,x10787,x10788),f812(x10783,x10784,x10785,x10786,x10782,x10787,x10788)) % 186.01/186.05 [1079]~E(x10791,x10792)+E(f812(x10793,x10794,x10795,x10796,x10797,x10791,x10798),f812(x10793,x10794,x10795,x10796,x10797,x10792,x10798)) % 186.01/186.05 [1080]~E(x10801,x10802)+E(f812(x10803,x10804,x10805,x10806,x10807,x10808,x10801),f812(x10803,x10804,x10805,x10806,x10807,x10808,x10802)) % 186.01/186.05 [1081]~E(x10811,x10812)+E(f506(x10811,x10813,x10814,x10815),f506(x10812,x10813,x10814,x10815)) % 186.01/186.05 [1082]~E(x10821,x10822)+E(f506(x10823,x10821,x10824,x10825),f506(x10823,x10822,x10824,x10825)) % 186.01/186.05 [1083]~E(x10831,x10832)+E(f506(x10833,x10834,x10831,x10835),f506(x10833,x10834,x10832,x10835)) % 186.01/186.05 [1084]~E(x10841,x10842)+E(f506(x10843,x10844,x10845,x10841),f506(x10843,x10844,x10845,x10842)) % 186.01/186.05 [1085]~E(x10851,x10852)+E(f136(x10851),f136(x10852)) % 186.01/186.05 [1086]~E(x10861,x10862)+E(f438(x10861,x10863,x10864,x10865),f438(x10862,x10863,x10864,x10865)) % 186.01/186.05 [1087]~E(x10871,x10872)+E(f438(x10873,x10871,x10874,x10875),f438(x10873,x10872,x10874,x10875)) % 186.01/186.05 [1088]~E(x10881,x10882)+E(f438(x10883,x10884,x10881,x10885),f438(x10883,x10884,x10882,x10885)) % 186.01/186.05 [1089]~E(x10891,x10892)+E(f438(x10893,x10894,x10895,x10891),f438(x10893,x10894,x10895,x10892)) % 186.01/186.05 [1090]~E(x10901,x10902)+E(f511(x10901,x10903,x10904,x10905),f511(x10902,x10903,x10904,x10905)) % 186.01/186.05 [1091]~E(x10911,x10912)+E(f511(x10913,x10911,x10914,x10915),f511(x10913,x10912,x10914,x10915)) % 186.01/186.05 [1092]~E(x10921,x10922)+E(f511(x10923,x10924,x10921,x10925),f511(x10923,x10924,x10922,x10925)) % 186.01/186.05 [1093]~E(x10931,x10932)+E(f511(x10933,x10934,x10935,x10931),f511(x10933,x10934,x10935,x10932)) % 186.01/186.05 [1094]~E(x10941,x10942)+E(f549(x10941,x10943,x10944,x10945,x10946,x10947,x10948,x10949),f549(x10942,x10943,x10944,x10945,x10946,x10947,x10948,x10949)) % 186.01/186.05 [1095]~E(x10951,x10952)+E(f549(x10953,x10951,x10954,x10955,x10956,x10957,x10958,x10959),f549(x10953,x10952,x10954,x10955,x10956,x10957,x10958,x10959)) % 186.01/186.05 [1096]~E(x10961,x10962)+E(f549(x10963,x10964,x10961,x10965,x10966,x10967,x10968,x10969),f549(x10963,x10964,x10962,x10965,x10966,x10967,x10968,x10969)) % 186.01/186.05 [1097]~E(x10971,x10972)+E(f549(x10973,x10974,x10975,x10971,x10976,x10977,x10978,x10979),f549(x10973,x10974,x10975,x10972,x10976,x10977,x10978,x10979)) % 186.01/186.05 [1098]~E(x10981,x10982)+E(f549(x10983,x10984,x10985,x10986,x10981,x10987,x10988,x10989),f549(x10983,x10984,x10985,x10986,x10982,x10987,x10988,x10989)) % 186.01/186.05 [1099]~E(x10991,x10992)+E(f549(x10993,x10994,x10995,x10996,x10997,x10991,x10998,x10999),f549(x10993,x10994,x10995,x10996,x10997,x10992,x10998,x10999)) % 186.01/186.05 [1100]~E(x11001,x11002)+E(f549(x11003,x11004,x11005,x11006,x11007,x11008,x11001,x11009),f549(x11003,x11004,x11005,x11006,x11007,x11008,x11002,x11009)) % 186.01/186.05 [1101]~E(x11011,x11012)+E(f549(x11013,x11014,x11015,x11016,x11017,x11018,x11019,x11011),f549(x11013,x11014,x11015,x11016,x11017,x11018,x11019,x11012)) % 186.01/186.05 [1102]~E(x11021,x11022)+E(f431(x11021,x11023,x11024,x11025,x11026,x11027),f431(x11022,x11023,x11024,x11025,x11026,x11027)) % 186.01/186.05 [1103]~E(x11031,x11032)+E(f431(x11033,x11031,x11034,x11035,x11036,x11037),f431(x11033,x11032,x11034,x11035,x11036,x11037)) % 186.01/186.05 [1104]~E(x11041,x11042)+E(f431(x11043,x11044,x11041,x11045,x11046,x11047),f431(x11043,x11044,x11042,x11045,x11046,x11047)) % 186.01/186.05 [1105]~E(x11051,x11052)+E(f431(x11053,x11054,x11055,x11051,x11056,x11057),f431(x11053,x11054,x11055,x11052,x11056,x11057)) % 186.01/186.05 [1106]~E(x11061,x11062)+E(f431(x11063,x11064,x11065,x11066,x11061,x11067),f431(x11063,x11064,x11065,x11066,x11062,x11067)) % 186.01/186.05 [1107]~E(x11071,x11072)+E(f431(x11073,x11074,x11075,x11076,x11077,x11071),f431(x11073,x11074,x11075,x11076,x11077,x11072)) % 186.01/186.05 [1108]~E(x11081,x11082)+E(f468(x11081,x11083,x11084),f468(x11082,x11083,x11084)) % 186.01/186.05 [1109]~E(x11091,x11092)+E(f468(x11093,x11091,x11094),f468(x11093,x11092,x11094)) % 186.01/186.05 [1110]~E(x11101,x11102)+E(f468(x11103,x11104,x11101),f468(x11103,x11104,x11102)) % 186.01/186.05 [1111]~E(x11111,x11112)+E(f129(x11111,x11113,x11114,x11115),f129(x11112,x11113,x11114,x11115)) % 186.01/186.05 [1112]~E(x11121,x11122)+E(f129(x11123,x11121,x11124,x11125),f129(x11123,x11122,x11124,x11125)) % 186.01/186.05 [1113]~E(x11131,x11132)+E(f129(x11133,x11134,x11131,x11135),f129(x11133,x11134,x11132,x11135)) % 186.01/186.05 [1114]~E(x11141,x11142)+E(f129(x11143,x11144,x11145,x11141),f129(x11143,x11144,x11145,x11142)) % 186.01/186.05 [1115]~E(x11151,x11152)+E(f545(x11151,x11153,x11154),f545(x11152,x11153,x11154)) % 186.01/186.05 [1116]~E(x11161,x11162)+E(f545(x11163,x11161,x11164),f545(x11163,x11162,x11164)) % 186.01/186.05 [1117]~E(x11171,x11172)+E(f545(x11173,x11174,x11171),f545(x11173,x11174,x11172)) % 186.01/186.05 [1118]~E(x11181,x11182)+E(f816(x11181,x11183),f816(x11182,x11183)) % 186.01/186.05 [1119]~E(x11191,x11192)+E(f816(x11193,x11191),f816(x11193,x11192)) % 186.01/186.05 [1120]~E(x11201,x11202)+E(f156(x11201,x11203,x11204,x11205,x11206),f156(x11202,x11203,x11204,x11205,x11206)) % 186.01/186.05 [1121]~E(x11211,x11212)+E(f156(x11213,x11211,x11214,x11215,x11216),f156(x11213,x11212,x11214,x11215,x11216)) % 186.01/186.05 [1122]~E(x11221,x11222)+E(f156(x11223,x11224,x11221,x11225,x11226),f156(x11223,x11224,x11222,x11225,x11226)) % 186.01/186.05 [1123]~E(x11231,x11232)+E(f156(x11233,x11234,x11235,x11231,x11236),f156(x11233,x11234,x11235,x11232,x11236)) % 186.01/186.05 [1124]~E(x11241,x11242)+E(f156(x11243,x11244,x11245,x11246,x11241),f156(x11243,x11244,x11245,x11246,x11242)) % 186.01/186.05 [1125]~E(x11251,x11252)+E(f732(x11251,x11253),f732(x11252,x11253)) % 186.01/186.05 [1126]~E(x11261,x11262)+E(f732(x11263,x11261),f732(x11263,x11262)) % 186.01/186.05 [1127]~E(x11271,x11272)+E(f298(x11271,x11273,x11274,x11275),f298(x11272,x11273,x11274,x11275)) % 186.01/186.05 [1128]~E(x11281,x11282)+E(f298(x11283,x11281,x11284,x11285),f298(x11283,x11282,x11284,x11285)) % 186.01/186.05 [1129]~E(x11291,x11292)+E(f298(x11293,x11294,x11291,x11295),f298(x11293,x11294,x11292,x11295)) % 186.01/186.05 [1130]~E(x11301,x11302)+E(f298(x11303,x11304,x11305,x11301),f298(x11303,x11304,x11305,x11302)) % 186.01/186.05 [1131]~E(x11311,x11312)+E(f743(x11311,x11313,x11314,x11315,x11316),f743(x11312,x11313,x11314,x11315,x11316)) % 186.01/186.05 [1132]~E(x11321,x11322)+E(f743(x11323,x11321,x11324,x11325,x11326),f743(x11323,x11322,x11324,x11325,x11326)) % 186.01/186.05 [1133]~E(x11331,x11332)+E(f743(x11333,x11334,x11331,x11335,x11336),f743(x11333,x11334,x11332,x11335,x11336)) % 186.01/186.05 [1134]~E(x11341,x11342)+E(f743(x11343,x11344,x11345,x11341,x11346),f743(x11343,x11344,x11345,x11342,x11346)) % 186.01/186.05 [1135]~E(x11351,x11352)+E(f743(x11353,x11354,x11355,x11356,x11351),f743(x11353,x11354,x11355,x11356,x11352)) % 186.01/186.05 [1136]~E(x11361,x11362)+E(f351(x11361,x11363,x11364),f351(x11362,x11363,x11364)) % 186.01/186.05 [1137]~E(x11371,x11372)+E(f351(x11373,x11371,x11374),f351(x11373,x11372,x11374)) % 186.01/186.05 [1138]~E(x11381,x11382)+E(f351(x11383,x11384,x11381),f351(x11383,x11384,x11382)) % 186.01/186.05 [1139]~E(x11391,x11392)+E(f471(x11391,x11393,x11394),f471(x11392,x11393,x11394)) % 186.01/186.05 [1140]~E(x11401,x11402)+E(f471(x11403,x11401,x11404),f471(x11403,x11402,x11404)) % 186.01/186.05 [1141]~E(x11411,x11412)+E(f471(x11413,x11414,x11411),f471(x11413,x11414,x11412)) % 186.01/186.05 [1142]~E(x11421,x11422)+E(f913(x11421,x11423),f913(x11422,x11423)) % 186.01/186.05 [1143]~E(x11431,x11432)+E(f913(x11433,x11431),f913(x11433,x11432)) % 186.01/186.05 [1144]~E(x11441,x11442)+E(f83(x11441,x11443,x11444,x11445),f83(x11442,x11443,x11444,x11445)) % 186.01/186.05 [1145]~E(x11451,x11452)+E(f83(x11453,x11451,x11454,x11455),f83(x11453,x11452,x11454,x11455)) % 186.01/186.05 [1146]~E(x11461,x11462)+E(f83(x11463,x11464,x11461,x11465),f83(x11463,x11464,x11462,x11465)) % 186.01/186.05 [1147]~E(x11471,x11472)+E(f83(x11473,x11474,x11475,x11471),f83(x11473,x11474,x11475,x11472)) % 186.01/186.05 [1148]~E(x11481,x11482)+E(f569(x11481,x11483,x11484),f569(x11482,x11483,x11484)) % 186.01/186.05 [1149]~E(x11491,x11492)+E(f569(x11493,x11491,x11494),f569(x11493,x11492,x11494)) % 186.01/186.05 [1150]~E(x11501,x11502)+E(f569(x11503,x11504,x11501),f569(x11503,x11504,x11502)) % 186.01/186.05 [1151]~E(x11511,x11512)+E(f694(x11511,x11513),f694(x11512,x11513)) % 186.01/186.05 [1152]~E(x11521,x11522)+E(f694(x11523,x11521),f694(x11523,x11522)) % 186.01/186.05 [1153]~E(x11531,x11532)+E(f660(x11531,x11533,x11534,x11535,x11536,x11537,x11538),f660(x11532,x11533,x11534,x11535,x11536,x11537,x11538)) % 186.01/186.05 [1154]~E(x11541,x11542)+E(f660(x11543,x11541,x11544,x11545,x11546,x11547,x11548),f660(x11543,x11542,x11544,x11545,x11546,x11547,x11548)) % 186.01/186.05 [1155]~E(x11551,x11552)+E(f660(x11553,x11554,x11551,x11555,x11556,x11557,x11558),f660(x11553,x11554,x11552,x11555,x11556,x11557,x11558)) % 186.01/186.05 [1156]~E(x11561,x11562)+E(f660(x11563,x11564,x11565,x11561,x11566,x11567,x11568),f660(x11563,x11564,x11565,x11562,x11566,x11567,x11568)) % 186.01/186.05 [1157]~E(x11571,x11572)+E(f660(x11573,x11574,x11575,x11576,x11571,x11577,x11578),f660(x11573,x11574,x11575,x11576,x11572,x11577,x11578)) % 186.01/186.05 [1158]~E(x11581,x11582)+E(f660(x11583,x11584,x11585,x11586,x11587,x11581,x11588),f660(x11583,x11584,x11585,x11586,x11587,x11582,x11588)) % 186.01/186.05 [1159]~E(x11591,x11592)+E(f660(x11593,x11594,x11595,x11596,x11597,x11598,x11591),f660(x11593,x11594,x11595,x11596,x11597,x11598,x11592)) % 186.01/186.05 [1160]~E(x11601,x11602)+E(f864(x11601,x11603,x11604,x11605,x11606,x11607,x11608,x11609),f864(x11602,x11603,x11604,x11605,x11606,x11607,x11608,x11609)) % 186.01/186.05 [1161]~E(x11611,x11612)+E(f864(x11613,x11611,x11614,x11615,x11616,x11617,x11618,x11619),f864(x11613,x11612,x11614,x11615,x11616,x11617,x11618,x11619)) % 186.01/186.05 [1162]~E(x11621,x11622)+E(f864(x11623,x11624,x11621,x11625,x11626,x11627,x11628,x11629),f864(x11623,x11624,x11622,x11625,x11626,x11627,x11628,x11629)) % 186.01/186.05 [1163]~E(x11631,x11632)+E(f864(x11633,x11634,x11635,x11631,x11636,x11637,x11638,x11639),f864(x11633,x11634,x11635,x11632,x11636,x11637,x11638,x11639)) % 186.01/186.05 [1164]~E(x11641,x11642)+E(f864(x11643,x11644,x11645,x11646,x11641,x11647,x11648,x11649),f864(x11643,x11644,x11645,x11646,x11642,x11647,x11648,x11649)) % 186.01/186.05 [1165]~E(x11651,x11652)+E(f864(x11653,x11654,x11655,x11656,x11657,x11651,x11658,x11659),f864(x11653,x11654,x11655,x11656,x11657,x11652,x11658,x11659)) % 186.01/186.05 [1166]~E(x11661,x11662)+E(f864(x11663,x11664,x11665,x11666,x11667,x11668,x11661,x11669),f864(x11663,x11664,x11665,x11666,x11667,x11668,x11662,x11669)) % 186.01/186.05 [1167]~E(x11671,x11672)+E(f864(x11673,x11674,x11675,x11676,x11677,x11678,x11679,x11671),f864(x11673,x11674,x11675,x11676,x11677,x11678,x11679,x11672)) % 186.01/186.05 [1168]~E(x11681,x11682)+E(f592(x11681,x11683,x11684,x11685),f592(x11682,x11683,x11684,x11685)) % 186.01/186.05 [1169]~E(x11691,x11692)+E(f592(x11693,x11691,x11694,x11695),f592(x11693,x11692,x11694,x11695)) % 186.01/186.05 [1170]~E(x11701,x11702)+E(f592(x11703,x11704,x11701,x11705),f592(x11703,x11704,x11702,x11705)) % 186.01/186.05 [1171]~E(x11711,x11712)+E(f592(x11713,x11714,x11715,x11711),f592(x11713,x11714,x11715,x11712)) % 186.01/186.05 [1172]~E(x11721,x11722)+E(f329(x11721,x11723,x11724),f329(x11722,x11723,x11724)) % 186.01/186.05 [1173]~E(x11731,x11732)+E(f329(x11733,x11731,x11734),f329(x11733,x11732,x11734)) % 186.01/186.05 [1174]~E(x11741,x11742)+E(f329(x11743,x11744,x11741),f329(x11743,x11744,x11742)) % 186.01/186.05 [1175]~E(x11751,x11752)+E(f803(x11751,x11753,x11754,x11755),f803(x11752,x11753,x11754,x11755)) % 186.01/186.05 [1176]~E(x11761,x11762)+E(f803(x11763,x11761,x11764,x11765),f803(x11763,x11762,x11764,x11765)) % 186.01/186.05 [1177]~E(x11771,x11772)+E(f803(x11773,x11774,x11771,x11775),f803(x11773,x11774,x11772,x11775)) % 186.01/186.05 [1178]~E(x11781,x11782)+E(f803(x11783,x11784,x11785,x11781),f803(x11783,x11784,x11785,x11782)) % 186.01/186.05 [1179]~E(x11791,x11792)+E(f843(x11791,x11793,x11794),f843(x11792,x11793,x11794)) % 186.01/186.05 [1180]~E(x11801,x11802)+E(f843(x11803,x11801,x11804),f843(x11803,x11802,x11804)) % 186.01/186.05 [1181]~E(x11811,x11812)+E(f843(x11813,x11814,x11811),f843(x11813,x11814,x11812)) % 186.01/186.05 [1182]~E(x11821,x11822)+E(f698(x11821,x11823,x11824),f698(x11822,x11823,x11824)) % 186.01/186.05 [1183]~E(x11831,x11832)+E(f698(x11833,x11831,x11834),f698(x11833,x11832,x11834)) % 186.01/186.05 [1184]~E(x11841,x11842)+E(f698(x11843,x11844,x11841),f698(x11843,x11844,x11842)) % 186.01/186.05 [1185]~E(x11851,x11852)+E(f811(x11851,x11853,x11854,x11855),f811(x11852,x11853,x11854,x11855)) % 186.01/186.05 [1186]~E(x11861,x11862)+E(f811(x11863,x11861,x11864,x11865),f811(x11863,x11862,x11864,x11865)) % 186.01/186.05 [1187]~E(x11871,x11872)+E(f811(x11873,x11874,x11871,x11875),f811(x11873,x11874,x11872,x11875)) % 186.01/186.05 [1188]~E(x11881,x11882)+E(f811(x11883,x11884,x11885,x11881),f811(x11883,x11884,x11885,x11882)) % 186.01/186.05 [1189]~E(x11891,x11892)+E(f139(x11891,x11893),f139(x11892,x11893)) % 186.01/186.05 [1190]~E(x11901,x11902)+E(f139(x11903,x11901),f139(x11903,x11902)) % 186.01/186.05 [1191]~E(x11911,x11912)+E(f690(x11911,x11913),f690(x11912,x11913)) % 186.01/186.05 [1192]~E(x11921,x11922)+E(f690(x11923,x11921),f690(x11923,x11922)) % 186.01/186.05 [1193]~E(x11931,x11932)+E(f651(x11931,x11933,x11934,x11935,x11936),f651(x11932,x11933,x11934,x11935,x11936)) % 186.01/186.05 [1194]~E(x11941,x11942)+E(f651(x11943,x11941,x11944,x11945,x11946),f651(x11943,x11942,x11944,x11945,x11946)) % 186.01/186.05 [1195]~E(x11951,x11952)+E(f651(x11953,x11954,x11951,x11955,x11956),f651(x11953,x11954,x11952,x11955,x11956)) % 186.01/186.05 [1196]~E(x11961,x11962)+E(f651(x11963,x11964,x11965,x11961,x11966),f651(x11963,x11964,x11965,x11962,x11966)) % 186.01/186.05 [1197]~E(x11971,x11972)+E(f651(x11973,x11974,x11975,x11976,x11971),f651(x11973,x11974,x11975,x11976,x11972)) % 186.01/186.05 [1198]~E(x11981,x11982)+E(f593(x11981,x11983),f593(x11982,x11983)) % 186.01/186.05 [1199]~E(x11991,x11992)+E(f593(x11993,x11991),f593(x11993,x11992)) % 186.01/186.05 [1200]~E(x12001,x12002)+E(f65(x12001,x12003,x12004,x12005),f65(x12002,x12003,x12004,x12005)) % 186.01/186.05 [1201]~E(x12011,x12012)+E(f65(x12013,x12011,x12014,x12015),f65(x12013,x12012,x12014,x12015)) % 186.01/186.05 [1202]~E(x12021,x12022)+E(f65(x12023,x12024,x12021,x12025),f65(x12023,x12024,x12022,x12025)) % 186.01/186.05 [1203]~E(x12031,x12032)+E(f65(x12033,x12034,x12035,x12031),f65(x12033,x12034,x12035,x12032)) % 186.01/186.05 [1204]~E(x12041,x12042)+E(f382(x12041,x12043),f382(x12042,x12043)) % 186.01/186.05 [1205]~E(x12051,x12052)+E(f382(x12053,x12051),f382(x12053,x12052)) % 186.01/186.05 [1206]~E(x12061,x12062)+E(f342(x12061,x12063),f342(x12062,x12063)) % 186.01/186.05 [1207]~E(x12071,x12072)+E(f342(x12073,x12071),f342(x12073,x12072)) % 186.01/186.05 [1208]~E(x12081,x12082)+E(f566(x12081,x12083,x12084),f566(x12082,x12083,x12084)) % 186.01/186.05 [1209]~E(x12091,x12092)+E(f566(x12093,x12091,x12094),f566(x12093,x12092,x12094)) % 186.01/186.05 [1210]~E(x12101,x12102)+E(f566(x12103,x12104,x12101),f566(x12103,x12104,x12102)) % 186.01/186.05 [1211]~E(x12111,x12112)+E(f755(x12111,x12113,x12114,x12115,x12116,x12117,x12118),f755(x12112,x12113,x12114,x12115,x12116,x12117,x12118)) % 186.01/186.05 [1212]~E(x12121,x12122)+E(f755(x12123,x12121,x12124,x12125,x12126,x12127,x12128),f755(x12123,x12122,x12124,x12125,x12126,x12127,x12128)) % 186.01/186.05 [1213]~E(x12131,x12132)+E(f755(x12133,x12134,x12131,x12135,x12136,x12137,x12138),f755(x12133,x12134,x12132,x12135,x12136,x12137,x12138)) % 186.01/186.05 [1214]~E(x12141,x12142)+E(f755(x12143,x12144,x12145,x12141,x12146,x12147,x12148),f755(x12143,x12144,x12145,x12142,x12146,x12147,x12148)) % 186.01/186.05 [1215]~E(x12151,x12152)+E(f755(x12153,x12154,x12155,x12156,x12151,x12157,x12158),f755(x12153,x12154,x12155,x12156,x12152,x12157,x12158)) % 186.01/186.05 [1216]~E(x12161,x12162)+E(f755(x12163,x12164,x12165,x12166,x12167,x12161,x12168),f755(x12163,x12164,x12165,x12166,x12167,x12162,x12168)) % 186.01/186.05 [1217]~E(x12171,x12172)+E(f755(x12173,x12174,x12175,x12176,x12177,x12178,x12171),f755(x12173,x12174,x12175,x12176,x12177,x12178,x12172)) % 186.01/186.05 [1218]~E(x12181,x12182)+E(f349(x12181,x12183),f349(x12182,x12183)) % 186.01/186.05 [1219]~E(x12191,x12192)+E(f349(x12193,x12191),f349(x12193,x12192)) % 186.01/186.05 [1220]~E(x12201,x12202)+E(f236(x12201,x12203),f236(x12202,x12203)) % 186.01/186.05 [1221]~E(x12211,x12212)+E(f236(x12213,x12211),f236(x12213,x12212)) % 186.01/186.05 [1222]~E(x12221,x12222)+E(f824(x12221,x12223,x12224,x12225,x12226),f824(x12222,x12223,x12224,x12225,x12226)) % 186.01/186.05 [1223]~E(x12231,x12232)+E(f824(x12233,x12231,x12234,x12235,x12236),f824(x12233,x12232,x12234,x12235,x12236)) % 186.01/186.05 [1224]~E(x12241,x12242)+E(f824(x12243,x12244,x12241,x12245,x12246),f824(x12243,x12244,x12242,x12245,x12246)) % 186.01/186.05 [1225]~E(x12251,x12252)+E(f824(x12253,x12254,x12255,x12251,x12256),f824(x12253,x12254,x12255,x12252,x12256)) % 186.01/186.05 [1226]~E(x12261,x12262)+E(f824(x12263,x12264,x12265,x12266,x12261),f824(x12263,x12264,x12265,x12266,x12262)) % 186.01/186.05 [1227]~E(x12271,x12272)+E(f722(x12271,x12273,x12274,x12275),f722(x12272,x12273,x12274,x12275)) % 186.01/186.05 [1228]~E(x12281,x12282)+E(f722(x12283,x12281,x12284,x12285),f722(x12283,x12282,x12284,x12285)) % 186.01/186.05 [1229]~E(x12291,x12292)+E(f722(x12293,x12294,x12291,x12295),f722(x12293,x12294,x12292,x12295)) % 186.01/186.05 [1230]~E(x12301,x12302)+E(f722(x12303,x12304,x12305,x12301),f722(x12303,x12304,x12305,x12302)) % 186.01/186.05 [1231]~E(x12311,x12312)+E(f910(x12311,x12313,x12314,x12315,x12316,x12317),f910(x12312,x12313,x12314,x12315,x12316,x12317)) % 186.01/186.05 [1232]~E(x12321,x12322)+E(f910(x12323,x12321,x12324,x12325,x12326,x12327),f910(x12323,x12322,x12324,x12325,x12326,x12327)) % 186.01/186.05 [1233]~E(x12331,x12332)+E(f910(x12333,x12334,x12331,x12335,x12336,x12337),f910(x12333,x12334,x12332,x12335,x12336,x12337)) % 186.01/186.05 [1234]~E(x12341,x12342)+E(f910(x12343,x12344,x12345,x12341,x12346,x12347),f910(x12343,x12344,x12345,x12342,x12346,x12347)) % 186.01/186.05 [1235]~E(x12351,x12352)+E(f910(x12353,x12354,x12355,x12356,x12351,x12357),f910(x12353,x12354,x12355,x12356,x12352,x12357)) % 186.01/186.05 [1236]~E(x12361,x12362)+E(f910(x12363,x12364,x12365,x12366,x12367,x12361),f910(x12363,x12364,x12365,x12366,x12367,x12362)) % 186.01/186.05 [1237]~E(x12371,x12372)+E(f669(x12371,x12373,x12374,x12375,x12376,x12377),f669(x12372,x12373,x12374,x12375,x12376,x12377)) % 186.01/186.05 [1238]~E(x12381,x12382)+E(f669(x12383,x12381,x12384,x12385,x12386,x12387),f669(x12383,x12382,x12384,x12385,x12386,x12387)) % 186.01/186.05 [1239]~E(x12391,x12392)+E(f669(x12393,x12394,x12391,x12395,x12396,x12397),f669(x12393,x12394,x12392,x12395,x12396,x12397)) % 186.01/186.05 [1240]~E(x12401,x12402)+E(f669(x12403,x12404,x12405,x12401,x12406,x12407),f669(x12403,x12404,x12405,x12402,x12406,x12407)) % 186.01/186.05 [1241]~E(x12411,x12412)+E(f669(x12413,x12414,x12415,x12416,x12411,x12417),f669(x12413,x12414,x12415,x12416,x12412,x12417)) % 186.01/186.05 [1242]~E(x12421,x12422)+E(f669(x12423,x12424,x12425,x12426,x12427,x12421),f669(x12423,x12424,x12425,x12426,x12427,x12422)) % 186.01/186.05 [1243]~E(x12431,x12432)+E(f276(x12431,x12433),f276(x12432,x12433)) % 186.01/186.05 [1244]~E(x12441,x12442)+E(f276(x12443,x12441),f276(x12443,x12442)) % 186.01/186.05 [1245]~E(x12451,x12452)+E(f356(x12451,x12453,x12454,x12455),f356(x12452,x12453,x12454,x12455)) % 186.01/186.05 [1246]~E(x12461,x12462)+E(f356(x12463,x12461,x12464,x12465),f356(x12463,x12462,x12464,x12465)) % 186.01/186.05 [1247]~E(x12471,x12472)+E(f356(x12473,x12474,x12471,x12475),f356(x12473,x12474,x12472,x12475)) % 186.01/186.05 [1248]~E(x12481,x12482)+E(f356(x12483,x12484,x12485,x12481),f356(x12483,x12484,x12485,x12482)) % 186.01/186.05 [1249]~E(x12491,x12492)+E(f135(x12491,x12493),f135(x12492,x12493)) % 186.01/186.05 [1250]~E(x12501,x12502)+E(f135(x12503,x12501),f135(x12503,x12502)) % 186.01/186.05 [1251]~E(x12511,x12512)+E(f48(x12511),f48(x12512)) % 186.01/186.05 [1252]~E(x12521,x12522)+E(f560(x12521,x12523,x12524),f560(x12522,x12523,x12524)) % 186.01/186.05 [1253]~E(x12531,x12532)+E(f560(x12533,x12531,x12534),f560(x12533,x12532,x12534)) % 186.01/186.05 [1254]~E(x12541,x12542)+E(f560(x12543,x12544,x12541),f560(x12543,x12544,x12542)) % 186.01/186.05 [1255]~E(x12551,x12552)+E(f353(x12551,x12553,x12554,x12555,x12556,x12557,x12558),f353(x12552,x12553,x12554,x12555,x12556,x12557,x12558)) % 186.01/186.05 [1256]~E(x12561,x12562)+E(f353(x12563,x12561,x12564,x12565,x12566,x12567,x12568),f353(x12563,x12562,x12564,x12565,x12566,x12567,x12568)) % 186.01/186.05 [1257]~E(x12571,x12572)+E(f353(x12573,x12574,x12571,x12575,x12576,x12577,x12578),f353(x12573,x12574,x12572,x12575,x12576,x12577,x12578)) % 186.01/186.05 [1258]~E(x12581,x12582)+E(f353(x12583,x12584,x12585,x12581,x12586,x12587,x12588),f353(x12583,x12584,x12585,x12582,x12586,x12587,x12588)) % 186.01/186.05 [1259]~E(x12591,x12592)+E(f353(x12593,x12594,x12595,x12596,x12591,x12597,x12598),f353(x12593,x12594,x12595,x12596,x12592,x12597,x12598)) % 186.01/186.05 [1260]~E(x12601,x12602)+E(f353(x12603,x12604,x12605,x12606,x12607,x12601,x12608),f353(x12603,x12604,x12605,x12606,x12607,x12602,x12608)) % 186.01/186.05 [1261]~E(x12611,x12612)+E(f353(x12613,x12614,x12615,x12616,x12617,x12618,x12611),f353(x12613,x12614,x12615,x12616,x12617,x12618,x12612)) % 186.01/186.05 [1262]~E(x12621,x12622)+E(f619(x12621,x12623,x12624,x12625,x12626),f619(x12622,x12623,x12624,x12625,x12626)) % 186.01/186.05 [1263]~E(x12631,x12632)+E(f619(x12633,x12631,x12634,x12635,x12636),f619(x12633,x12632,x12634,x12635,x12636)) % 186.01/186.05 [1264]~E(x12641,x12642)+E(f619(x12643,x12644,x12641,x12645,x12646),f619(x12643,x12644,x12642,x12645,x12646)) % 186.01/186.05 [1265]~E(x12651,x12652)+E(f619(x12653,x12654,x12655,x12651,x12656),f619(x12653,x12654,x12655,x12652,x12656)) % 186.01/186.05 [1266]~E(x12661,x12662)+E(f619(x12663,x12664,x12665,x12666,x12661),f619(x12663,x12664,x12665,x12666,x12662)) % 186.01/186.05 [1267]~E(x12671,x12672)+E(f371(x12671,x12673),f371(x12672,x12673)) % 186.01/186.05 [1268]~E(x12681,x12682)+E(f371(x12683,x12681),f371(x12683,x12682)) % 186.01/186.05 [1269]~E(x12691,x12692)+E(f736(x12691,x12693,x12694),f736(x12692,x12693,x12694)) % 186.01/186.05 [1270]~E(x12701,x12702)+E(f736(x12703,x12701,x12704),f736(x12703,x12702,x12704)) % 186.01/186.05 [1271]~E(x12711,x12712)+E(f736(x12713,x12714,x12711),f736(x12713,x12714,x12712)) % 186.01/186.05 [1272]~E(x12721,x12722)+E(f283(x12721,x12723),f283(x12722,x12723)) % 186.01/186.05 [1273]~E(x12731,x12732)+E(f283(x12733,x12731),f283(x12733,x12732)) % 186.01/186.05 [1274]~E(x12741,x12742)+E(f413(x12741,x12743),f413(x12742,x12743)) % 186.01/186.05 [1275]~E(x12751,x12752)+E(f413(x12753,x12751),f413(x12753,x12752)) % 186.01/186.05 [1276]~E(x12761,x12762)+E(f817(x12761,x12763),f817(x12762,x12763)) % 186.01/186.05 [1277]~E(x12771,x12772)+E(f817(x12773,x12771),f817(x12773,x12772)) % 186.01/186.05 [1278]~E(x12781,x12782)+E(f895(x12781,x12783,x12784,x12785),f895(x12782,x12783,x12784,x12785)) % 186.01/186.05 [1279]~E(x12791,x12792)+E(f895(x12793,x12791,x12794,x12795),f895(x12793,x12792,x12794,x12795)) % 186.01/186.05 [1280]~E(x12801,x12802)+E(f895(x12803,x12804,x12801,x12805),f895(x12803,x12804,x12802,x12805)) % 186.01/186.05 [1281]~E(x12811,x12812)+E(f895(x12813,x12814,x12815,x12811),f895(x12813,x12814,x12815,x12812)) % 186.01/186.05 [1282]~E(x12821,x12822)+E(f555(x12821,x12823,x12824,x12825,x12826),f555(x12822,x12823,x12824,x12825,x12826)) % 186.01/186.05 [1283]~E(x12831,x12832)+E(f555(x12833,x12831,x12834,x12835,x12836),f555(x12833,x12832,x12834,x12835,x12836)) % 186.01/186.05 [1284]~E(x12841,x12842)+E(f555(x12843,x12844,x12841,x12845,x12846),f555(x12843,x12844,x12842,x12845,x12846)) % 186.01/186.05 [1285]~E(x12851,x12852)+E(f555(x12853,x12854,x12855,x12851,x12856),f555(x12853,x12854,x12855,x12852,x12856)) % 186.01/186.05 [1286]~E(x12861,x12862)+E(f555(x12863,x12864,x12865,x12866,x12861),f555(x12863,x12864,x12865,x12866,x12862)) % 186.01/186.05 [1287]~E(x12871,x12872)+E(f576(x12871,x12873),f576(x12872,x12873)) % 186.01/186.05 [1288]~E(x12881,x12882)+E(f576(x12883,x12881),f576(x12883,x12882)) % 186.01/186.05 [1289]~E(x12891,x12892)+E(f836(x12891,x12893,x12894,x12895,x12896,x12897),f836(x12892,x12893,x12894,x12895,x12896,x12897)) % 186.01/186.05 [1290]~E(x12901,x12902)+E(f836(x12903,x12901,x12904,x12905,x12906,x12907),f836(x12903,x12902,x12904,x12905,x12906,x12907)) % 186.01/186.05 [1291]~E(x12911,x12912)+E(f836(x12913,x12914,x12911,x12915,x12916,x12917),f836(x12913,x12914,x12912,x12915,x12916,x12917)) % 186.01/186.05 [1292]~E(x12921,x12922)+E(f836(x12923,x12924,x12925,x12921,x12926,x12927),f836(x12923,x12924,x12925,x12922,x12926,x12927)) % 186.01/186.05 [1293]~E(x12931,x12932)+E(f836(x12933,x12934,x12935,x12936,x12931,x12937),f836(x12933,x12934,x12935,x12936,x12932,x12937)) % 186.01/186.05 [1294]~E(x12941,x12942)+E(f836(x12943,x12944,x12945,x12946,x12947,x12941),f836(x12943,x12944,x12945,x12946,x12947,x12942)) % 186.01/186.05 [1295]~E(x12951,x12952)+E(f208(x12951,x12953),f208(x12952,x12953)) % 186.01/186.05 [1296]~E(x12961,x12962)+E(f208(x12963,x12961),f208(x12963,x12962)) % 186.01/186.05 [1297]~E(x12971,x12972)+E(f68(x12971,x12973,x12974),f68(x12972,x12973,x12974)) % 186.01/186.05 [1298]~E(x12981,x12982)+E(f68(x12983,x12981,x12984),f68(x12983,x12982,x12984)) % 186.01/186.05 [1299]~E(x12991,x12992)+E(f68(x12993,x12994,x12991),f68(x12993,x12994,x12992)) % 186.01/186.05 [1300]~E(x13001,x13002)+E(f886(x13001,x13003,x13004,x13005),f886(x13002,x13003,x13004,x13005)) % 186.01/186.05 [1301]~E(x13011,x13012)+E(f886(x13013,x13011,x13014,x13015),f886(x13013,x13012,x13014,x13015)) % 186.01/186.05 [1302]~E(x13021,x13022)+E(f886(x13023,x13024,x13021,x13025),f886(x13023,x13024,x13022,x13025)) % 186.01/186.05 [1303]~E(x13031,x13032)+E(f886(x13033,x13034,x13035,x13031),f886(x13033,x13034,x13035,x13032)) % 186.01/186.05 [1304]~E(x13041,x13042)+E(f476(x13041,x13043,x13044),f476(x13042,x13043,x13044)) % 186.01/186.05 [1305]~E(x13051,x13052)+E(f476(x13053,x13051,x13054),f476(x13053,x13052,x13054)) % 186.01/186.05 [1306]~E(x13061,x13062)+E(f476(x13063,x13064,x13061),f476(x13063,x13064,x13062)) % 186.01/186.05 [1307]~E(x13071,x13072)+E(f799(x13071,x13073,x13074,x13075,x13076,x13077,x13078),f799(x13072,x13073,x13074,x13075,x13076,x13077,x13078)) % 186.01/186.05 [1308]~E(x13081,x13082)+E(f799(x13083,x13081,x13084,x13085,x13086,x13087,x13088),f799(x13083,x13082,x13084,x13085,x13086,x13087,x13088)) % 186.01/186.05 [1309]~E(x13091,x13092)+E(f799(x13093,x13094,x13091,x13095,x13096,x13097,x13098),f799(x13093,x13094,x13092,x13095,x13096,x13097,x13098)) % 186.01/186.05 [1310]~E(x13101,x13102)+E(f799(x13103,x13104,x13105,x13101,x13106,x13107,x13108),f799(x13103,x13104,x13105,x13102,x13106,x13107,x13108)) % 186.01/186.05 [1311]~E(x13111,x13112)+E(f799(x13113,x13114,x13115,x13116,x13111,x13117,x13118),f799(x13113,x13114,x13115,x13116,x13112,x13117,x13118)) % 186.01/186.05 [1312]~E(x13121,x13122)+E(f799(x13123,x13124,x13125,x13126,x13127,x13121,x13128),f799(x13123,x13124,x13125,x13126,x13127,x13122,x13128)) % 186.01/186.05 [1313]~E(x13131,x13132)+E(f799(x13133,x13134,x13135,x13136,x13137,x13138,x13131),f799(x13133,x13134,x13135,x13136,x13137,x13138,x13132)) % 186.01/186.05 [1314]~E(x13141,x13142)+E(f142(x13141),f142(x13142)) % 186.01/186.05 [1315]~E(x13151,x13152)+E(f687(x13151,x13153,x13154),f687(x13152,x13153,x13154)) % 186.01/186.05 [1316]~E(x13161,x13162)+E(f687(x13163,x13161,x13164),f687(x13163,x13162,x13164)) % 186.01/186.05 [1317]~E(x13171,x13172)+E(f687(x13173,x13174,x13171),f687(x13173,x13174,x13172)) % 186.01/186.05 [1318]~E(x13181,x13182)+E(f447(x13181,x13183),f447(x13182,x13183)) % 186.01/186.05 [1319]~E(x13191,x13192)+E(f447(x13193,x13191),f447(x13193,x13192)) % 186.01/186.05 [1320]~E(x13201,x13202)+E(f124(x13201,x13203,x13204),f124(x13202,x13203,x13204)) % 186.01/186.05 [1321]~E(x13211,x13212)+E(f124(x13213,x13211,x13214),f124(x13213,x13212,x13214)) % 186.01/186.05 [1322]~E(x13221,x13222)+E(f124(x13223,x13224,x13221),f124(x13223,x13224,x13222)) % 186.01/186.05 [1323]~E(x13231,x13232)+E(f668(x13231,x13233,x13234,x13235,x13236,x13237),f668(x13232,x13233,x13234,x13235,x13236,x13237)) % 186.01/186.05 [1324]~E(x13241,x13242)+E(f668(x13243,x13241,x13244,x13245,x13246,x13247),f668(x13243,x13242,x13244,x13245,x13246,x13247)) % 186.01/186.05 [1325]~E(x13251,x13252)+E(f668(x13253,x13254,x13251,x13255,x13256,x13257),f668(x13253,x13254,x13252,x13255,x13256,x13257)) % 186.01/186.05 [1326]~E(x13261,x13262)+E(f668(x13263,x13264,x13265,x13261,x13266,x13267),f668(x13263,x13264,x13265,x13262,x13266,x13267)) % 186.01/186.05 [1327]~E(x13271,x13272)+E(f668(x13273,x13274,x13275,x13276,x13271,x13277),f668(x13273,x13274,x13275,x13276,x13272,x13277)) % 186.01/186.05 [1328]~E(x13281,x13282)+E(f668(x13283,x13284,x13285,x13286,x13287,x13281),f668(x13283,x13284,x13285,x13286,x13287,x13282)) % 186.01/186.05 [1329]~E(x13291,x13292)+E(f201(x13291,x13293),f201(x13292,x13293)) % 186.01/186.05 [1330]~E(x13301,x13302)+E(f201(x13303,x13301),f201(x13303,x13302)) % 186.01/186.05 [1331]~E(x13311,x13312)+E(f700(x13311,x13313,x13314,x13315),f700(x13312,x13313,x13314,x13315)) % 186.01/186.05 [1332]~E(x13321,x13322)+E(f700(x13323,x13321,x13324,x13325),f700(x13323,x13322,x13324,x13325)) % 186.01/186.05 [1333]~E(x13331,x13332)+E(f700(x13333,x13334,x13331,x13335),f700(x13333,x13334,x13332,x13335)) % 186.01/186.05 [1334]~E(x13341,x13342)+E(f700(x13343,x13344,x13345,x13341),f700(x13343,x13344,x13345,x13342)) % 186.01/186.05 [1335]~E(x13351,x13352)+E(f779(x13351,x13353,x13354),f779(x13352,x13353,x13354)) % 186.01/186.05 [1336]~E(x13361,x13362)+E(f779(x13363,x13361,x13364),f779(x13363,x13362,x13364)) % 186.01/186.05 [1337]~E(x13371,x13372)+E(f779(x13373,x13374,x13371),f779(x13373,x13374,x13372)) % 186.01/186.05 [1338]~E(x13381,x13382)+E(f663(x13381,x13383,x13384,x13385,x13386),f663(x13382,x13383,x13384,x13385,x13386)) % 186.01/186.05 [1339]~E(x13391,x13392)+E(f663(x13393,x13391,x13394,x13395,x13396),f663(x13393,x13392,x13394,x13395,x13396)) % 186.01/186.05 [1340]~E(x13401,x13402)+E(f663(x13403,x13404,x13401,x13405,x13406),f663(x13403,x13404,x13402,x13405,x13406)) % 186.01/186.05 [1341]~E(x13411,x13412)+E(f663(x13413,x13414,x13415,x13411,x13416),f663(x13413,x13414,x13415,x13412,x13416)) % 186.01/186.05 [1342]~E(x13421,x13422)+E(f663(x13423,x13424,x13425,x13426,x13421),f663(x13423,x13424,x13425,x13426,x13422)) % 186.01/186.05 [1343]~E(x13431,x13432)+E(f288(x13431,x13433,x13434,x13435),f288(x13432,x13433,x13434,x13435)) % 186.01/186.05 [1344]~E(x13441,x13442)+E(f288(x13443,x13441,x13444,x13445),f288(x13443,x13442,x13444,x13445)) % 186.01/186.05 [1345]~E(x13451,x13452)+E(f288(x13453,x13454,x13451,x13455),f288(x13453,x13454,x13452,x13455)) % 186.01/186.05 [1346]~E(x13461,x13462)+E(f288(x13463,x13464,x13465,x13461),f288(x13463,x13464,x13465,x13462)) % 186.01/186.05 [1347]~E(x13471,x13472)+E(f805(x13471,x13473,x13474),f805(x13472,x13473,x13474)) % 186.01/186.05 [1348]~E(x13481,x13482)+E(f805(x13483,x13481,x13484),f805(x13483,x13482,x13484)) % 186.01/186.05 [1349]~E(x13491,x13492)+E(f805(x13493,x13494,x13491),f805(x13493,x13494,x13492)) % 186.01/186.05 [1350]~E(x13501,x13502)+E(f180(x13501,x13503,x13504),f180(x13502,x13503,x13504)) % 186.01/186.05 [1351]~E(x13511,x13512)+E(f180(x13513,x13511,x13514),f180(x13513,x13512,x13514)) % 186.01/186.05 [1352]~E(x13521,x13522)+E(f180(x13523,x13524,x13521),f180(x13523,x13524,x13522)) % 186.01/186.05 [1353]~E(x13531,x13532)+E(f460(x13531,x13533,x13534),f460(x13532,x13533,x13534)) % 186.01/186.05 [1354]~E(x13541,x13542)+E(f460(x13543,x13541,x13544),f460(x13543,x13542,x13544)) % 186.01/186.05 [1355]~E(x13551,x13552)+E(f460(x13553,x13554,x13551),f460(x13553,x13554,x13552)) % 186.01/186.05 [1356]~E(x13561,x13562)+E(f878(x13561,x13563,x13564,x13565,x13566),f878(x13562,x13563,x13564,x13565,x13566)) % 186.01/186.05 [1357]~E(x13571,x13572)+E(f878(x13573,x13571,x13574,x13575,x13576),f878(x13573,x13572,x13574,x13575,x13576)) % 186.01/186.05 [1358]~E(x13581,x13582)+E(f878(x13583,x13584,x13581,x13585,x13586),f878(x13583,x13584,x13582,x13585,x13586)) % 186.01/186.05 [1359]~E(x13591,x13592)+E(f878(x13593,x13594,x13595,x13591,x13596),f878(x13593,x13594,x13595,x13592,x13596)) % 186.01/186.05 [1360]~E(x13601,x13602)+E(f878(x13603,x13604,x13605,x13606,x13601),f878(x13603,x13604,x13605,x13606,x13602)) % 186.01/186.05 [1361]~E(x13611,x13612)+E(f632(x13611,x13613,x13614,x13615),f632(x13612,x13613,x13614,x13615)) % 186.01/186.05 [1362]~E(x13621,x13622)+E(f632(x13623,x13621,x13624,x13625),f632(x13623,x13622,x13624,x13625)) % 186.01/186.05 [1363]~E(x13631,x13632)+E(f632(x13633,x13634,x13631,x13635),f632(x13633,x13634,x13632,x13635)) % 186.01/186.05 [1364]~E(x13641,x13642)+E(f632(x13643,x13644,x13645,x13641),f632(x13643,x13644,x13645,x13642)) % 186.01/186.05 [1365]~E(x13651,x13652)+E(f450(x13651,x13653),f450(x13652,x13653)) % 186.01/186.05 [1366]~E(x13661,x13662)+E(f450(x13663,x13661),f450(x13663,x13662)) % 186.01/186.05 [1367]~E(x13671,x13672)+E(f448(x13671,x13673),f448(x13672,x13673)) % 186.01/186.05 [1368]~E(x13681,x13682)+E(f448(x13683,x13681),f448(x13683,x13682)) % 186.01/186.05 [1369]~E(x13691,x13692)+E(f606(x13691,x13693,x13694),f606(x13692,x13693,x13694)) % 186.01/186.05 [1370]~E(x13701,x13702)+E(f606(x13703,x13701,x13704),f606(x13703,x13702,x13704)) % 186.01/186.05 [1371]~E(x13711,x13712)+E(f606(x13713,x13714,x13711),f606(x13713,x13714,x13712)) % 186.01/186.05 [1372]~E(x13721,x13722)+E(f870(x13721,x13723,x13724),f870(x13722,x13723,x13724)) % 186.01/186.05 [1373]~E(x13731,x13732)+E(f870(x13733,x13731,x13734),f870(x13733,x13732,x13734)) % 186.01/186.05 [1374]~E(x13741,x13742)+E(f870(x13743,x13744,x13741),f870(x13743,x13744,x13742)) % 186.01/186.05 [1375]~E(x13751,x13752)+E(f487(x13751,x13753,x13754),f487(x13752,x13753,x13754)) % 186.01/186.05 [1376]~E(x13761,x13762)+E(f487(x13763,x13761,x13764),f487(x13763,x13762,x13764)) % 186.01/186.05 [1377]~E(x13771,x13772)+E(f487(x13773,x13774,x13771),f487(x13773,x13774,x13772)) % 186.01/186.05 [1378]~E(x13781,x13782)+E(f428(x13781,x13783,x13784,x13785),f428(x13782,x13783,x13784,x13785)) % 186.01/186.05 [1379]~E(x13791,x13792)+E(f428(x13793,x13791,x13794,x13795),f428(x13793,x13792,x13794,x13795)) % 186.01/186.05 [1380]~E(x13801,x13802)+E(f428(x13803,x13804,x13801,x13805),f428(x13803,x13804,x13802,x13805)) % 186.01/186.05 [1381]~E(x13811,x13812)+E(f428(x13813,x13814,x13815,x13811),f428(x13813,x13814,x13815,x13812)) % 186.01/186.05 [1382]~E(x13821,x13822)+E(f595(x13821,x13823,x13824,x13825),f595(x13822,x13823,x13824,x13825)) % 186.01/186.05 [1383]~E(x13831,x13832)+E(f595(x13833,x13831,x13834,x13835),f595(x13833,x13832,x13834,x13835)) % 186.01/186.05 [1384]~E(x13841,x13842)+E(f595(x13843,x13844,x13841,x13845),f595(x13843,x13844,x13842,x13845)) % 186.01/186.05 [1385]~E(x13851,x13852)+E(f595(x13853,x13854,x13855,x13851),f595(x13853,x13854,x13855,x13852)) % 186.01/186.05 [1386]~E(x13861,x13862)+E(f791(x13861,x13863,x13864),f791(x13862,x13863,x13864)) % 186.01/186.05 [1387]~E(x13871,x13872)+E(f791(x13873,x13871,x13874),f791(x13873,x13872,x13874)) % 186.01/186.05 [1388]~E(x13881,x13882)+E(f791(x13883,x13884,x13881),f791(x13883,x13884,x13882)) % 186.01/186.05 [1389]~E(x13891,x13892)+E(f802(x13891,x13893,x13894,x13895),f802(x13892,x13893,x13894,x13895)) % 186.01/186.05 [1390]~E(x13901,x13902)+E(f802(x13903,x13901,x13904,x13905),f802(x13903,x13902,x13904,x13905)) % 186.01/186.05 [1391]~E(x13911,x13912)+E(f802(x13913,x13914,x13911,x13915),f802(x13913,x13914,x13912,x13915)) % 186.01/186.05 [1392]~E(x13921,x13922)+E(f802(x13923,x13924,x13925,x13921),f802(x13923,x13924,x13925,x13922)) % 186.01/186.05 [1393]~E(x13931,x13932)+E(f731(x13931,x13933),f731(x13932,x13933)) % 186.01/186.05 [1394]~E(x13941,x13942)+E(f731(x13943,x13941),f731(x13943,x13942)) % 186.01/186.05 [1395]~E(x13951,x13952)+E(f541(x13951,x13953,x13954,x13955,x13956),f541(x13952,x13953,x13954,x13955,x13956)) % 186.01/186.05 [1396]~E(x13961,x13962)+E(f541(x13963,x13961,x13964,x13965,x13966),f541(x13963,x13962,x13964,x13965,x13966)) % 186.01/186.05 [1397]~E(x13971,x13972)+E(f541(x13973,x13974,x13971,x13975,x13976),f541(x13973,x13974,x13972,x13975,x13976)) % 186.01/186.05 [1398]~E(x13981,x13982)+E(f541(x13983,x13984,x13985,x13981,x13986),f541(x13983,x13984,x13985,x13982,x13986)) % 186.01/186.05 [1399]~E(x13991,x13992)+E(f541(x13993,x13994,x13995,x13996,x13991),f541(x13993,x13994,x13995,x13996,x13992)) % 186.01/186.05 [1400]~E(x14001,x14002)+E(f720(x14001,x14003),f720(x14002,x14003)) % 186.01/186.05 [1401]~E(x14011,x14012)+E(f720(x14013,x14011),f720(x14013,x14012)) % 186.01/186.05 [1402]~E(x14021,x14022)+E(f831(x14021),f831(x14022)) % 186.01/186.05 [1403]~E(x14031,x14032)+E(f611(x14031,x14033,x14034,x14035,x14036),f611(x14032,x14033,x14034,x14035,x14036)) % 186.01/186.05 [1404]~E(x14041,x14042)+E(f611(x14043,x14041,x14044,x14045,x14046),f611(x14043,x14042,x14044,x14045,x14046)) % 186.01/186.05 [1405]~E(x14051,x14052)+E(f611(x14053,x14054,x14051,x14055,x14056),f611(x14053,x14054,x14052,x14055,x14056)) % 186.01/186.05 [1406]~E(x14061,x14062)+E(f611(x14063,x14064,x14065,x14061,x14066),f611(x14063,x14064,x14065,x14062,x14066)) % 186.01/186.05 [1407]~E(x14071,x14072)+E(f611(x14073,x14074,x14075,x14076,x14071),f611(x14073,x14074,x14075,x14076,x14072)) % 186.01/186.05 [1408]~E(x14081,x14082)+E(f504(x14081,x14083,x14084),f504(x14082,x14083,x14084)) % 186.01/186.05 [1409]~E(x14091,x14092)+E(f504(x14093,x14091,x14094),f504(x14093,x14092,x14094)) % 186.01/186.05 [1410]~E(x14101,x14102)+E(f504(x14103,x14104,x14101),f504(x14103,x14104,x14102)) % 186.01/186.05 [1411]~E(x14111,x14112)+E(f790(x14111,x14113,x14114,x14115,x14116,x14117,x14118),f790(x14112,x14113,x14114,x14115,x14116,x14117,x14118)) % 186.01/186.05 [1412]~E(x14121,x14122)+E(f790(x14123,x14121,x14124,x14125,x14126,x14127,x14128),f790(x14123,x14122,x14124,x14125,x14126,x14127,x14128)) % 186.01/186.05 [1413]~E(x14131,x14132)+E(f790(x14133,x14134,x14131,x14135,x14136,x14137,x14138),f790(x14133,x14134,x14132,x14135,x14136,x14137,x14138)) % 186.01/186.05 [1414]~E(x14141,x14142)+E(f790(x14143,x14144,x14145,x14141,x14146,x14147,x14148),f790(x14143,x14144,x14145,x14142,x14146,x14147,x14148)) % 186.01/186.05 [1415]~E(x14151,x14152)+E(f790(x14153,x14154,x14155,x14156,x14151,x14157,x14158),f790(x14153,x14154,x14155,x14156,x14152,x14157,x14158)) % 186.01/186.05 [1416]~E(x14161,x14162)+E(f790(x14163,x14164,x14165,x14166,x14167,x14161,x14168),f790(x14163,x14164,x14165,x14166,x14167,x14162,x14168)) % 186.01/186.05 [1417]~E(x14171,x14172)+E(f790(x14173,x14174,x14175,x14176,x14177,x14178,x14171),f790(x14173,x14174,x14175,x14176,x14177,x14178,x14172)) % 186.01/186.05 [1418]~E(x14181,x14182)+E(f900(x14181,x14183,x14184,x14185),f900(x14182,x14183,x14184,x14185)) % 186.01/186.05 [1419]~E(x14191,x14192)+E(f900(x14193,x14191,x14194,x14195),f900(x14193,x14192,x14194,x14195)) % 186.01/186.05 [1420]~E(x14201,x14202)+E(f900(x14203,x14204,x14201,x14205),f900(x14203,x14204,x14202,x14205)) % 186.01/186.05 [1421]~E(x14211,x14212)+E(f900(x14213,x14214,x14215,x14211),f900(x14213,x14214,x14215,x14212)) % 186.01/186.05 [1422]~E(x14221,x14222)+E(f847(x14221,x14223,x14224,x14225,x14226),f847(x14222,x14223,x14224,x14225,x14226)) % 186.01/186.05 [1423]~E(x14231,x14232)+E(f847(x14233,x14231,x14234,x14235,x14236),f847(x14233,x14232,x14234,x14235,x14236)) % 186.01/186.05 [1424]~E(x14241,x14242)+E(f847(x14243,x14244,x14241,x14245,x14246),f847(x14243,x14244,x14242,x14245,x14246)) % 186.01/186.05 [1425]~E(x14251,x14252)+E(f847(x14253,x14254,x14255,x14251,x14256),f847(x14253,x14254,x14255,x14252,x14256)) % 186.01/186.05 [1426]~E(x14261,x14262)+E(f847(x14263,x14264,x14265,x14266,x14261),f847(x14263,x14264,x14265,x14266,x14262)) % 186.01/186.05 [1427]~E(x14271,x14272)+E(f903(x14271,x14273,x14274),f903(x14272,x14273,x14274)) % 186.01/186.05 [1428]~E(x14281,x14282)+E(f903(x14283,x14281,x14284),f903(x14283,x14282,x14284)) % 186.01/186.05 [1429]~E(x14291,x14292)+E(f903(x14293,x14294,x14291),f903(x14293,x14294,x14292)) % 186.01/186.05 [1430]~E(x14301,x14302)+E(f574(x14301),f574(x14302)) % 186.01/186.05 [1431]~E(x14311,x14312)+E(f871(x14311,x14313,x14314,x14315,x14316,x14317,x14318),f871(x14312,x14313,x14314,x14315,x14316,x14317,x14318)) % 186.01/186.05 [1432]~E(x14321,x14322)+E(f871(x14323,x14321,x14324,x14325,x14326,x14327,x14328),f871(x14323,x14322,x14324,x14325,x14326,x14327,x14328)) % 186.01/186.05 [1433]~E(x14331,x14332)+E(f871(x14333,x14334,x14331,x14335,x14336,x14337,x14338),f871(x14333,x14334,x14332,x14335,x14336,x14337,x14338)) % 186.01/186.05 [1434]~E(x14341,x14342)+E(f871(x14343,x14344,x14345,x14341,x14346,x14347,x14348),f871(x14343,x14344,x14345,x14342,x14346,x14347,x14348)) % 186.01/186.05 [1435]~E(x14351,x14352)+E(f871(x14353,x14354,x14355,x14356,x14351,x14357,x14358),f871(x14353,x14354,x14355,x14356,x14352,x14357,x14358)) % 186.01/186.05 [1436]~E(x14361,x14362)+E(f871(x14363,x14364,x14365,x14366,x14367,x14361,x14368),f871(x14363,x14364,x14365,x14366,x14367,x14362,x14368)) % 186.01/186.05 [1437]~E(x14371,x14372)+E(f871(x14373,x14374,x14375,x14376,x14377,x14378,x14371),f871(x14373,x14374,x14375,x14376,x14377,x14378,x14372)) % 186.01/186.05 [1438]~E(x14381,x14382)+E(f383(x14381,x14383),f383(x14382,x14383)) % 186.01/186.05 [1439]~E(x14391,x14392)+E(f383(x14393,x14391),f383(x14393,x14392)) % 186.01/186.05 [1440]~E(x14401,x14402)+E(f398(x14401,x14403,x14404),f398(x14402,x14403,x14404)) % 186.01/186.05 [1441]~E(x14411,x14412)+E(f398(x14413,x14411,x14414),f398(x14413,x14412,x14414)) % 186.01/186.05 [1442]~E(x14421,x14422)+E(f398(x14423,x14424,x14421),f398(x14423,x14424,x14422)) % 186.01/186.05 [1443]~E(x14431,x14432)+E(f394(x14431,x14433,x14434),f394(x14432,x14433,x14434)) % 186.01/186.05 [1444]~E(x14441,x14442)+E(f394(x14443,x14441,x14444),f394(x14443,x14442,x14444)) % 186.01/186.05 [1445]~E(x14451,x14452)+E(f394(x14453,x14454,x14451),f394(x14453,x14454,x14452)) % 186.01/186.05 [1446]~E(x14461,x14462)+E(f708(x14461,x14463,x14464,x14465),f708(x14462,x14463,x14464,x14465)) % 186.01/186.05 [1447]~E(x14471,x14472)+E(f708(x14473,x14471,x14474,x14475),f708(x14473,x14472,x14474,x14475)) % 186.01/186.05 [1448]~E(x14481,x14482)+E(f708(x14483,x14484,x14481,x14485),f708(x14483,x14484,x14482,x14485)) % 186.01/186.05 [1449]~E(x14491,x14492)+E(f708(x14493,x14494,x14495,x14491),f708(x14493,x14494,x14495,x14492)) % 186.01/186.05 [1450]~E(x14501,x14502)+E(f858(x14501,x14503,x14504,x14505,x14506,x14507,x14508,x14509),f858(x14502,x14503,x14504,x14505,x14506,x14507,x14508,x14509)) % 186.01/186.05 [1451]~E(x14511,x14512)+E(f858(x14513,x14511,x14514,x14515,x14516,x14517,x14518,x14519),f858(x14513,x14512,x14514,x14515,x14516,x14517,x14518,x14519)) % 186.01/186.05 [1452]~E(x14521,x14522)+E(f858(x14523,x14524,x14521,x14525,x14526,x14527,x14528,x14529),f858(x14523,x14524,x14522,x14525,x14526,x14527,x14528,x14529)) % 186.01/186.05 [1453]~E(x14531,x14532)+E(f858(x14533,x14534,x14535,x14531,x14536,x14537,x14538,x14539),f858(x14533,x14534,x14535,x14532,x14536,x14537,x14538,x14539)) % 186.01/186.05 [1454]~E(x14541,x14542)+E(f858(x14543,x14544,x14545,x14546,x14541,x14547,x14548,x14549),f858(x14543,x14544,x14545,x14546,x14542,x14547,x14548,x14549)) % 186.01/186.05 [1455]~E(x14551,x14552)+E(f858(x14553,x14554,x14555,x14556,x14557,x14551,x14558,x14559),f858(x14553,x14554,x14555,x14556,x14557,x14552,x14558,x14559)) % 186.01/186.05 [1456]~E(x14561,x14562)+E(f858(x14563,x14564,x14565,x14566,x14567,x14568,x14561,x14569),f858(x14563,x14564,x14565,x14566,x14567,x14568,x14562,x14569)) % 186.01/186.05 [1457]~E(x14571,x14572)+E(f858(x14573,x14574,x14575,x14576,x14577,x14578,x14579,x14571),f858(x14573,x14574,x14575,x14576,x14577,x14578,x14579,x14572)) % 186.01/186.05 [1458]~E(x14581,x14582)+E(f729(x14581,x14583),f729(x14582,x14583)) % 186.01/186.05 [1459]~E(x14591,x14592)+E(f729(x14593,x14591),f729(x14593,x14592)) % 186.01/186.05 [1460]~E(x14601,x14602)+E(f513(x14601,x14603,x14604),f513(x14602,x14603,x14604)) % 186.01/186.05 [1461]~E(x14611,x14612)+E(f513(x14613,x14611,x14614),f513(x14613,x14612,x14614)) % 186.01/186.05 [1462]~E(x14621,x14622)+E(f513(x14623,x14624,x14621),f513(x14623,x14624,x14622)) % 186.01/186.05 [1463]~E(x14631,x14632)+E(f644(x14631,x14633,x14634),f644(x14632,x14633,x14634)) % 186.01/186.05 [1464]~E(x14641,x14642)+E(f644(x14643,x14641,x14644),f644(x14643,x14642,x14644)) % 186.01/186.05 [1465]~E(x14651,x14652)+E(f644(x14653,x14654,x14651),f644(x14653,x14654,x14652)) % 186.01/186.05 [1466]~E(x14661,x14662)+E(f400(x14661,x14663,x14664),f400(x14662,x14663,x14664)) % 186.01/186.05 [1467]~E(x14671,x14672)+E(f400(x14673,x14671,x14674),f400(x14673,x14672,x14674)) % 186.01/186.05 [1468]~E(x14681,x14682)+E(f400(x14683,x14684,x14681),f400(x14683,x14684,x14682)) % 186.01/186.05 [1469]~E(x14691,x14692)+E(f770(x14691,x14693,x14694,x14695,x14696,x14697,x14698),f770(x14692,x14693,x14694,x14695,x14696,x14697,x14698)) % 186.01/186.05 [1470]~E(x14701,x14702)+E(f770(x14703,x14701,x14704,x14705,x14706,x14707,x14708),f770(x14703,x14702,x14704,x14705,x14706,x14707,x14708)) % 186.01/186.05 [1471]~E(x14711,x14712)+E(f770(x14713,x14714,x14711,x14715,x14716,x14717,x14718),f770(x14713,x14714,x14712,x14715,x14716,x14717,x14718)) % 186.01/186.05 [1472]~E(x14721,x14722)+E(f770(x14723,x14724,x14725,x14721,x14726,x14727,x14728),f770(x14723,x14724,x14725,x14722,x14726,x14727,x14728)) % 186.01/186.05 [1473]~E(x14731,x14732)+E(f770(x14733,x14734,x14735,x14736,x14731,x14737,x14738),f770(x14733,x14734,x14735,x14736,x14732,x14737,x14738)) % 186.01/186.05 [1474]~E(x14741,x14742)+E(f770(x14743,x14744,x14745,x14746,x14747,x14741,x14748),f770(x14743,x14744,x14745,x14746,x14747,x14742,x14748)) % 186.01/186.05 [1475]~E(x14751,x14752)+E(f770(x14753,x14754,x14755,x14756,x14757,x14758,x14751),f770(x14753,x14754,x14755,x14756,x14757,x14758,x14752)) % 186.01/186.05 [1476]~E(x14761,x14762)+E(f406(x14761,x14763,x14764),f406(x14762,x14763,x14764)) % 186.01/186.05 [1477]~E(x14771,x14772)+E(f406(x14773,x14771,x14774),f406(x14773,x14772,x14774)) % 186.01/186.05 [1478]~E(x14781,x14782)+E(f406(x14783,x14784,x14781),f406(x14783,x14784,x14782)) % 186.01/186.05 [1479]~E(x14791,x14792)+E(f237(x14791,x14793,x14794),f237(x14792,x14793,x14794)) % 186.01/186.05 [1480]~E(x14801,x14802)+E(f237(x14803,x14801,x14804),f237(x14803,x14802,x14804)) % 186.01/186.05 [1481]~E(x14811,x14812)+E(f237(x14813,x14814,x14811),f237(x14813,x14814,x14812)) % 186.01/186.05 [1482]~E(x14821,x14822)+E(f263(x14821,x14823,x14824,x14825),f263(x14822,x14823,x14824,x14825)) % 186.01/186.05 [1483]~E(x14831,x14832)+E(f263(x14833,x14831,x14834,x14835),f263(x14833,x14832,x14834,x14835)) % 186.01/186.05 [1484]~E(x14841,x14842)+E(f263(x14843,x14844,x14841,x14845),f263(x14843,x14844,x14842,x14845)) % 186.01/186.05 [1485]~E(x14851,x14852)+E(f263(x14853,x14854,x14855,x14851),f263(x14853,x14854,x14855,x14852)) % 186.01/186.05 [1486]~E(x14861,x14862)+E(f725(x14861,x14863,x14864,x14865,x14866),f725(x14862,x14863,x14864,x14865,x14866)) % 186.01/186.05 [1487]~E(x14871,x14872)+E(f725(x14873,x14871,x14874,x14875,x14876),f725(x14873,x14872,x14874,x14875,x14876)) % 186.01/186.05 [1488]~E(x14881,x14882)+E(f725(x14883,x14884,x14881,x14885,x14886),f725(x14883,x14884,x14882,x14885,x14886)) % 186.01/186.05 [1489]~E(x14891,x14892)+E(f725(x14893,x14894,x14895,x14891,x14896),f725(x14893,x14894,x14895,x14892,x14896)) % 186.01/186.05 [1490]~E(x14901,x14902)+E(f725(x14903,x14904,x14905,x14906,x14901),f725(x14903,x14904,x14905,x14906,x14902)) % 186.01/186.05 [1491]~E(x14911,x14912)+E(f480(x14911,x14913,x14914),f480(x14912,x14913,x14914)) % 186.01/186.05 [1492]~E(x14921,x14922)+E(f480(x14923,x14921,x14924),f480(x14923,x14922,x14924)) % 186.01/186.05 [1493]~E(x14931,x14932)+E(f480(x14933,x14934,x14931),f480(x14933,x14934,x14932)) % 186.01/186.05 [1494]~E(x14941,x14942)+E(f801(x14941,x14943,x14944,x14945,x14946),f801(x14942,x14943,x14944,x14945,x14946)) % 186.01/186.05 [1495]~E(x14951,x14952)+E(f801(x14953,x14951,x14954,x14955,x14956),f801(x14953,x14952,x14954,x14955,x14956)) % 186.01/186.05 [1496]~E(x14961,x14962)+E(f801(x14963,x14964,x14961,x14965,x14966),f801(x14963,x14964,x14962,x14965,x14966)) % 186.01/186.05 [1497]~E(x14971,x14972)+E(f801(x14973,x14974,x14975,x14971,x14976),f801(x14973,x14974,x14975,x14972,x14976)) % 186.01/186.05 [1498]~E(x14981,x14982)+E(f801(x14983,x14984,x14985,x14986,x14981),f801(x14983,x14984,x14985,x14986,x14982)) % 186.01/186.05 [1499]~E(x14991,x14992)+E(f519(x14991,x14993,x14994,x14995),f519(x14992,x14993,x14994,x14995)) % 186.01/186.05 [1500]~E(x15001,x15002)+E(f519(x15003,x15001,x15004,x15005),f519(x15003,x15002,x15004,x15005)) % 186.01/186.05 [1501]~E(x15011,x15012)+E(f519(x15013,x15014,x15011,x15015),f519(x15013,x15014,x15012,x15015)) % 186.01/186.05 [1502]~E(x15021,x15022)+E(f519(x15023,x15024,x15025,x15021),f519(x15023,x15024,x15025,x15022)) % 186.01/186.05 [1503]~E(x15031,x15032)+E(f522(x15031,x15033,x15034,x15035),f522(x15032,x15033,x15034,x15035)) % 186.01/186.05 [1504]~E(x15041,x15042)+E(f522(x15043,x15041,x15044,x15045),f522(x15043,x15042,x15044,x15045)) % 186.01/186.05 [1505]~E(x15051,x15052)+E(f522(x15053,x15054,x15051,x15055),f522(x15053,x15054,x15052,x15055)) % 186.01/186.05 [1506]~E(x15061,x15062)+E(f522(x15063,x15064,x15065,x15061),f522(x15063,x15064,x15065,x15062)) % 186.01/186.05 [1507]~E(x15071,x15072)+E(f469(x15071,x15073,x15074),f469(x15072,x15073,x15074)) % 186.01/186.05 [1508]~E(x15081,x15082)+E(f469(x15083,x15081,x15084),f469(x15083,x15082,x15084)) % 186.01/186.05 [1509]~E(x15091,x15092)+E(f469(x15093,x15094,x15091),f469(x15093,x15094,x15092)) % 186.01/186.05 [1510]~E(x15101,x15102)+E(f590(x15101,x15103),f590(x15102,x15103)) % 186.01/186.05 [1511]~E(x15111,x15112)+E(f590(x15113,x15111),f590(x15113,x15112)) % 186.01/186.05 [1512]~E(x15121,x15122)+E(f842(x15121),f842(x15122)) % 186.01/186.05 [1513]~E(x15131,x15132)+E(f458(x15131,x15133,x15134,x15135),f458(x15132,x15133,x15134,x15135)) % 186.01/186.05 [1514]~E(x15141,x15142)+E(f458(x15143,x15141,x15144,x15145),f458(x15143,x15142,x15144,x15145)) % 186.01/186.05 [1515]~E(x15151,x15152)+E(f458(x15153,x15154,x15151,x15155),f458(x15153,x15154,x15152,x15155)) % 186.01/186.05 [1516]~E(x15161,x15162)+E(f458(x15163,x15164,x15165,x15161),f458(x15163,x15164,x15165,x15162)) % 186.01/186.05 [1517]~E(x15171,x15172)+E(f908(x15171,x15173,x15174,x15175,x15176,x15177),f908(x15172,x15173,x15174,x15175,x15176,x15177)) % 186.01/186.05 [1518]~E(x15181,x15182)+E(f908(x15183,x15181,x15184,x15185,x15186,x15187),f908(x15183,x15182,x15184,x15185,x15186,x15187)) % 186.01/186.05 [1519]~E(x15191,x15192)+E(f908(x15193,x15194,x15191,x15195,x15196,x15197),f908(x15193,x15194,x15192,x15195,x15196,x15197)) % 186.01/186.05 [1520]~E(x15201,x15202)+E(f908(x15203,x15204,x15205,x15201,x15206,x15207),f908(x15203,x15204,x15205,x15202,x15206,x15207)) % 186.01/186.05 [1521]~E(x15211,x15212)+E(f908(x15213,x15214,x15215,x15216,x15211,x15217),f908(x15213,x15214,x15215,x15216,x15212,x15217)) % 186.01/186.05 [1522]~E(x15221,x15222)+E(f908(x15223,x15224,x15225,x15226,x15227,x15221),f908(x15223,x15224,x15225,x15226,x15227,x15222)) % 186.01/186.05 [1523]~E(x15231,x15232)+E(f134(x15231,x15233,x15234,x15235,x15236),f134(x15232,x15233,x15234,x15235,x15236)) % 186.01/186.05 [1524]~E(x15241,x15242)+E(f134(x15243,x15241,x15244,x15245,x15246),f134(x15243,x15242,x15244,x15245,x15246)) % 186.01/186.05 [1525]~E(x15251,x15252)+E(f134(x15253,x15254,x15251,x15255,x15256),f134(x15253,x15254,x15252,x15255,x15256)) % 186.01/186.05 [1526]~E(x15261,x15262)+E(f134(x15263,x15264,x15265,x15261,x15266),f134(x15263,x15264,x15265,x15262,x15266)) % 186.01/186.05 [1527]~E(x15271,x15272)+E(f134(x15273,x15274,x15275,x15276,x15271),f134(x15273,x15274,x15275,x15276,x15272)) % 186.01/186.05 [1528]~E(x15281,x15282)+E(f162(x15281,x15283,x15284),f162(x15282,x15283,x15284)) % 186.01/186.05 [1529]~E(x15291,x15292)+E(f162(x15293,x15291,x15294),f162(x15293,x15292,x15294)) % 186.01/186.05 [1530]~E(x15301,x15302)+E(f162(x15303,x15304,x15301),f162(x15303,x15304,x15302)) % 186.01/186.05 [1531]~E(x15311,x15312)+E(f884(x15311,x15313,x15314,x15315),f884(x15312,x15313,x15314,x15315)) % 186.01/186.05 [1532]~E(x15321,x15322)+E(f884(x15323,x15321,x15324,x15325),f884(x15323,x15322,x15324,x15325)) % 186.01/186.05 [1533]~E(x15331,x15332)+E(f884(x15333,x15334,x15331,x15335),f884(x15333,x15334,x15332,x15335)) % 186.01/186.05 [1534]~E(x15341,x15342)+E(f884(x15343,x15344,x15345,x15341),f884(x15343,x15344,x15345,x15342)) % 186.01/186.05 [1535]~E(x15351,x15352)+E(f440(x15351),f440(x15352)) % 186.01/186.05 [1536]~E(x15361,x15362)+E(f502(x15361,x15363,x15364),f502(x15362,x15363,x15364)) % 186.01/186.05 [1537]~E(x15371,x15372)+E(f502(x15373,x15371,x15374),f502(x15373,x15372,x15374)) % 186.01/186.05 [1538]~E(x15381,x15382)+E(f502(x15383,x15384,x15381),f502(x15383,x15384,x15382)) % 186.01/186.05 [1539]~E(x15391,x15392)+E(f538(x15391,x15393,x15394),f538(x15392,x15393,x15394)) % 186.01/186.05 [1540]~E(x15401,x15402)+E(f538(x15403,x15401,x15404),f538(x15403,x15402,x15404)) % 186.01/186.05 [1541]~E(x15411,x15412)+E(f538(x15413,x15414,x15411),f538(x15413,x15414,x15412)) % 186.01/186.05 [1542]~E(x15421,x15422)+E(f846(x15421,x15423,x15424),f846(x15422,x15423,x15424)) % 186.01/186.05 [1543]~E(x15431,x15432)+E(f846(x15433,x15431,x15434),f846(x15433,x15432,x15434)) % 186.01/186.05 [1544]~E(x15441,x15442)+E(f846(x15443,x15444,x15441),f846(x15443,x15444,x15442)) % 186.01/186.05 [1545]~E(x15451,x15452)+E(f771(x15451,x15453,x15454,x15455,x15456,x15457,x15458),f771(x15452,x15453,x15454,x15455,x15456,x15457,x15458)) % 186.01/186.05 [1546]~E(x15461,x15462)+E(f771(x15463,x15461,x15464,x15465,x15466,x15467,x15468),f771(x15463,x15462,x15464,x15465,x15466,x15467,x15468)) % 186.01/186.05 [1547]~E(x15471,x15472)+E(f771(x15473,x15474,x15471,x15475,x15476,x15477,x15478),f771(x15473,x15474,x15472,x15475,x15476,x15477,x15478)) % 186.01/186.05 [1548]~E(x15481,x15482)+E(f771(x15483,x15484,x15485,x15481,x15486,x15487,x15488),f771(x15483,x15484,x15485,x15482,x15486,x15487,x15488)) % 186.01/186.05 [1549]~E(x15491,x15492)+E(f771(x15493,x15494,x15495,x15496,x15491,x15497,x15498),f771(x15493,x15494,x15495,x15496,x15492,x15497,x15498)) % 186.01/186.05 [1550]~E(x15501,x15502)+E(f771(x15503,x15504,x15505,x15506,x15507,x15501,x15508),f771(x15503,x15504,x15505,x15506,x15507,x15502,x15508)) % 186.01/186.05 [1551]~E(x15511,x15512)+E(f771(x15513,x15514,x15515,x15516,x15517,x15518,x15511),f771(x15513,x15514,x15515,x15516,x15517,x15518,x15512)) % 186.01/186.05 [1552]~E(x15521,x15522)+E(f800(x15521,x15523,x15524),f800(x15522,x15523,x15524)) % 186.01/186.05 [1553]~E(x15531,x15532)+E(f800(x15533,x15531,x15534),f800(x15533,x15532,x15534)) % 186.01/186.05 [1554]~E(x15541,x15542)+E(f800(x15543,x15544,x15541),f800(x15543,x15544,x15542)) % 186.01/186.05 [1555]~E(x15551,x15552)+E(f739(x15551,x15553),f739(x15552,x15553)) % 186.01/186.05 [1556]~E(x15561,x15562)+E(f739(x15563,x15561),f739(x15563,x15562)) % 186.01/186.05 [1557]~E(x15571,x15572)+E(f822(x15571,x15573,x15574,x15575),f822(x15572,x15573,x15574,x15575)) % 186.01/186.05 [1558]~E(x15581,x15582)+E(f822(x15583,x15581,x15584,x15585),f822(x15583,x15582,x15584,x15585)) % 186.01/186.05 [1559]~E(x15591,x15592)+E(f822(x15593,x15594,x15591,x15595),f822(x15593,x15594,x15592,x15595)) % 186.01/186.05 [1560]~E(x15601,x15602)+E(f822(x15603,x15604,x15605,x15601),f822(x15603,x15604,x15605,x15602)) % 186.01/186.05 [1561]~E(x15611,x15612)+E(f656(x15611,x15613,x15614,x15615,x15616),f656(x15612,x15613,x15614,x15615,x15616)) % 186.01/186.05 [1562]~E(x15621,x15622)+E(f656(x15623,x15621,x15624,x15625,x15626),f656(x15623,x15622,x15624,x15625,x15626)) % 186.01/186.05 [1563]~E(x15631,x15632)+E(f656(x15633,x15634,x15631,x15635,x15636),f656(x15633,x15634,x15632,x15635,x15636)) % 186.01/186.05 [1564]~E(x15641,x15642)+E(f656(x15643,x15644,x15645,x15641,x15646),f656(x15643,x15644,x15645,x15642,x15646)) % 186.01/186.05 [1565]~E(x15651,x15652)+E(f656(x15653,x15654,x15655,x15656,x15651),f656(x15653,x15654,x15655,x15656,x15652)) % 186.01/186.05 [1566]~E(x15661,x15662)+E(f430(x15661,x15663,x15664,x15665,x15666,x15667),f430(x15662,x15663,x15664,x15665,x15666,x15667)) % 186.01/186.05 [1567]~E(x15671,x15672)+E(f430(x15673,x15671,x15674,x15675,x15676,x15677),f430(x15673,x15672,x15674,x15675,x15676,x15677)) % 186.01/186.05 [1568]~E(x15681,x15682)+E(f430(x15683,x15684,x15681,x15685,x15686,x15687),f430(x15683,x15684,x15682,x15685,x15686,x15687)) % 186.01/186.05 [1569]~E(x15691,x15692)+E(f430(x15693,x15694,x15695,x15691,x15696,x15697),f430(x15693,x15694,x15695,x15692,x15696,x15697)) % 186.01/186.05 [1570]~E(x15701,x15702)+E(f430(x15703,x15704,x15705,x15706,x15701,x15707),f430(x15703,x15704,x15705,x15706,x15702,x15707)) % 186.01/186.05 [1571]~E(x15711,x15712)+E(f430(x15713,x15714,x15715,x15716,x15717,x15711),f430(x15713,x15714,x15715,x15716,x15717,x15712)) % 186.01/186.05 [1572]~E(x15721,x15722)+E(f603(x15721,x15723,x15724),f603(x15722,x15723,x15724)) % 186.01/186.05 [1573]~E(x15731,x15732)+E(f603(x15733,x15731,x15734),f603(x15733,x15732,x15734)) % 186.01/186.05 [1574]~E(x15741,x15742)+E(f603(x15743,x15744,x15741),f603(x15743,x15744,x15742)) % 186.01/186.05 [1575]~E(x15751,x15752)+E(f641(x15751,x15753,x15754,x15755,x15756),f641(x15752,x15753,x15754,x15755,x15756)) % 186.01/186.05 [1576]~E(x15761,x15762)+E(f641(x15763,x15761,x15764,x15765,x15766),f641(x15763,x15762,x15764,x15765,x15766)) % 186.01/186.05 [1577]~E(x15771,x15772)+E(f641(x15773,x15774,x15771,x15775,x15776),f641(x15773,x15774,x15772,x15775,x15776)) % 186.01/186.05 [1578]~E(x15781,x15782)+E(f641(x15783,x15784,x15785,x15781,x15786),f641(x15783,x15784,x15785,x15782,x15786)) % 186.01/186.05 [1579]~E(x15791,x15792)+E(f641(x15793,x15794,x15795,x15796,x15791),f641(x15793,x15794,x15795,x15796,x15792)) % 186.01/186.05 [1580]~E(x15801,x15802)+E(f552(x15801,x15803,x15804),f552(x15802,x15803,x15804)) % 186.01/186.05 [1581]~E(x15811,x15812)+E(f552(x15813,x15811,x15814),f552(x15813,x15812,x15814)) % 186.01/186.05 [1582]~E(x15821,x15822)+E(f552(x15823,x15824,x15821),f552(x15823,x15824,x15822)) % 186.01/186.05 [1583]~E(x15831,x15832)+E(f419(x15831,x15833),f419(x15832,x15833)) % 186.01/186.05 [1584]~E(x15841,x15842)+E(f419(x15843,x15841),f419(x15843,x15842)) % 186.01/186.05 [1585]~E(x15851,x15852)+E(f604(x15851,x15853),f604(x15852,x15853)) % 186.01/186.05 [1586]~E(x15861,x15862)+E(f604(x15863,x15861),f604(x15863,x15862)) % 186.01/186.05 [1587]~E(x15871,x15872)+E(f877(x15871,x15873,x15874),f877(x15872,x15873,x15874)) % 186.01/186.05 [1588]~E(x15881,x15882)+E(f877(x15883,x15881,x15884),f877(x15883,x15882,x15884)) % 186.01/186.05 [1589]~E(x15891,x15892)+E(f877(x15893,x15894,x15891),f877(x15893,x15894,x15892)) % 186.01/186.05 [1590]~E(x15901,x15902)+E(f147(x15901,x15903,x15904),f147(x15902,x15903,x15904)) % 186.01/186.05 [1591]~E(x15911,x15912)+E(f147(x15913,x15911,x15914),f147(x15913,x15912,x15914)) % 186.01/186.05 [1592]~E(x15921,x15922)+E(f147(x15923,x15924,x15921),f147(x15923,x15924,x15922)) % 186.01/186.05 [1593]~E(x15931,x15932)+E(f648(x15931,x15933,x15934,x15935),f648(x15932,x15933,x15934,x15935)) % 186.01/186.05 [1594]~E(x15941,x15942)+E(f648(x15943,x15941,x15944,x15945),f648(x15943,x15942,x15944,x15945)) % 186.01/186.05 [1595]~E(x15951,x15952)+E(f648(x15953,x15954,x15951,x15955),f648(x15953,x15954,x15952,x15955)) % 186.01/186.05 [1596]~E(x15961,x15962)+E(f648(x15963,x15964,x15965,x15961),f648(x15963,x15964,x15965,x15962)) % 186.01/186.05 [1597]~E(x15971,x15972)+E(f689(x15971,x15973),f689(x15972,x15973)) % 186.01/186.05 [1598]~E(x15981,x15982)+E(f689(x15983,x15981),f689(x15983,x15982)) % 186.01/186.05 [1599]~E(x15991,x15992)+E(f348(x15991,x15993,x15994,x15995),f348(x15992,x15993,x15994,x15995)) % 186.01/186.05 [1600]~E(x16001,x16002)+E(f348(x16003,x16001,x16004,x16005),f348(x16003,x16002,x16004,x16005)) % 186.01/186.05 [1601]~E(x16011,x16012)+E(f348(x16013,x16014,x16011,x16015),f348(x16013,x16014,x16012,x16015)) % 186.01/186.05 [1602]~E(x16021,x16022)+E(f348(x16023,x16024,x16025,x16021),f348(x16023,x16024,x16025,x16022)) % 186.01/186.05 [1603]~E(x16031,x16032)+E(f582(x16031,x16033,x16034),f582(x16032,x16033,x16034)) % 186.01/186.05 [1604]~E(x16041,x16042)+E(f582(x16043,x16041,x16044),f582(x16043,x16042,x16044)) % 186.01/186.05 [1605]~E(x16051,x16052)+E(f582(x16053,x16054,x16051),f582(x16053,x16054,x16052)) % 186.01/186.05 [1606]~E(x16061,x16062)+E(f215(x16061,x16063,x16064,x16065),f215(x16062,x16063,x16064,x16065)) % 186.01/186.05 [1607]~E(x16071,x16072)+E(f215(x16073,x16071,x16074,x16075),f215(x16073,x16072,x16074,x16075)) % 186.01/186.05 [1608]~E(x16081,x16082)+E(f215(x16083,x16084,x16081,x16085),f215(x16083,x16084,x16082,x16085)) % 186.01/186.05 [1609]~E(x16091,x16092)+E(f215(x16093,x16094,x16095,x16091),f215(x16093,x16094,x16095,x16092)) % 186.01/186.05 [1610]~E(x16101,x16102)+E(f635(x16101,x16103,x16104,x16105),f635(x16102,x16103,x16104,x16105)) % 186.01/186.05 [1611]~E(x16111,x16112)+E(f635(x16113,x16111,x16114,x16115),f635(x16113,x16112,x16114,x16115)) % 186.01/186.05 [1612]~E(x16121,x16122)+E(f635(x16123,x16124,x16121,x16125),f635(x16123,x16124,x16122,x16125)) % 186.01/186.05 [1613]~E(x16131,x16132)+E(f635(x16133,x16134,x16135,x16131),f635(x16133,x16134,x16135,x16132)) % 186.01/186.05 [1614]~E(x16141,x16142)+E(f281(x16141,x16143,x16144,x16145),f281(x16142,x16143,x16144,x16145)) % 186.01/186.05 [1615]~E(x16151,x16152)+E(f281(x16153,x16151,x16154,x16155),f281(x16153,x16152,x16154,x16155)) % 186.01/186.05 [1616]~E(x16161,x16162)+E(f281(x16163,x16164,x16161,x16165),f281(x16163,x16164,x16162,x16165)) % 186.01/186.05 [1617]~E(x16171,x16172)+E(f281(x16173,x16174,x16175,x16171),f281(x16173,x16174,x16175,x16172)) % 186.01/186.05 [1618]~E(x16181,x16182)+E(f485(x16181,x16183,x16184,x16185,x16186),f485(x16182,x16183,x16184,x16185,x16186)) % 186.01/186.05 [1619]~E(x16191,x16192)+E(f485(x16193,x16191,x16194,x16195,x16196),f485(x16193,x16192,x16194,x16195,x16196)) % 186.01/186.05 [1620]~E(x16201,x16202)+E(f485(x16203,x16204,x16201,x16205,x16206),f485(x16203,x16204,x16202,x16205,x16206)) % 186.01/186.05 [1621]~E(x16211,x16212)+E(f485(x16213,x16214,x16215,x16211,x16216),f485(x16213,x16214,x16215,x16212,x16216)) % 186.01/186.05 [1622]~E(x16221,x16222)+E(f485(x16223,x16224,x16225,x16226,x16221),f485(x16223,x16224,x16225,x16226,x16222)) % 186.01/186.05 [1623]~E(x16231,x16232)+E(f490(x16231,x16233,x16234),f490(x16232,x16233,x16234)) % 186.01/186.05 [1624]~E(x16241,x16242)+E(f490(x16243,x16241,x16244),f490(x16243,x16242,x16244)) % 186.01/186.05 [1625]~E(x16251,x16252)+E(f490(x16253,x16254,x16251),f490(x16253,x16254,x16252)) % 186.01/186.05 [1626]~E(x16261,x16262)+E(f554(x16261,x16263,x16264),f554(x16262,x16263,x16264)) % 186.01/186.05 [1627]~E(x16271,x16272)+E(f554(x16273,x16271,x16274),f554(x16273,x16272,x16274)) % 186.01/186.05 [1628]~E(x16281,x16282)+E(f554(x16283,x16284,x16281),f554(x16283,x16284,x16282)) % 186.01/186.05 [1629]~E(x16291,x16292)+E(f461(x16291,x16293,x16294),f461(x16292,x16293,x16294)) % 186.01/186.05 [1630]~E(x16301,x16302)+E(f461(x16303,x16301,x16304),f461(x16303,x16302,x16304)) % 186.01/186.05 [1631]~E(x16311,x16312)+E(f461(x16313,x16314,x16311),f461(x16313,x16314,x16312)) % 186.01/186.05 [1632]~E(x16321,x16322)+E(f507(x16321,x16323,x16324),f507(x16322,x16323,x16324)) % 186.01/186.05 [1633]~E(x16331,x16332)+E(f507(x16333,x16331,x16334),f507(x16333,x16332,x16334)) % 186.01/186.05 [1634]~E(x16341,x16342)+E(f507(x16343,x16344,x16341),f507(x16343,x16344,x16342)) % 186.01/186.05 [1635]~E(x16351,x16352)+E(f901(x16351,x16353,x16354,x16355),f901(x16352,x16353,x16354,x16355)) % 186.01/186.05 [1636]~E(x16361,x16362)+E(f901(x16363,x16361,x16364,x16365),f901(x16363,x16362,x16364,x16365)) % 186.01/186.05 [1637]~E(x16371,x16372)+E(f901(x16373,x16374,x16371,x16375),f901(x16373,x16374,x16372,x16375)) % 186.01/186.05 [1638]~E(x16381,x16382)+E(f901(x16383,x16384,x16385,x16381),f901(x16383,x16384,x16385,x16382)) % 186.01/186.05 [1639]~E(x16391,x16392)+E(f169(x16391,x16393),f169(x16392,x16393)) % 186.01/186.05 [1640]~E(x16401,x16402)+E(f169(x16403,x16401),f169(x16403,x16402)) % 186.01/186.05 [1641]~E(x16411,x16412)+E(f897(x16411,x16413,x16414),f897(x16412,x16413,x16414)) % 186.01/186.05 [1642]~E(x16421,x16422)+E(f897(x16423,x16421,x16424),f897(x16423,x16422,x16424)) % 186.01/186.05 [1643]~E(x16431,x16432)+E(f897(x16433,x16434,x16431),f897(x16433,x16434,x16432)) % 186.01/186.05 [1644]~E(x16441,x16442)+E(f763(x16441,x16443,x16444,x16445),f763(x16442,x16443,x16444,x16445)) % 186.01/186.05 [1645]~E(x16451,x16452)+E(f763(x16453,x16451,x16454,x16455),f763(x16453,x16452,x16454,x16455)) % 186.01/186.05 [1646]~E(x16461,x16462)+E(f763(x16463,x16464,x16461,x16465),f763(x16463,x16464,x16462,x16465)) % 186.01/186.05 [1647]~E(x16471,x16472)+E(f763(x16473,x16474,x16475,x16471),f763(x16473,x16474,x16475,x16472)) % 186.01/186.05 [1648]~E(x16481,x16482)+E(f601(x16481,x16483,x16484),f601(x16482,x16483,x16484)) % 186.01/186.05 [1649]~E(x16491,x16492)+E(f601(x16493,x16491,x16494),f601(x16493,x16492,x16494)) % 186.01/186.05 [1650]~E(x16501,x16502)+E(f601(x16503,x16504,x16501),f601(x16503,x16504,x16502)) % 186.01/186.05 [1651]~E(x16511,x16512)+E(f637(x16511,x16513,x16514,x16515,x16516),f637(x16512,x16513,x16514,x16515,x16516)) % 186.01/186.05 [1652]~E(x16521,x16522)+E(f637(x16523,x16521,x16524,x16525,x16526),f637(x16523,x16522,x16524,x16525,x16526)) % 186.01/186.05 [1653]~E(x16531,x16532)+E(f637(x16533,x16534,x16531,x16535,x16536),f637(x16533,x16534,x16532,x16535,x16536)) % 186.01/186.05 [1654]~E(x16541,x16542)+E(f637(x16543,x16544,x16545,x16541,x16546),f637(x16543,x16544,x16545,x16542,x16546)) % 186.01/186.05 [1655]~E(x16551,x16552)+E(f637(x16553,x16554,x16555,x16556,x16551),f637(x16553,x16554,x16555,x16556,x16552)) % 186.01/186.05 [1656]~E(x16561,x16562)+E(f676(x16561,x16563,x16564,x16565,x16566),f676(x16562,x16563,x16564,x16565,x16566)) % 186.01/186.05 [1657]~E(x16571,x16572)+E(f676(x16573,x16571,x16574,x16575,x16576),f676(x16573,x16572,x16574,x16575,x16576)) % 186.01/186.05 [1658]~E(x16581,x16582)+E(f676(x16583,x16584,x16581,x16585,x16586),f676(x16583,x16584,x16582,x16585,x16586)) % 186.01/186.05 [1659]~E(x16591,x16592)+E(f676(x16593,x16594,x16595,x16591,x16596),f676(x16593,x16594,x16595,x16592,x16596)) % 186.01/186.05 [1660]~E(x16601,x16602)+E(f676(x16603,x16604,x16605,x16606,x16601),f676(x16603,x16604,x16605,x16606,x16602)) % 186.01/186.05 [1661]~E(x16611,x16612)+E(f558(x16611,x16613,x16614),f558(x16612,x16613,x16614)) % 186.01/186.05 [1662]~E(x16621,x16622)+E(f558(x16623,x16621,x16624),f558(x16623,x16622,x16624)) % 186.01/186.05 [1663]~E(x16631,x16632)+E(f558(x16633,x16634,x16631),f558(x16633,x16634,x16632)) % 186.01/186.05 [1664]~E(x16641,x16642)+E(f548(x16641,x16643,x16644,x16645,x16646,x16647,x16648,x16649),f548(x16642,x16643,x16644,x16645,x16646,x16647,x16648,x16649)) % 186.01/186.05 [1665]~E(x16651,x16652)+E(f548(x16653,x16651,x16654,x16655,x16656,x16657,x16658,x16659),f548(x16653,x16652,x16654,x16655,x16656,x16657,x16658,x16659)) % 186.01/186.05 [1666]~E(x16661,x16662)+E(f548(x16663,x16664,x16661,x16665,x16666,x16667,x16668,x16669),f548(x16663,x16664,x16662,x16665,x16666,x16667,x16668,x16669)) % 186.01/186.05 [1667]~E(x16671,x16672)+E(f548(x16673,x16674,x16675,x16671,x16676,x16677,x16678,x16679),f548(x16673,x16674,x16675,x16672,x16676,x16677,x16678,x16679)) % 186.01/186.05 [1668]~E(x16681,x16682)+E(f548(x16683,x16684,x16685,x16686,x16681,x16687,x16688,x16689),f548(x16683,x16684,x16685,x16686,x16682,x16687,x16688,x16689)) % 186.01/186.05 [1669]~E(x16691,x16692)+E(f548(x16693,x16694,x16695,x16696,x16697,x16691,x16698,x16699),f548(x16693,x16694,x16695,x16696,x16697,x16692,x16698,x16699)) % 186.01/186.05 [1670]~E(x16701,x16702)+E(f548(x16703,x16704,x16705,x16706,x16707,x16708,x16701,x16709),f548(x16703,x16704,x16705,x16706,x16707,x16708,x16702,x16709)) % 186.01/186.05 [1671]~E(x16711,x16712)+E(f548(x16713,x16714,x16715,x16716,x16717,x16718,x16719,x16711),f548(x16713,x16714,x16715,x16716,x16717,x16718,x16719,x16712)) % 186.01/186.05 [1672]~E(x16721,x16722)+E(f600(x16721,x16723,x16724),f600(x16722,x16723,x16724)) % 186.01/186.05 [1673]~E(x16731,x16732)+E(f600(x16733,x16731,x16734),f600(x16733,x16732,x16734)) % 186.01/186.05 [1674]~E(x16741,x16742)+E(f600(x16743,x16744,x16741),f600(x16743,x16744,x16742)) % 186.01/186.05 [1675]~E(x16751,x16752)+E(f218(x16751,x16753,x16754,x16755),f218(x16752,x16753,x16754,x16755)) % 186.01/186.05 [1676]~E(x16761,x16762)+E(f218(x16763,x16761,x16764,x16765),f218(x16763,x16762,x16764,x16765)) % 186.01/186.05 [1677]~E(x16771,x16772)+E(f218(x16773,x16774,x16771,x16775),f218(x16773,x16774,x16772,x16775)) % 186.01/186.05 [1678]~E(x16781,x16782)+E(f218(x16783,x16784,x16785,x16781),f218(x16783,x16784,x16785,x16782)) % 186.01/186.05 [1679]~E(x16791,x16792)+E(f760(x16791,x16793),f760(x16792,x16793)) % 186.01/186.05 [1680]~E(x16801,x16802)+E(f760(x16803,x16801),f760(x16803,x16802)) % 186.01/186.05 [1681]~E(x16811,x16812)+E(f844(x16811,x16813,x16814),f844(x16812,x16813,x16814)) % 186.01/186.05 [1682]~E(x16821,x16822)+E(f844(x16823,x16821,x16824),f844(x16823,x16822,x16824)) % 186.01/186.05 [1683]~E(x16831,x16832)+E(f844(x16833,x16834,x16831),f844(x16833,x16834,x16832)) % 186.01/186.05 [1684]~E(x16841,x16842)+E(f608(x16841,x16843,x16844,x16845,x16846),f608(x16842,x16843,x16844,x16845,x16846)) % 186.01/186.05 [1685]~E(x16851,x16852)+E(f608(x16853,x16851,x16854,x16855,x16856),f608(x16853,x16852,x16854,x16855,x16856)) % 186.01/186.05 [1686]~E(x16861,x16862)+E(f608(x16863,x16864,x16861,x16865,x16866),f608(x16863,x16864,x16862,x16865,x16866)) % 186.01/186.05 [1687]~E(x16871,x16872)+E(f608(x16873,x16874,x16875,x16871,x16876),f608(x16873,x16874,x16875,x16872,x16876)) % 186.01/186.05 [1688]~E(x16881,x16882)+E(f608(x16883,x16884,x16885,x16886,x16881),f608(x16883,x16884,x16885,x16886,x16882)) % 186.01/186.05 [1689]~E(x16891,x16892)+E(f796(x16891,x16893,x16894,x16895),f796(x16892,x16893,x16894,x16895)) % 186.01/186.05 [1690]~E(x16901,x16902)+E(f796(x16903,x16901,x16904,x16905),f796(x16903,x16902,x16904,x16905)) % 186.01/186.05 [1691]~E(x16911,x16912)+E(f796(x16913,x16914,x16911,x16915),f796(x16913,x16914,x16912,x16915)) % 186.01/186.05 [1692]~E(x16921,x16922)+E(f796(x16923,x16924,x16925,x16921),f796(x16923,x16924,x16925,x16922)) % 186.01/186.05 [1693]~E(x16931,x16932)+E(f564(x16931,x16933,x16934),f564(x16932,x16933,x16934)) % 186.01/186.05 [1694]~E(x16941,x16942)+E(f564(x16943,x16941,x16944),f564(x16943,x16942,x16944)) % 186.01/186.05 [1695]~E(x16951,x16952)+E(f564(x16953,x16954,x16951),f564(x16953,x16954,x16952)) % 186.01/186.05 [1696]~E(x16961,x16962)+E(f369(x16961,x16963,x16964),f369(x16962,x16963,x16964)) % 186.01/186.05 [1697]~E(x16971,x16972)+E(f369(x16973,x16971,x16974),f369(x16973,x16972,x16974)) % 186.01/186.05 [1698]~E(x16981,x16982)+E(f369(x16983,x16984,x16981),f369(x16983,x16984,x16982)) % 186.01/186.05 [1699]~E(x16991,x16992)+E(f424(x16991),f424(x16992)) % 186.01/186.05 [1700]~E(x17001,x17002)+E(f362(x17001,x17003,x17004,x17005),f362(x17002,x17003,x17004,x17005)) % 186.01/186.05 [1701]~E(x17011,x17012)+E(f362(x17013,x17011,x17014,x17015),f362(x17013,x17012,x17014,x17015)) % 186.01/186.05 [1702]~E(x17021,x17022)+E(f362(x17023,x17024,x17021,x17025),f362(x17023,x17024,x17022,x17025)) % 186.01/186.05 [1703]~E(x17031,x17032)+E(f362(x17033,x17034,x17035,x17031),f362(x17033,x17034,x17035,x17032)) % 186.01/186.05 [1704]~E(x17041,x17042)+E(f905(x17041,x17043,x17044,x17045),f905(x17042,x17043,x17044,x17045)) % 186.01/186.05 [1705]~E(x17051,x17052)+E(f905(x17053,x17051,x17054,x17055),f905(x17053,x17052,x17054,x17055)) % 186.01/186.05 [1706]~E(x17061,x17062)+E(f905(x17063,x17064,x17061,x17065),f905(x17063,x17064,x17062,x17065)) % 186.01/186.05 [1707]~E(x17071,x17072)+E(f905(x17073,x17074,x17075,x17071),f905(x17073,x17074,x17075,x17072)) % 186.01/186.05 [1708]~E(x17081,x17082)+E(f919(x17081,x17083,x17084),f919(x17082,x17083,x17084)) % 186.01/186.05 [1709]~E(x17091,x17092)+E(f919(x17093,x17091,x17094),f919(x17093,x17092,x17094)) % 186.01/186.05 [1710]~E(x17101,x17102)+E(f919(x17103,x17104,x17101),f919(x17103,x17104,x17102)) % 186.01/186.05 [1711]~E(x17111,x17112)+E(f777(x17111,x17113,x17114),f777(x17112,x17113,x17114)) % 186.01/186.05 [1712]~E(x17121,x17122)+E(f777(x17123,x17121,x17124),f777(x17123,x17122,x17124)) % 186.01/186.05 [1713]~E(x17131,x17132)+E(f777(x17133,x17134,x17131),f777(x17133,x17134,x17132)) % 186.01/186.05 [1714]~E(x17141,x17142)+E(f361(x17141,x17143,x17144,x17145),f361(x17142,x17143,x17144,x17145)) % 186.01/186.05 [1715]~E(x17151,x17152)+E(f361(x17153,x17151,x17154,x17155),f361(x17153,x17152,x17154,x17155)) % 186.01/186.05 [1716]~E(x17161,x17162)+E(f361(x17163,x17164,x17161,x17165),f361(x17163,x17164,x17162,x17165)) % 186.01/186.05 [1717]~E(x17171,x17172)+E(f361(x17173,x17174,x17175,x17171),f361(x17173,x17174,x17175,x17172)) % 186.01/186.05 [1718]~E(x17181,x17182)+E(f704(x17181,x17183,x17184,x17185,x17186),f704(x17182,x17183,x17184,x17185,x17186)) % 186.01/186.05 [1719]~E(x17191,x17192)+E(f704(x17193,x17191,x17194,x17195,x17196),f704(x17193,x17192,x17194,x17195,x17196)) % 186.01/186.05 [1720]~E(x17201,x17202)+E(f704(x17203,x17204,x17201,x17205,x17206),f704(x17203,x17204,x17202,x17205,x17206)) % 186.01/186.05 [1721]~E(x17211,x17212)+E(f704(x17213,x17214,x17215,x17211,x17216),f704(x17213,x17214,x17215,x17212,x17216)) % 186.01/186.05 [1722]~E(x17221,x17222)+E(f704(x17223,x17224,x17225,x17226,x17221),f704(x17223,x17224,x17225,x17226,x17222)) % 186.01/186.05 [1723]~E(x17231,x17232)+E(f699(x17231,x17233),f699(x17232,x17233)) % 186.01/186.05 [1724]~E(x17241,x17242)+E(f699(x17243,x17241),f699(x17243,x17242)) % 186.01/186.05 [1725]~E(x17251,x17252)+E(f620(x17251,x17253),f620(x17252,x17253)) % 186.01/186.05 [1726]~E(x17261,x17262)+E(f620(x17263,x17261),f620(x17263,x17262)) % 186.01/186.05 [1727]~E(x17271,x17272)+E(f446(x17271,x17273,x17274,x17275),f446(x17272,x17273,x17274,x17275)) % 186.01/186.05 [1728]~E(x17281,x17282)+E(f446(x17283,x17281,x17284,x17285),f446(x17283,x17282,x17284,x17285)) % 186.01/186.05 [1729]~E(x17291,x17292)+E(f446(x17293,x17294,x17291,x17295),f446(x17293,x17294,x17292,x17295)) % 186.01/186.05 [1730]~E(x17301,x17302)+E(f446(x17303,x17304,x17305,x17301),f446(x17303,x17304,x17305,x17302)) % 186.01/186.05 [1731]~E(x17311,x17312)+E(f787(x17311,x17313,x17314),f787(x17312,x17313,x17314)) % 186.01/186.05 [1732]~E(x17321,x17322)+E(f787(x17323,x17321,x17324),f787(x17323,x17322,x17324)) % 186.01/186.05 [1733]~E(x17331,x17332)+E(f787(x17333,x17334,x17331),f787(x17333,x17334,x17332)) % 186.01/186.05 [1734]~E(x17341,x17342)+E(f192(x17341,x17343,x17344,x17345),f192(x17342,x17343,x17344,x17345)) % 186.01/186.05 [1735]~E(x17351,x17352)+E(f192(x17353,x17351,x17354,x17355),f192(x17353,x17352,x17354,x17355)) % 186.01/186.05 [1736]~E(x17361,x17362)+E(f192(x17363,x17364,x17361,x17365),f192(x17363,x17364,x17362,x17365)) % 186.01/186.05 [1737]~E(x17371,x17372)+E(f192(x17373,x17374,x17375,x17371),f192(x17373,x17374,x17375,x17372)) % 186.01/186.05 [1738]~E(x17381,x17382)+E(f536(x17381,x17383),f536(x17382,x17383)) % 186.01/186.05 [1739]~E(x17391,x17392)+E(f536(x17393,x17391),f536(x17393,x17392)) % 186.01/186.05 [1740]~E(x17401,x17402)+E(f588(x17401,x17403,x17404),f588(x17402,x17403,x17404)) % 186.01/186.05 [1741]~E(x17411,x17412)+E(f588(x17413,x17411,x17414),f588(x17413,x17412,x17414)) % 186.01/186.05 [1742]~E(x17421,x17422)+E(f588(x17423,x17424,x17421),f588(x17423,x17424,x17422)) % 186.01/186.05 [1743]~E(x17431,x17432)+E(f613(x17431,x17433,x17434,x17435,x17436,x17437),f613(x17432,x17433,x17434,x17435,x17436,x17437)) % 186.01/186.05 [1744]~E(x17441,x17442)+E(f613(x17443,x17441,x17444,x17445,x17446,x17447),f613(x17443,x17442,x17444,x17445,x17446,x17447)) % 186.01/186.05 [1745]~E(x17451,x17452)+E(f613(x17453,x17454,x17451,x17455,x17456,x17457),f613(x17453,x17454,x17452,x17455,x17456,x17457)) % 186.01/186.05 [1746]~E(x17461,x17462)+E(f613(x17463,x17464,x17465,x17461,x17466,x17467),f613(x17463,x17464,x17465,x17462,x17466,x17467)) % 186.01/186.05 [1747]~E(x17471,x17472)+E(f613(x17473,x17474,x17475,x17476,x17471,x17477),f613(x17473,x17474,x17475,x17476,x17472,x17477)) % 186.01/186.05 [1748]~E(x17481,x17482)+E(f613(x17483,x17484,x17485,x17486,x17487,x17481),f613(x17483,x17484,x17485,x17486,x17487,x17482)) % 186.01/186.05 [1749]~E(x17491,x17492)+E(f920(x17491,x17493,x17494,x17495,x17496,x17497,x17498),f920(x17492,x17493,x17494,x17495,x17496,x17497,x17498)) % 186.01/186.05 [1750]~E(x17501,x17502)+E(f920(x17503,x17501,x17504,x17505,x17506,x17507,x17508),f920(x17503,x17502,x17504,x17505,x17506,x17507,x17508)) % 186.01/186.05 [1751]~E(x17511,x17512)+E(f920(x17513,x17514,x17511,x17515,x17516,x17517,x17518),f920(x17513,x17514,x17512,x17515,x17516,x17517,x17518)) % 186.01/186.05 [1752]~E(x17521,x17522)+E(f920(x17523,x17524,x17525,x17521,x17526,x17527,x17528),f920(x17523,x17524,x17525,x17522,x17526,x17527,x17528)) % 186.01/186.05 [1753]~E(x17531,x17532)+E(f920(x17533,x17534,x17535,x17536,x17531,x17537,x17538),f920(x17533,x17534,x17535,x17536,x17532,x17537,x17538)) % 186.01/186.05 [1754]~E(x17541,x17542)+E(f920(x17543,x17544,x17545,x17546,x17547,x17541,x17548),f920(x17543,x17544,x17545,x17546,x17547,x17542,x17548)) % 186.01/186.05 [1755]~E(x17551,x17552)+E(f920(x17553,x17554,x17555,x17556,x17557,x17558,x17551),f920(x17553,x17554,x17555,x17556,x17557,x17558,x17552)) % 186.01/186.05 [1756]~E(x17561,x17562)+E(f888(x17561),f888(x17562)) % 186.01/186.05 [1757]~E(x17571,x17572)+E(f358(x17571,x17573,x17574,x17575),f358(x17572,x17573,x17574,x17575)) % 186.01/186.05 [1758]~E(x17581,x17582)+E(f358(x17583,x17581,x17584,x17585),f358(x17583,x17582,x17584,x17585)) % 186.01/186.05 [1759]~E(x17591,x17592)+E(f358(x17593,x17594,x17591,x17595),f358(x17593,x17594,x17592,x17595)) % 186.01/186.05 [1760]~E(x17601,x17602)+E(f358(x17603,x17604,x17605,x17601),f358(x17603,x17604,x17605,x17602)) % 186.01/186.05 [1761]~E(x17611,x17612)+E(f537(x17611,x17613,x17614),f537(x17612,x17613,x17614)) % 186.01/186.05 [1762]~E(x17621,x17622)+E(f537(x17623,x17621,x17624),f537(x17623,x17622,x17624)) % 186.01/186.05 [1763]~E(x17631,x17632)+E(f537(x17633,x17634,x17631),f537(x17633,x17634,x17632)) % 186.01/186.05 [1764]~E(x17641,x17642)+E(f880(x17641,x17643,x17644,x17645,x17646),f880(x17642,x17643,x17644,x17645,x17646)) % 186.01/186.05 [1765]~E(x17651,x17652)+E(f880(x17653,x17651,x17654,x17655,x17656),f880(x17653,x17652,x17654,x17655,x17656)) % 186.01/186.05 [1766]~E(x17661,x17662)+E(f880(x17663,x17664,x17661,x17665,x17666),f880(x17663,x17664,x17662,x17665,x17666)) % 186.01/186.05 [1767]~E(x17671,x17672)+E(f880(x17673,x17674,x17675,x17671,x17676),f880(x17673,x17674,x17675,x17672,x17676)) % 186.01/186.05 [1768]~E(x17681,x17682)+E(f880(x17683,x17684,x17685,x17686,x17681),f880(x17683,x17684,x17685,x17686,x17682)) % 186.01/186.05 [1769]~E(x17691,x17692)+E(f435(x17691),f435(x17692)) % 186.01/186.05 [1770]~E(x17701,x17702)+E(f808(x17701,x17703,x17704,x17705),f808(x17702,x17703,x17704,x17705)) % 186.01/186.05 [1771]~E(x17711,x17712)+E(f808(x17713,x17711,x17714,x17715),f808(x17713,x17712,x17714,x17715)) % 186.01/186.05 [1772]~E(x17721,x17722)+E(f808(x17723,x17724,x17721,x17725),f808(x17723,x17724,x17722,x17725)) % 186.01/186.05 [1773]~E(x17731,x17732)+E(f808(x17733,x17734,x17735,x17731),f808(x17733,x17734,x17735,x17732)) % 186.01/186.05 [1774]~E(x17741,x17742)+E(f909(x17741,x17743,x17744,x17745,x17746,x17747),f909(x17742,x17743,x17744,x17745,x17746,x17747)) % 186.01/186.05 [1775]~E(x17751,x17752)+E(f909(x17753,x17751,x17754,x17755,x17756,x17757),f909(x17753,x17752,x17754,x17755,x17756,x17757)) % 186.01/186.05 [1776]~E(x17761,x17762)+E(f909(x17763,x17764,x17761,x17765,x17766,x17767),f909(x17763,x17764,x17762,x17765,x17766,x17767)) % 186.01/186.05 [1777]~E(x17771,x17772)+E(f909(x17773,x17774,x17775,x17771,x17776,x17777),f909(x17773,x17774,x17775,x17772,x17776,x17777)) % 186.01/186.05 [1778]~E(x17781,x17782)+E(f909(x17783,x17784,x17785,x17786,x17781,x17787),f909(x17783,x17784,x17785,x17786,x17782,x17787)) % 186.01/186.05 [1779]~E(x17791,x17792)+E(f909(x17793,x17794,x17795,x17796,x17797,x17791),f909(x17793,x17794,x17795,x17796,x17797,x17792)) % 186.01/186.05 [1780]~E(x17801,x17802)+E(f759(x17801,x17803,x17804,x17805,x17806),f759(x17802,x17803,x17804,x17805,x17806)) % 186.01/186.05 [1781]~E(x17811,x17812)+E(f759(x17813,x17811,x17814,x17815,x17816),f759(x17813,x17812,x17814,x17815,x17816)) % 186.01/186.05 [1782]~E(x17821,x17822)+E(f759(x17823,x17824,x17821,x17825,x17826),f759(x17823,x17824,x17822,x17825,x17826)) % 186.01/186.05 [1783]~E(x17831,x17832)+E(f759(x17833,x17834,x17835,x17831,x17836),f759(x17833,x17834,x17835,x17832,x17836)) % 186.01/186.05 [1784]~E(x17841,x17842)+E(f759(x17843,x17844,x17845,x17846,x17841),f759(x17843,x17844,x17845,x17846,x17842)) % 186.01/186.05 [1785]~E(x17851,x17852)+E(f532(x17851,x17853,x17854,x17855),f532(x17852,x17853,x17854,x17855)) % 186.01/186.05 [1786]~E(x17861,x17862)+E(f532(x17863,x17861,x17864,x17865),f532(x17863,x17862,x17864,x17865)) % 186.01/186.05 [1787]~E(x17871,x17872)+E(f532(x17873,x17874,x17871,x17875),f532(x17873,x17874,x17872,x17875)) % 186.01/186.05 [1788]~E(x17881,x17882)+E(f532(x17883,x17884,x17885,x17881),f532(x17883,x17884,x17885,x17882)) % 186.01/186.05 [1789]~E(x17891,x17892)+E(f412(x17891,x17893,x17894,x17895,x17896),f412(x17892,x17893,x17894,x17895,x17896)) % 186.01/186.05 [1790]~E(x17901,x17902)+E(f412(x17903,x17901,x17904,x17905,x17906),f412(x17903,x17902,x17904,x17905,x17906)) % 186.01/186.05 [1791]~E(x17911,x17912)+E(f412(x17913,x17914,x17911,x17915,x17916),f412(x17913,x17914,x17912,x17915,x17916)) % 186.01/186.05 [1792]~E(x17921,x17922)+E(f412(x17923,x17924,x17925,x17921,x17926),f412(x17923,x17924,x17925,x17922,x17926)) % 186.01/186.05 [1793]~E(x17931,x17932)+E(f412(x17933,x17934,x17935,x17936,x17931),f412(x17933,x17934,x17935,x17936,x17932)) % 186.01/186.05 [1794]~E(x17941,x17942)+E(f219(x17941,x17943,x17944,x17945),f219(x17942,x17943,x17944,x17945)) % 186.01/186.05 [1795]~E(x17951,x17952)+E(f219(x17953,x17951,x17954,x17955),f219(x17953,x17952,x17954,x17955)) % 186.01/186.05 [1796]~E(x17961,x17962)+E(f219(x17963,x17964,x17961,x17965),f219(x17963,x17964,x17962,x17965)) % 186.01/186.05 [1797]~E(x17971,x17972)+E(f219(x17973,x17974,x17975,x17971),f219(x17973,x17974,x17975,x17972)) % 186.01/186.05 [1798]~E(x17981,x17982)+E(f388(x17981,x17983,x17984,x17985,x17986),f388(x17982,x17983,x17984,x17985,x17986)) % 186.01/186.05 [1799]~E(x17991,x17992)+E(f388(x17993,x17991,x17994,x17995,x17996),f388(x17993,x17992,x17994,x17995,x17996)) % 186.01/186.05 [1800]~E(x18001,x18002)+E(f388(x18003,x18004,x18001,x18005,x18006),f388(x18003,x18004,x18002,x18005,x18006)) % 186.01/186.05 [1801]~E(x18011,x18012)+E(f388(x18013,x18014,x18015,x18011,x18016),f388(x18013,x18014,x18015,x18012,x18016)) % 186.01/186.05 [1802]~E(x18021,x18022)+E(f388(x18023,x18024,x18025,x18026,x18021),f388(x18023,x18024,x18025,x18026,x18022)) % 186.01/186.05 [1803]~E(x18031,x18032)+E(f740(x18031,x18033,x18034),f740(x18032,x18033,x18034)) % 186.01/186.05 [1804]~E(x18041,x18042)+E(f740(x18043,x18041,x18044),f740(x18043,x18042,x18044)) % 186.01/186.05 [1805]~E(x18051,x18052)+E(f740(x18053,x18054,x18051),f740(x18053,x18054,x18052)) % 186.01/186.05 [1806]~E(x18061,x18062)+E(f876(x18061,x18063,x18064,x18065,x18066),f876(x18062,x18063,x18064,x18065,x18066)) % 186.01/186.05 [1807]~E(x18071,x18072)+E(f876(x18073,x18071,x18074,x18075,x18076),f876(x18073,x18072,x18074,x18075,x18076)) % 186.01/186.05 [1808]~E(x18081,x18082)+E(f876(x18083,x18084,x18081,x18085,x18086),f876(x18083,x18084,x18082,x18085,x18086)) % 186.01/186.05 [1809]~E(x18091,x18092)+E(f876(x18093,x18094,x18095,x18091,x18096),f876(x18093,x18094,x18095,x18092,x18096)) % 186.01/186.05 [1810]~E(x18101,x18102)+E(f876(x18103,x18104,x18105,x18106,x18101),f876(x18103,x18104,x18105,x18106,x18102)) % 186.01/186.05 [1811]~E(x18111,x18112)+E(f405(x18111,x18113,x18114,x18115),f405(x18112,x18113,x18114,x18115)) % 186.01/186.05 [1812]~E(x18121,x18122)+E(f405(x18123,x18121,x18124,x18125),f405(x18123,x18122,x18124,x18125)) % 186.01/186.05 [1813]~E(x18131,x18132)+E(f405(x18133,x18134,x18131,x18135),f405(x18133,x18134,x18132,x18135)) % 186.01/186.05 [1814]~E(x18141,x18142)+E(f405(x18143,x18144,x18145,x18141),f405(x18143,x18144,x18145,x18142)) % 186.01/186.05 [1815]~E(x18151,x18152)+E(f615(x18151,x18153,x18154),f615(x18152,x18153,x18154)) % 186.01/186.05 [1816]~E(x18161,x18162)+E(f615(x18163,x18161,x18164),f615(x18163,x18162,x18164)) % 186.01/186.05 [1817]~E(x18171,x18172)+E(f615(x18173,x18174,x18171),f615(x18173,x18174,x18172)) % 186.01/186.05 [1818]~E(x18181,x18182)+E(f806(x18181,x18183),f806(x18182,x18183)) % 186.01/186.05 [1819]~E(x18191,x18192)+E(f806(x18193,x18191),f806(x18193,x18192)) % 186.01/186.05 [1820]~E(x18201,x18202)+E(f254(x18201,x18203,x18204,x18205,x18206,x18207),f254(x18202,x18203,x18204,x18205,x18206,x18207)) % 186.01/186.05 [1821]~E(x18211,x18212)+E(f254(x18213,x18211,x18214,x18215,x18216,x18217),f254(x18213,x18212,x18214,x18215,x18216,x18217)) % 186.01/186.05 [1822]~E(x18221,x18222)+E(f254(x18223,x18224,x18221,x18225,x18226,x18227),f254(x18223,x18224,x18222,x18225,x18226,x18227)) % 186.01/186.05 [1823]~E(x18231,x18232)+E(f254(x18233,x18234,x18235,x18231,x18236,x18237),f254(x18233,x18234,x18235,x18232,x18236,x18237)) % 186.01/186.05 [1824]~E(x18241,x18242)+E(f254(x18243,x18244,x18245,x18246,x18241,x18247),f254(x18243,x18244,x18245,x18246,x18242,x18247)) % 186.01/186.05 [1825]~E(x18251,x18252)+E(f254(x18253,x18254,x18255,x18256,x18257,x18251),f254(x18253,x18254,x18255,x18256,x18257,x18252)) % 186.01/186.05 [1826]~E(x18261,x18262)+E(f454(x18261,x18263,x18264),f454(x18262,x18263,x18264)) % 186.01/186.05 [1827]~E(x18271,x18272)+E(f454(x18273,x18271,x18274),f454(x18273,x18272,x18274)) % 186.01/186.05 [1828]~E(x18281,x18282)+E(f454(x18283,x18284,x18281),f454(x18283,x18284,x18282)) % 186.01/186.05 [1829]~E(x18291,x18292)+E(f344(x18291,x18293,x18294),f344(x18292,x18293,x18294)) % 186.01/186.05 [1830]~E(x18301,x18302)+E(f344(x18303,x18301,x18304),f344(x18303,x18302,x18304)) % 186.01/186.05 [1831]~E(x18311,x18312)+E(f344(x18313,x18314,x18311),f344(x18313,x18314,x18312)) % 186.01/186.05 [1832]~E(x18321,x18322)+E(f916(x18321,x18323),f916(x18322,x18323)) % 186.01/186.05 [1833]~E(x18331,x18332)+E(f916(x18333,x18331),f916(x18333,x18332)) % 186.01/186.05 [1834]~E(x18341,x18342)+E(f514(x18341,x18343,x18344,x18345),f514(x18342,x18343,x18344,x18345)) % 186.01/186.05 [1835]~E(x18351,x18352)+E(f514(x18353,x18351,x18354,x18355),f514(x18353,x18352,x18354,x18355)) % 186.01/186.05 [1836]~E(x18361,x18362)+E(f514(x18363,x18364,x18361,x18365),f514(x18363,x18364,x18362,x18365)) % 186.01/186.05 [1837]~E(x18371,x18372)+E(f514(x18373,x18374,x18375,x18371),f514(x18373,x18374,x18375,x18372)) % 186.01/186.05 [1838]~E(x18381,x18382)+E(f245(x18381,x18383),f245(x18382,x18383)) % 186.01/186.05 [1839]~E(x18391,x18392)+E(f245(x18393,x18391),f245(x18393,x18392)) % 186.01/186.05 [1840]~E(x18401,x18402)+E(f407(x18401,x18403,x18404,x18405),f407(x18402,x18403,x18404,x18405)) % 186.01/186.05 [1841]~E(x18411,x18412)+E(f407(x18413,x18411,x18414,x18415),f407(x18413,x18412,x18414,x18415)) % 186.01/186.05 [1842]~E(x18421,x18422)+E(f407(x18423,x18424,x18421,x18425),f407(x18423,x18424,x18422,x18425)) % 186.01/186.05 [1843]~E(x18431,x18432)+E(f407(x18433,x18434,x18435,x18431),f407(x18433,x18434,x18435,x18432)) % 186.01/186.05 [1844]~E(x18441,x18442)+E(f456(x18441,x18443,x18444),f456(x18442,x18443,x18444)) % 186.01/186.05 [1845]~E(x18451,x18452)+E(f456(x18453,x18451,x18454),f456(x18453,x18452,x18454)) % 186.01/186.05 [1846]~E(x18461,x18462)+E(f456(x18463,x18464,x18461),f456(x18463,x18464,x18462)) % 186.01/186.05 [1847]~E(x18471,x18472)+E(f47(x18471),f47(x18472)) % 186.01/186.05 [1848]~E(x18481,x18482)+E(f744(x18481,x18483),f744(x18482,x18483)) % 186.01/186.05 [1849]~E(x18491,x18492)+E(f744(x18493,x18491),f744(x18493,x18492)) % 186.01/186.05 [1850]~E(x18501,x18502)+E(f711(x18501,x18503,x18504,x18505),f711(x18502,x18503,x18504,x18505)) % 186.01/186.05 [1851]~E(x18511,x18512)+E(f711(x18513,x18511,x18514,x18515),f711(x18513,x18512,x18514,x18515)) % 186.01/186.05 [1852]~E(x18521,x18522)+E(f711(x18523,x18524,x18521,x18525),f711(x18523,x18524,x18522,x18525)) % 186.01/186.05 [1853]~E(x18531,x18532)+E(f711(x18533,x18534,x18535,x18531),f711(x18533,x18534,x18535,x18532)) % 186.01/186.05 [1854]~E(x18541,x18542)+E(f749(x18541,x18543),f749(x18542,x18543)) % 186.01/186.05 [1855]~E(x18551,x18552)+E(f749(x18553,x18551),f749(x18553,x18552)) % 186.01/186.05 [1856]~E(x18561,x18562)+E(f819(x18561,x18563,x18564),f819(x18562,x18563,x18564)) % 186.01/186.05 [1857]~E(x18571,x18572)+E(f819(x18573,x18571,x18574),f819(x18573,x18572,x18574)) % 186.01/186.05 [1858]~E(x18581,x18582)+E(f819(x18583,x18584,x18581),f819(x18583,x18584,x18582)) % 186.01/186.05 [1859]~E(x18591,x18592)+E(f681(x18591,x18593,x18594),f681(x18592,x18593,x18594)) % 186.01/186.05 [1860]~E(x18601,x18602)+E(f681(x18603,x18601,x18604),f681(x18603,x18602,x18604)) % 186.01/186.05 [1861]~E(x18611,x18612)+E(f681(x18613,x18614,x18611),f681(x18613,x18614,x18612)) % 186.01/186.05 [1862]~E(x18621,x18622)+E(f547(x18621,x18623,x18624,x18625,x18626),f547(x18622,x18623,x18624,x18625,x18626)) % 186.01/186.05 [1863]~E(x18631,x18632)+E(f547(x18633,x18631,x18634,x18635,x18636),f547(x18633,x18632,x18634,x18635,x18636)) % 186.01/186.05 [1864]~E(x18641,x18642)+E(f547(x18643,x18644,x18641,x18645,x18646),f547(x18643,x18644,x18642,x18645,x18646)) % 186.01/186.05 [1865]~E(x18651,x18652)+E(f547(x18653,x18654,x18655,x18651,x18656),f547(x18653,x18654,x18655,x18652,x18656)) % 186.01/186.05 [1866]~E(x18661,x18662)+E(f547(x18663,x18664,x18665,x18666,x18661),f547(x18663,x18664,x18665,x18666,x18662)) % 186.01/186.05 [1867]~E(x18671,x18672)+E(f501(x18671,x18673,x18674),f501(x18672,x18673,x18674)) % 186.01/186.05 [1868]~E(x18681,x18682)+E(f501(x18683,x18681,x18684),f501(x18683,x18682,x18684)) % 186.01/186.05 [1869]~E(x18691,x18692)+E(f501(x18693,x18694,x18691),f501(x18693,x18694,x18692)) % 186.01/186.05 [1870]~E(x18701,x18702)+E(f170(x18701,x18703,x18704,x18705),f170(x18702,x18703,x18704,x18705)) % 186.01/186.05 [1871]~E(x18711,x18712)+E(f170(x18713,x18711,x18714,x18715),f170(x18713,x18712,x18714,x18715)) % 186.01/186.05 [1872]~E(x18721,x18722)+E(f170(x18723,x18724,x18721,x18725),f170(x18723,x18724,x18722,x18725)) % 186.01/186.05 [1873]~E(x18731,x18732)+E(f170(x18733,x18734,x18735,x18731),f170(x18733,x18734,x18735,x18732)) % 186.01/186.05 [1874]~E(x18741,x18742)+E(f470(x18741,x18743,x18744,x18745),f470(x18742,x18743,x18744,x18745)) % 186.01/186.05 [1875]~E(x18751,x18752)+E(f470(x18753,x18751,x18754,x18755),f470(x18753,x18752,x18754,x18755)) % 186.01/186.05 [1876]~E(x18761,x18762)+E(f470(x18763,x18764,x18761,x18765),f470(x18763,x18764,x18762,x18765)) % 186.01/186.05 [1877]~E(x18771,x18772)+E(f470(x18773,x18774,x18775,x18771),f470(x18773,x18774,x18775,x18772)) % 186.01/186.05 [1878]~E(x18781,x18782)+E(f390(x18781,x18783,x18784,x18785,x18786),f390(x18782,x18783,x18784,x18785,x18786)) % 186.01/186.05 [1879]~E(x18791,x18792)+E(f390(x18793,x18791,x18794,x18795,x18796),f390(x18793,x18792,x18794,x18795,x18796)) % 186.01/186.05 [1880]~E(x18801,x18802)+E(f390(x18803,x18804,x18801,x18805,x18806),f390(x18803,x18804,x18802,x18805,x18806)) % 186.01/186.05 [1881]~E(x18811,x18812)+E(f390(x18813,x18814,x18815,x18811,x18816),f390(x18813,x18814,x18815,x18812,x18816)) % 186.01/186.05 [1882]~E(x18821,x18822)+E(f390(x18823,x18824,x18825,x18826,x18821),f390(x18823,x18824,x18825,x18826,x18822)) % 186.01/186.05 [1883]~E(x18831,x18832)+E(f899(x18831,x18833,x18834,x18835),f899(x18832,x18833,x18834,x18835)) % 186.01/186.05 [1884]~E(x18841,x18842)+E(f899(x18843,x18841,x18844,x18845),f899(x18843,x18842,x18844,x18845)) % 186.01/186.05 [1885]~E(x18851,x18852)+E(f899(x18853,x18854,x18851,x18855),f899(x18853,x18854,x18852,x18855)) % 186.01/186.05 [1886]~E(x18861,x18862)+E(f899(x18863,x18864,x18865,x18861),f899(x18863,x18864,x18865,x18862)) % 186.01/186.05 [1887]~E(x18871,x18872)+E(f737(x18871,x18873,x18874),f737(x18872,x18873,x18874)) % 186.01/186.05 [1888]~E(x18881,x18882)+E(f737(x18883,x18881,x18884),f737(x18883,x18882,x18884)) % 186.01/186.05 [1889]~E(x18891,x18892)+E(f737(x18893,x18894,x18891),f737(x18893,x18894,x18892)) % 186.01/186.05 [1890]~E(x18901,x18902)+E(f577(x18901,x18903,x18904),f577(x18902,x18903,x18904)) % 186.01/186.05 [1891]~E(x18911,x18912)+E(f577(x18913,x18911,x18914),f577(x18913,x18912,x18914)) % 186.01/186.05 [1892]~E(x18921,x18922)+E(f577(x18923,x18924,x18921),f577(x18923,x18924,x18922)) % 186.01/186.05 [1893]~E(x18931,x18932)+E(f217(x18931),f217(x18932)) % 186.01/186.05 [1894]~E(x18941,x18942)+E(f404(x18941,x18943,x18944),f404(x18942,x18943,x18944)) % 186.01/186.05 [1895]~E(x18951,x18952)+E(f404(x18953,x18951,x18954),f404(x18953,x18952,x18954)) % 186.01/186.05 [1896]~E(x18961,x18962)+E(f404(x18963,x18964,x18961),f404(x18963,x18964,x18962)) % 186.01/186.05 [1897]~E(x18971,x18972)+E(f384(x18971,x18973,x18974,x18975,x18976),f384(x18972,x18973,x18974,x18975,x18976)) % 186.01/186.05 [1898]~E(x18981,x18982)+E(f384(x18983,x18981,x18984,x18985,x18986),f384(x18983,x18982,x18984,x18985,x18986)) % 186.01/186.05 [1899]~E(x18991,x18992)+E(f384(x18993,x18994,x18991,x18995,x18996),f384(x18993,x18994,x18992,x18995,x18996)) % 186.01/186.05 [1900]~E(x19001,x19002)+E(f384(x19003,x19004,x19005,x19001,x19006),f384(x19003,x19004,x19005,x19002,x19006)) % 186.01/186.05 [1901]~E(x19011,x19012)+E(f384(x19013,x19014,x19015,x19016,x19011),f384(x19013,x19014,x19015,x19016,x19012)) % 186.01/186.05 [1902]~E(x19021,x19022)+E(f675(x19021,x19023,x19024,x19025,x19026),f675(x19022,x19023,x19024,x19025,x19026)) % 186.01/186.05 [1903]~E(x19031,x19032)+E(f675(x19033,x19031,x19034,x19035,x19036),f675(x19033,x19032,x19034,x19035,x19036)) % 186.01/186.05 [1904]~E(x19041,x19042)+E(f675(x19043,x19044,x19041,x19045,x19046),f675(x19043,x19044,x19042,x19045,x19046)) % 186.01/186.05 [1905]~E(x19051,x19052)+E(f675(x19053,x19054,x19055,x19051,x19056),f675(x19053,x19054,x19055,x19052,x19056)) % 186.01/186.05 [1906]~E(x19061,x19062)+E(f675(x19063,x19064,x19065,x19066,x19061),f675(x19063,x19064,x19065,x19066,x19062)) % 186.01/186.05 [1907]~E(x19071,x19072)+E(f670(x19071,x19073,x19074,x19075),f670(x19072,x19073,x19074,x19075)) % 186.01/186.05 [1908]~E(x19081,x19082)+E(f670(x19083,x19081,x19084,x19085),f670(x19083,x19082,x19084,x19085)) % 186.01/186.05 [1909]~E(x19091,x19092)+E(f670(x19093,x19094,x19091,x19095),f670(x19093,x19094,x19092,x19095)) % 186.01/186.05 [1910]~E(x19101,x19102)+E(f670(x19103,x19104,x19105,x19101),f670(x19103,x19104,x19105,x19102)) % 186.01/186.05 [1911]~E(x19111,x19112)+E(f517(x19111,x19113,x19114,x19115),f517(x19112,x19113,x19114,x19115)) % 186.01/186.05 [1912]~E(x19121,x19122)+E(f517(x19123,x19121,x19124,x19125),f517(x19123,x19122,x19124,x19125)) % 186.01/186.05 [1913]~E(x19131,x19132)+E(f517(x19133,x19134,x19131,x19135),f517(x19133,x19134,x19132,x19135)) % 186.01/186.05 [1914]~E(x19141,x19142)+E(f517(x19143,x19144,x19145,x19141),f517(x19143,x19144,x19145,x19142)) % 186.01/186.05 [1915]~E(x19151,x19152)+E(f209(x19151),f209(x19152)) % 186.01/186.05 [1916]~E(x19161,x19162)+E(f101(x19161,x19163,x19164,x19165),f101(x19162,x19163,x19164,x19165)) % 186.01/186.05 [1917]~E(x19171,x19172)+E(f101(x19173,x19171,x19174,x19175),f101(x19173,x19172,x19174,x19175)) % 186.01/186.05 [1918]~E(x19181,x19182)+E(f101(x19183,x19184,x19181,x19185),f101(x19183,x19184,x19182,x19185)) % 186.01/186.05 [1919]~E(x19191,x19192)+E(f101(x19193,x19194,x19195,x19191),f101(x19193,x19194,x19195,x19192)) % 186.01/186.05 [1920]~E(x19201,x19202)+E(f734(x19201,x19203,x19204),f734(x19202,x19203,x19204)) % 186.01/186.05 [1921]~E(x19211,x19212)+E(f734(x19213,x19211,x19214),f734(x19213,x19212,x19214)) % 186.01/186.05 [1922]~E(x19221,x19222)+E(f734(x19223,x19224,x19221),f734(x19223,x19224,x19222)) % 186.01/186.05 [1923]~E(x19231,x19232)+E(f389(x19231,x19233,x19234,x19235),f389(x19232,x19233,x19234,x19235)) % 186.01/186.05 [1924]~E(x19241,x19242)+E(f389(x19243,x19241,x19244,x19245),f389(x19243,x19242,x19244,x19245)) % 186.01/186.05 [1925]~E(x19251,x19252)+E(f389(x19253,x19254,x19251,x19255),f389(x19253,x19254,x19252,x19255)) % 186.01/186.05 [1926]~E(x19261,x19262)+E(f389(x19263,x19264,x19265,x19261),f389(x19263,x19264,x19265,x19262)) % 186.01/186.05 [1927]~E(x19271,x19272)+E(f380(x19271,x19273,x19274),f380(x19272,x19273,x19274)) % 186.01/186.05 [1928]~E(x19281,x19282)+E(f380(x19283,x19281,x19284),f380(x19283,x19282,x19284)) % 186.01/186.05 [1929]~E(x19291,x19292)+E(f380(x19293,x19294,x19291),f380(x19293,x19294,x19292)) % 186.01/186.05 [1930]~E(x19301,x19302)+E(f138(x19301,x19303,x19304,x19305),f138(x19302,x19303,x19304,x19305)) % 186.01/186.05 [1931]~E(x19311,x19312)+E(f138(x19313,x19311,x19314,x19315),f138(x19313,x19312,x19314,x19315)) % 186.01/186.05 [1932]~E(x19321,x19322)+E(f138(x19323,x19324,x19321,x19325),f138(x19323,x19324,x19322,x19325)) % 186.01/186.05 [1933]~E(x19331,x19332)+E(f138(x19333,x19334,x19335,x19331),f138(x19333,x19334,x19335,x19332)) % 186.01/186.05 [1934]~E(x19341,x19342)+E(f723(x19341,x19343,x19344,x19345,x19346),f723(x19342,x19343,x19344,x19345,x19346)) % 186.01/186.05 [1935]~E(x19351,x19352)+E(f723(x19353,x19351,x19354,x19355,x19356),f723(x19353,x19352,x19354,x19355,x19356)) % 186.01/186.05 [1936]~E(x19361,x19362)+E(f723(x19363,x19364,x19361,x19365,x19366),f723(x19363,x19364,x19362,x19365,x19366)) % 186.01/186.05 [1937]~E(x19371,x19372)+E(f723(x19373,x19374,x19375,x19371,x19376),f723(x19373,x19374,x19375,x19372,x19376)) % 186.01/186.05 [1938]~E(x19381,x19382)+E(f723(x19383,x19384,x19385,x19386,x19381),f723(x19383,x19384,x19385,x19386,x19382)) % 186.01/186.05 [1939]~E(x19391,x19392)+E(f550(x19391,x19393,x19394,x19395,x19396),f550(x19392,x19393,x19394,x19395,x19396)) % 186.01/186.05 [1940]~E(x19401,x19402)+E(f550(x19403,x19401,x19404,x19405,x19406),f550(x19403,x19402,x19404,x19405,x19406)) % 186.01/186.05 [1941]~E(x19411,x19412)+E(f550(x19413,x19414,x19411,x19415,x19416),f550(x19413,x19414,x19412,x19415,x19416)) % 186.01/186.05 [1942]~E(x19421,x19422)+E(f550(x19423,x19424,x19425,x19421,x19426),f550(x19423,x19424,x19425,x19422,x19426)) % 186.01/186.05 [1943]~E(x19431,x19432)+E(f550(x19433,x19434,x19435,x19436,x19431),f550(x19433,x19434,x19435,x19436,x19432)) % 186.01/186.05 [1944]~E(x19441,x19442)+E(f559(x19441,x19443,x19444),f559(x19442,x19443,x19444)) % 186.01/186.05 [1945]~E(x19451,x19452)+E(f559(x19453,x19451,x19454),f559(x19453,x19452,x19454)) % 186.01/186.05 [1946]~E(x19461,x19462)+E(f559(x19463,x19464,x19461),f559(x19463,x19464,x19462)) % 186.01/186.05 [1947]~E(x19471,x19472)+E(f150(x19471,x19473),f150(x19472,x19473)) % 186.01/186.05 [1948]~E(x19481,x19482)+E(f150(x19483,x19481),f150(x19483,x19482)) % 186.01/186.05 [1949]~E(x19491,x19492)+E(f879(x19491,x19493,x19494,x19495,x19496),f879(x19492,x19493,x19494,x19495,x19496)) % 186.01/186.05 [1950]~E(x19501,x19502)+E(f879(x19503,x19501,x19504,x19505,x19506),f879(x19503,x19502,x19504,x19505,x19506)) % 186.01/186.05 [1951]~E(x19511,x19512)+E(f879(x19513,x19514,x19511,x19515,x19516),f879(x19513,x19514,x19512,x19515,x19516)) % 186.01/186.05 [1952]~E(x19521,x19522)+E(f879(x19523,x19524,x19525,x19521,x19526),f879(x19523,x19524,x19525,x19522,x19526)) % 186.01/186.05 [1953]~E(x19531,x19532)+E(f879(x19533,x19534,x19535,x19536,x19531),f879(x19533,x19534,x19535,x19536,x19532)) % 186.01/186.05 [1954]~E(x19541,x19542)+E(f667(x19541,x19543,x19544,x19545,x19546,x19547),f667(x19542,x19543,x19544,x19545,x19546,x19547)) % 186.01/186.05 [1955]~E(x19551,x19552)+E(f667(x19553,x19551,x19554,x19555,x19556,x19557),f667(x19553,x19552,x19554,x19555,x19556,x19557)) % 186.01/186.05 [1956]~E(x19561,x19562)+E(f667(x19563,x19564,x19561,x19565,x19566,x19567),f667(x19563,x19564,x19562,x19565,x19566,x19567)) % 186.01/186.05 [1957]~E(x19571,x19572)+E(f667(x19573,x19574,x19575,x19571,x19576,x19577),f667(x19573,x19574,x19575,x19572,x19576,x19577)) % 186.01/186.05 [1958]~E(x19581,x19582)+E(f667(x19583,x19584,x19585,x19586,x19581,x19587),f667(x19583,x19584,x19585,x19586,x19582,x19587)) % 186.01/186.05 [1959]~E(x19591,x19592)+E(f667(x19593,x19594,x19595,x19596,x19597,x19591),f667(x19593,x19594,x19595,x19596,x19597,x19592)) % 186.01/186.05 [1960]~E(x19601,x19602)+E(f685(x19601,x19603,x19604),f685(x19602,x19603,x19604)) % 186.01/186.05 [1961]~E(x19611,x19612)+E(f685(x19613,x19611,x19614),f685(x19613,x19612,x19614)) % 186.01/186.05 [1962]~E(x19621,x19622)+E(f685(x19623,x19624,x19621),f685(x19623,x19624,x19622)) % 186.01/186.05 [1963]~E(x19631,x19632)+E(f837(x19631,x19633,x19634,x19635,x19636,x19637),f837(x19632,x19633,x19634,x19635,x19636,x19637)) % 186.01/186.05 [1964]~E(x19641,x19642)+E(f837(x19643,x19641,x19644,x19645,x19646,x19647),f837(x19643,x19642,x19644,x19645,x19646,x19647)) % 186.01/186.05 [1965]~E(x19651,x19652)+E(f837(x19653,x19654,x19651,x19655,x19656,x19657),f837(x19653,x19654,x19652,x19655,x19656,x19657)) % 186.01/186.05 [1966]~E(x19661,x19662)+E(f837(x19663,x19664,x19665,x19661,x19666,x19667),f837(x19663,x19664,x19665,x19662,x19666,x19667)) % 186.01/186.05 [1967]~E(x19671,x19672)+E(f837(x19673,x19674,x19675,x19676,x19671,x19677),f837(x19673,x19674,x19675,x19676,x19672,x19677)) % 186.01/186.05 [1968]~E(x19681,x19682)+E(f837(x19683,x19684,x19685,x19686,x19687,x19681),f837(x19683,x19684,x19685,x19686,x19687,x19682)) % 186.01/186.05 [1969]~E(x19691,x19692)+E(f621(x19691,x19693,x19694,x19695,x19696),f621(x19692,x19693,x19694,x19695,x19696)) % 186.01/186.05 [1970]~E(x19701,x19702)+E(f621(x19703,x19701,x19704,x19705,x19706),f621(x19703,x19702,x19704,x19705,x19706)) % 186.01/186.05 [1971]~E(x19711,x19712)+E(f621(x19713,x19714,x19711,x19715,x19716),f621(x19713,x19714,x19712,x19715,x19716)) % 186.01/186.05 [1972]~E(x19721,x19722)+E(f621(x19723,x19724,x19725,x19721,x19726),f621(x19723,x19724,x19725,x19722,x19726)) % 186.01/186.05 [1973]~E(x19731,x19732)+E(f621(x19733,x19734,x19735,x19736,x19731),f621(x19733,x19734,x19735,x19736,x19732)) % 186.01/186.05 [1974]~E(x19741,x19742)+E(f494(x19741,x19743,x19744),f494(x19742,x19743,x19744)) % 186.01/186.05 [1975]~E(x19751,x19752)+E(f494(x19753,x19751,x19754),f494(x19753,x19752,x19754)) % 186.01/186.05 [1976]~E(x19761,x19762)+E(f494(x19763,x19764,x19761),f494(x19763,x19764,x19762)) % 186.01/186.05 [1977]~E(x19771,x19772)+E(f60(x19771,x19773),f60(x19772,x19773)) % 186.01/186.05 [1978]~E(x19781,x19782)+E(f60(x19783,x19781),f60(x19783,x19782)) % 186.01/186.05 [1979]~E(x19791,x19792)+E(f677(x19791,x19793,x19794,x19795,x19796),f677(x19792,x19793,x19794,x19795,x19796)) % 186.01/186.05 [1980]~E(x19801,x19802)+E(f677(x19803,x19801,x19804,x19805,x19806),f677(x19803,x19802,x19804,x19805,x19806)) % 186.01/186.05 [1981]~E(x19811,x19812)+E(f677(x19813,x19814,x19811,x19815,x19816),f677(x19813,x19814,x19812,x19815,x19816)) % 186.01/186.05 [1982]~E(x19821,x19822)+E(f677(x19823,x19824,x19825,x19821,x19826),f677(x19823,x19824,x19825,x19822,x19826)) % 186.01/186.05 [1983]~E(x19831,x19832)+E(f677(x19833,x19834,x19835,x19836,x19831),f677(x19833,x19834,x19835,x19836,x19832)) % 186.01/186.05 [1984]~E(x19841,x19842)+E(f378(x19841,x19843,x19844),f378(x19842,x19843,x19844)) % 186.01/186.05 [1985]~E(x19851,x19852)+E(f378(x19853,x19851,x19854),f378(x19853,x19852,x19854)) % 186.01/186.05 [1986]~E(x19861,x19862)+E(f378(x19863,x19864,x19861),f378(x19863,x19864,x19862)) % 186.01/186.05 [1987]~E(x19871,x19872)+E(f539(x19871,x19873,x19874,x19875,x19876),f539(x19872,x19873,x19874,x19875,x19876)) % 186.01/186.05 [1988]~E(x19881,x19882)+E(f539(x19883,x19881,x19884,x19885,x19886),f539(x19883,x19882,x19884,x19885,x19886)) % 186.01/186.05 [1989]~E(x19891,x19892)+E(f539(x19893,x19894,x19891,x19895,x19896),f539(x19893,x19894,x19892,x19895,x19896)) % 186.01/186.05 [1990]~E(x19901,x19902)+E(f539(x19903,x19904,x19905,x19901,x19906),f539(x19903,x19904,x19905,x19902,x19906)) % 186.01/186.05 [1991]~E(x19911,x19912)+E(f539(x19913,x19914,x19915,x19916,x19911),f539(x19913,x19914,x19915,x19916,x19912)) % 186.01/186.05 [1992]~E(x19921,x19922)+E(f705(x19921,x19923,x19924,x19925,x19926),f705(x19922,x19923,x19924,x19925,x19926)) % 186.01/186.05 [1993]~E(x19931,x19932)+E(f705(x19933,x19931,x19934,x19935,x19936),f705(x19933,x19932,x19934,x19935,x19936)) % 186.01/186.05 [1994]~E(x19941,x19942)+E(f705(x19943,x19944,x19941,x19945,x19946),f705(x19943,x19944,x19942,x19945,x19946)) % 186.01/186.05 [1995]~E(x19951,x19952)+E(f705(x19953,x19954,x19955,x19951,x19956),f705(x19953,x19954,x19955,x19952,x19956)) % 186.01/186.05 [1996]~E(x19961,x19962)+E(f705(x19963,x19964,x19965,x19966,x19961),f705(x19963,x19964,x19965,x19966,x19962)) % 186.01/186.05 [1997]~E(x19971,x19972)+E(f568(x19971,x19973,x19974),f568(x19972,x19973,x19974)) % 186.01/186.05 [1998]~E(x19981,x19982)+E(f568(x19983,x19981,x19984),f568(x19983,x19982,x19984)) % 186.01/186.05 [1999]~E(x19991,x19992)+E(f568(x19993,x19994,x19991),f568(x19993,x19994,x19992)) % 186.01/186.05 [2000]~E(x20001,x20002)+E(f360(x20001,x20003,x20004,x20005,x20006),f360(x20002,x20003,x20004,x20005,x20006)) % 186.01/186.05 [2001]~E(x20011,x20012)+E(f360(x20013,x20011,x20014,x20015,x20016),f360(x20013,x20012,x20014,x20015,x20016)) % 186.01/186.05 [2002]~E(x20021,x20022)+E(f360(x20023,x20024,x20021,x20025,x20026),f360(x20023,x20024,x20022,x20025,x20026)) % 186.01/186.05 [2003]~E(x20031,x20032)+E(f360(x20033,x20034,x20035,x20031,x20036),f360(x20033,x20034,x20035,x20032,x20036)) % 186.01/186.05 [2004]~E(x20041,x20042)+E(f360(x20043,x20044,x20045,x20046,x20041),f360(x20043,x20044,x20045,x20046,x20042)) % 186.01/186.05 [2005]~E(x20051,x20052)+E(f863(x20051,x20053,x20054,x20055,x20056,x20057,x20058,x20059),f863(x20052,x20053,x20054,x20055,x20056,x20057,x20058,x20059)) % 186.01/186.05 [2006]~E(x20061,x20062)+E(f863(x20063,x20061,x20064,x20065,x20066,x20067,x20068,x20069),f863(x20063,x20062,x20064,x20065,x20066,x20067,x20068,x20069)) % 186.01/186.05 [2007]~E(x20071,x20072)+E(f863(x20073,x20074,x20071,x20075,x20076,x20077,x20078,x20079),f863(x20073,x20074,x20072,x20075,x20076,x20077,x20078,x20079)) % 186.01/186.05 [2008]~E(x20081,x20082)+E(f863(x20083,x20084,x20085,x20081,x20086,x20087,x20088,x20089),f863(x20083,x20084,x20085,x20082,x20086,x20087,x20088,x20089)) % 186.01/186.05 [2009]~E(x20091,x20092)+E(f863(x20093,x20094,x20095,x20096,x20091,x20097,x20098,x20099),f863(x20093,x20094,x20095,x20096,x20092,x20097,x20098,x20099)) % 186.01/186.05 [2010]~E(x20101,x20102)+E(f863(x20103,x20104,x20105,x20106,x20107,x20101,x20108,x20109),f863(x20103,x20104,x20105,x20106,x20107,x20102,x20108,x20109)) % 186.01/186.05 [2011]~E(x20111,x20112)+E(f863(x20113,x20114,x20115,x20116,x20117,x20118,x20111,x20119),f863(x20113,x20114,x20115,x20116,x20117,x20118,x20112,x20119)) % 186.01/186.05 [2012]~E(x20121,x20122)+E(f863(x20123,x20124,x20125,x20126,x20127,x20128,x20129,x20121),f863(x20123,x20124,x20125,x20126,x20127,x20128,x20129,x20122)) % 186.01/186.05 [2013]~E(x20131,x20132)+E(f856(x20131,x20133,x20134,x20135,x20136,x20137),f856(x20132,x20133,x20134,x20135,x20136,x20137)) % 186.01/186.05 [2014]~E(x20141,x20142)+E(f856(x20143,x20141,x20144,x20145,x20146,x20147),f856(x20143,x20142,x20144,x20145,x20146,x20147)) % 186.01/186.05 [2015]~E(x20151,x20152)+E(f856(x20153,x20154,x20151,x20155,x20156,x20157),f856(x20153,x20154,x20152,x20155,x20156,x20157)) % 186.01/186.05 [2016]~E(x20161,x20162)+E(f856(x20163,x20164,x20165,x20161,x20166,x20167),f856(x20163,x20164,x20165,x20162,x20166,x20167)) % 186.01/186.05 [2017]~E(x20171,x20172)+E(f856(x20173,x20174,x20175,x20176,x20171,x20177),f856(x20173,x20174,x20175,x20176,x20172,x20177)) % 186.01/186.05 [2018]~E(x20181,x20182)+E(f856(x20183,x20184,x20185,x20186,x20187,x20181),f856(x20183,x20184,x20185,x20186,x20187,x20182)) % 186.01/186.05 [2019]~E(x20191,x20192)+E(f366(x20191,x20193),f366(x20192,x20193)) % 186.01/186.05 [2020]~E(x20201,x20202)+E(f366(x20203,x20201),f366(x20203,x20202)) % 186.01/186.05 [2021]~E(x20211,x20212)+E(f279(x20211,x20213,x20214,x20215),f279(x20212,x20213,x20214,x20215)) % 186.01/186.05 [2022]~E(x20221,x20222)+E(f279(x20223,x20221,x20224,x20225),f279(x20223,x20222,x20224,x20225)) % 186.01/186.05 [2023]~E(x20231,x20232)+E(f279(x20233,x20234,x20231,x20235),f279(x20233,x20234,x20232,x20235)) % 186.01/186.05 [2024]~E(x20241,x20242)+E(f279(x20243,x20244,x20245,x20241),f279(x20243,x20244,x20245,x20242)) % 186.01/186.05 [2025]~E(x20251,x20252)+E(f466(x20251,x20253),f466(x20252,x20253)) % 186.01/186.05 [2026]~E(x20261,x20262)+E(f466(x20263,x20261),f466(x20263,x20262)) % 186.01/186.05 [2027]~E(x20271,x20272)+E(f457(x20271,x20273,x20274),f457(x20272,x20273,x20274)) % 186.01/186.05 [2028]~E(x20281,x20282)+E(f457(x20283,x20281,x20284),f457(x20283,x20282,x20284)) % 186.01/186.05 [2029]~E(x20291,x20292)+E(f457(x20293,x20294,x20291),f457(x20293,x20294,x20292)) % 186.01/186.05 [2030]~E(x20301,x20302)+E(f210(x20301),f210(x20302)) % 186.01/186.05 [2031]~E(x20311,x20312)+E(f486(x20311,x20313,x20314,x20315,x20316,x20317),f486(x20312,x20313,x20314,x20315,x20316,x20317)) % 186.01/186.05 [2032]~E(x20321,x20322)+E(f486(x20323,x20321,x20324,x20325,x20326,x20327),f486(x20323,x20322,x20324,x20325,x20326,x20327)) % 186.01/186.05 [2033]~E(x20331,x20332)+E(f486(x20333,x20334,x20331,x20335,x20336,x20337),f486(x20333,x20334,x20332,x20335,x20336,x20337)) % 186.01/186.05 [2034]~E(x20341,x20342)+E(f486(x20343,x20344,x20345,x20341,x20346,x20347),f486(x20343,x20344,x20345,x20342,x20346,x20347)) % 186.01/186.05 [2035]~E(x20351,x20352)+E(f486(x20353,x20354,x20355,x20356,x20351,x20357),f486(x20353,x20354,x20355,x20356,x20352,x20357)) % 186.01/186.05 [2036]~E(x20361,x20362)+E(f486(x20363,x20364,x20365,x20366,x20367,x20361),f486(x20363,x20364,x20365,x20366,x20367,x20362)) % 186.01/186.05 [2037]~E(x20371,x20372)+E(f231(x20371,x20373,x20374),f231(x20372,x20373,x20374)) % 186.01/186.05 [2038]~E(x20381,x20382)+E(f231(x20383,x20381,x20384),f231(x20383,x20382,x20384)) % 186.01/186.05 [2039]~E(x20391,x20392)+E(f231(x20393,x20394,x20391),f231(x20393,x20394,x20392)) % 186.01/186.05 [2040]~E(x20401,x20402)+E(f918(x20401,x20403,x20404),f918(x20402,x20403,x20404)) % 186.01/186.05 [2041]~E(x20411,x20412)+E(f918(x20413,x20411,x20414),f918(x20413,x20412,x20414)) % 186.01/186.05 [2042]~E(x20421,x20422)+E(f918(x20423,x20424,x20421),f918(x20423,x20424,x20422)) % 186.01/186.05 [2043]~E(x20431,x20432)+E(f211(x20431,x20433),f211(x20432,x20433)) % 186.01/186.05 [2044]~E(x20441,x20442)+E(f211(x20443,x20441),f211(x20443,x20442)) % 186.01/186.05 [2045]~E(x20451,x20452)+E(f693(x20451,x20453,x20454,x20455),f693(x20452,x20453,x20454,x20455)) % 186.01/186.05 [2046]~E(x20461,x20462)+E(f693(x20463,x20461,x20464,x20465),f693(x20463,x20462,x20464,x20465)) % 186.01/186.05 [2047]~E(x20471,x20472)+E(f693(x20473,x20474,x20471,x20475),f693(x20473,x20474,x20472,x20475)) % 186.01/186.05 [2048]~E(x20481,x20482)+E(f693(x20483,x20484,x20485,x20481),f693(x20483,x20484,x20485,x20482)) % 186.01/186.05 [2049]~E(x20491,x20492)+E(f225(x20491,x20493),f225(x20492,x20493)) % 186.01/186.05 [2050]~E(x20501,x20502)+E(f225(x20503,x20501),f225(x20503,x20502)) % 186.01/186.05 [2051]~E(x20511,x20512)+E(f702(x20511,x20513,x20514,x20515),f702(x20512,x20513,x20514,x20515)) % 186.01/186.05 [2052]~E(x20521,x20522)+E(f702(x20523,x20521,x20524,x20525),f702(x20523,x20522,x20524,x20525)) % 186.01/186.05 [2053]~E(x20531,x20532)+E(f702(x20533,x20534,x20531,x20535),f702(x20533,x20534,x20532,x20535)) % 186.01/186.05 [2054]~E(x20541,x20542)+E(f702(x20543,x20544,x20545,x20541),f702(x20543,x20544,x20545,x20542)) % 186.01/186.05 [2055]~E(x20551,x20552)+E(f616(x20551,x20553,x20554),f616(x20552,x20553,x20554)) % 186.01/186.05 [2056]~E(x20561,x20562)+E(f616(x20563,x20561,x20564),f616(x20563,x20562,x20564)) % 186.01/186.05 [2057]~E(x20571,x20572)+E(f616(x20573,x20574,x20571),f616(x20573,x20574,x20572)) % 186.01/186.05 [2058]~E(x20581,x20582)+E(f50(x20581),f50(x20582)) % 186.01/186.05 [2059]~E(x20591,x20592)+E(f780(x20591,x20593,x20594),f780(x20592,x20593,x20594)) % 186.01/186.05 [2060]~E(x20601,x20602)+E(f780(x20603,x20601,x20604),f780(x20603,x20602,x20604)) % 186.01/186.05 [2061]~E(x20611,x20612)+E(f780(x20613,x20614,x20611),f780(x20613,x20614,x20612)) % 186.01/186.05 [2062]~E(x20621,x20622)+E(f793(x20621,x20623,x20624),f793(x20622,x20623,x20624)) % 186.01/186.05 [2063]~E(x20631,x20632)+E(f793(x20633,x20631,x20634),f793(x20633,x20632,x20634)) % 186.01/186.05 [2064]~E(x20641,x20642)+E(f793(x20643,x20644,x20641),f793(x20643,x20644,x20642)) % 186.01/186.05 [2065]~E(x20651,x20652)+E(f633(x20651,x20653,x20654,x20655),f633(x20652,x20653,x20654,x20655)) % 186.01/186.05 [2066]~E(x20661,x20662)+E(f633(x20663,x20661,x20664,x20665),f633(x20663,x20662,x20664,x20665)) % 186.01/186.05 [2067]~E(x20671,x20672)+E(f633(x20673,x20674,x20671,x20675),f633(x20673,x20674,x20672,x20675)) % 186.01/186.05 [2068]~E(x20681,x20682)+E(f633(x20683,x20684,x20685,x20681),f633(x20683,x20684,x20685,x20682)) % 186.01/186.05 [2069]~E(x20691,x20692)+E(f665(x20691,x20693,x20694,x20695),f665(x20692,x20693,x20694,x20695)) % 186.01/186.05 [2070]~E(x20701,x20702)+E(f665(x20703,x20701,x20704,x20705),f665(x20703,x20702,x20704,x20705)) % 186.01/186.05 [2071]~E(x20711,x20712)+E(f665(x20713,x20714,x20711,x20715),f665(x20713,x20714,x20712,x20715)) % 186.01/186.05 [2072]~E(x20721,x20722)+E(f665(x20723,x20724,x20725,x20721),f665(x20723,x20724,x20725,x20722)) % 186.01/186.05 [2073]~E(x20731,x20732)+E(f589(x20731,x20733,x20734),f589(x20732,x20733,x20734)) % 186.01/186.05 [2074]~E(x20741,x20742)+E(f589(x20743,x20741,x20744),f589(x20743,x20742,x20744)) % 186.01/186.05 [2075]~E(x20751,x20752)+E(f589(x20753,x20754,x20751),f589(x20753,x20754,x20752)) % 186.01/186.05 [2076]~E(x20761,x20762)+E(f671(x20761,x20763,x20764,x20765),f671(x20762,x20763,x20764,x20765)) % 186.01/186.05 [2077]~E(x20771,x20772)+E(f671(x20773,x20771,x20774,x20775),f671(x20773,x20772,x20774,x20775)) % 186.01/186.05 [2078]~E(x20781,x20782)+E(f671(x20783,x20784,x20781,x20785),f671(x20783,x20784,x20782,x20785)) % 186.01/186.05 [2079]~E(x20791,x20792)+E(f671(x20793,x20794,x20795,x20791),f671(x20793,x20794,x20795,x20792)) % 186.01/186.05 [2080]~E(x20801,x20802)+E(f546(x20801,x20803,x20804,x20805,x20806),f546(x20802,x20803,x20804,x20805,x20806)) % 186.01/186.05 [2081]~E(x20811,x20812)+E(f546(x20813,x20811,x20814,x20815,x20816),f546(x20813,x20812,x20814,x20815,x20816)) % 186.01/186.05 [2082]~E(x20821,x20822)+E(f546(x20823,x20824,x20821,x20825,x20826),f546(x20823,x20824,x20822,x20825,x20826)) % 186.01/186.05 [2083]~E(x20831,x20832)+E(f546(x20833,x20834,x20835,x20831,x20836),f546(x20833,x20834,x20835,x20832,x20836)) % 186.01/186.05 [2084]~E(x20841,x20842)+E(f546(x20843,x20844,x20845,x20846,x20841),f546(x20843,x20844,x20845,x20846,x20842)) % 186.01/186.05 [2085]~E(x20851,x20852)+E(f638(x20851,x20853,x20854,x20855,x20856),f638(x20852,x20853,x20854,x20855,x20856)) % 186.01/186.05 [2086]~E(x20861,x20862)+E(f638(x20863,x20861,x20864,x20865,x20866),f638(x20863,x20862,x20864,x20865,x20866)) % 186.01/186.05 [2087]~E(x20871,x20872)+E(f638(x20873,x20874,x20871,x20875,x20876),f638(x20873,x20874,x20872,x20875,x20876)) % 186.01/186.05 [2088]~E(x20881,x20882)+E(f638(x20883,x20884,x20885,x20881,x20886),f638(x20883,x20884,x20885,x20882,x20886)) % 186.01/186.05 [2089]~E(x20891,x20892)+E(f638(x20893,x20894,x20895,x20896,x20891),f638(x20893,x20894,x20895,x20896,x20892)) % 186.01/186.05 [2090]~E(x20901,x20902)+E(f376(x20901,x20903,x20904),f376(x20902,x20903,x20904)) % 186.01/186.05 [2091]~E(x20911,x20912)+E(f376(x20913,x20911,x20914),f376(x20913,x20912,x20914)) % 186.01/186.05 [2092]~E(x20921,x20922)+E(f376(x20923,x20924,x20921),f376(x20923,x20924,x20922)) % 186.01/186.05 [2093]~E(x20931,x20932)+E(f678(x20931,x20933,x20934,x20935,x20936),f678(x20932,x20933,x20934,x20935,x20936)) % 186.01/186.05 [2094]~E(x20941,x20942)+E(f678(x20943,x20941,x20944,x20945,x20946),f678(x20943,x20942,x20944,x20945,x20946)) % 186.01/186.05 [2095]~E(x20951,x20952)+E(f678(x20953,x20954,x20951,x20955,x20956),f678(x20953,x20954,x20952,x20955,x20956)) % 186.01/186.05 [2096]~E(x20961,x20962)+E(f678(x20963,x20964,x20965,x20961,x20966),f678(x20963,x20964,x20965,x20962,x20966)) % 186.01/186.05 [2097]~E(x20971,x20972)+E(f678(x20973,x20974,x20975,x20976,x20971),f678(x20973,x20974,x20975,x20976,x20972)) % 186.01/186.05 [2098]~E(x20981,x20982)+E(f495(x20981,x20983,x20984),f495(x20982,x20983,x20984)) % 186.01/186.05 [2099]~E(x20991,x20992)+E(f495(x20993,x20991,x20994),f495(x20993,x20992,x20994)) % 186.01/186.05 [2100]~E(x21001,x21002)+E(f495(x21003,x21004,x21001),f495(x21003,x21004,x21002)) % 186.01/186.05 [2101]~E(x21011,x21012)+E(f442(x21011),f442(x21012)) % 186.01/186.05 [2102]~E(x21021,x21022)+E(f345(x21021,x21023,x21024,x21025),f345(x21022,x21023,x21024,x21025)) % 186.01/186.05 [2103]~E(x21031,x21032)+E(f345(x21033,x21031,x21034,x21035),f345(x21033,x21032,x21034,x21035)) % 186.01/186.05 [2104]~E(x21041,x21042)+E(f345(x21043,x21044,x21041,x21045),f345(x21043,x21044,x21042,x21045)) % 186.01/186.05 [2105]~E(x21051,x21052)+E(f345(x21053,x21054,x21055,x21051),f345(x21053,x21054,x21055,x21052)) % 186.01/186.05 [2106]~E(x21061,x21062)+E(f528(x21061,x21063),f528(x21062,x21063)) % 186.01/186.05 [2107]~E(x21071,x21072)+E(f528(x21073,x21071),f528(x21073,x21072)) % 186.01/186.05 [2108]~E(x21081,x21082)+E(f396(x21081,x21083,x21084),f396(x21082,x21083,x21084)) % 186.01/186.05 [2109]~E(x21091,x21092)+E(f396(x21093,x21091,x21094),f396(x21093,x21092,x21094)) % 186.01/186.05 [2110]~E(x21101,x21102)+E(f396(x21103,x21104,x21101),f396(x21103,x21104,x21102)) % 186.01/186.05 [2111]~E(x21111,x21112)+E(f795(x21111,x21113,x21114,x21115),f795(x21112,x21113,x21114,x21115)) % 186.01/186.05 [2112]~E(x21121,x21122)+E(f795(x21123,x21121,x21124,x21125),f795(x21123,x21122,x21124,x21125)) % 186.01/186.05 [2113]~E(x21131,x21132)+E(f795(x21133,x21134,x21131,x21135),f795(x21133,x21134,x21132,x21135)) % 186.01/186.05 [2114]~E(x21141,x21142)+E(f795(x21143,x21144,x21145,x21141),f795(x21143,x21144,x21145,x21142)) % 186.01/186.05 [2115]~E(x21151,x21152)+E(f510(x21151,x21153,x21154,x21155),f510(x21152,x21153,x21154,x21155)) % 186.01/186.05 [2116]~E(x21161,x21162)+E(f510(x21163,x21161,x21164,x21165),f510(x21163,x21162,x21164,x21165)) % 186.01/186.05 [2117]~E(x21171,x21172)+E(f510(x21173,x21174,x21171,x21175),f510(x21173,x21174,x21172,x21175)) % 186.01/186.05 [2118]~E(x21181,x21182)+E(f510(x21183,x21184,x21185,x21181),f510(x21183,x21184,x21185,x21182)) % 186.01/186.05 [2119]~E(x21191,x21192)+E(f350(x21191),f350(x21192)) % 186.01/186.05 [2120]~E(x21201,x21202)+E(f904(x21201,x21203,x21204),f904(x21202,x21203,x21204)) % 186.01/186.05 [2121]~E(x21211,x21212)+E(f904(x21213,x21211,x21214),f904(x21213,x21212,x21214)) % 186.01/186.05 [2122]~E(x21221,x21222)+E(f904(x21223,x21224,x21221),f904(x21223,x21224,x21222)) % 186.01/186.05 [2123]~E(x21231,x21232)+E(f697(x21231,x21233,x21234),f697(x21232,x21233,x21234)) % 186.01/186.05 [2124]~E(x21241,x21242)+E(f697(x21243,x21241,x21244),f697(x21243,x21242,x21244)) % 186.01/186.05 [2125]~E(x21251,x21252)+E(f697(x21253,x21254,x21251),f697(x21253,x21254,x21252)) % 186.01/186.05 [2126]~E(x21261,x21262)+E(f631(x21261,x21263,x21264),f631(x21262,x21263,x21264)) % 186.01/186.05 [2127]~E(x21271,x21272)+E(f631(x21273,x21271,x21274),f631(x21273,x21272,x21274)) % 186.01/186.05 [2128]~E(x21281,x21282)+E(f631(x21283,x21284,x21281),f631(x21283,x21284,x21282)) % 186.01/186.05 [2129]~E(x21291,x21292)+E(f659(x21291,x21293,x21294,x21295,x21296,x21297),f659(x21292,x21293,x21294,x21295,x21296,x21297)) % 186.01/186.05 [2130]~E(x21301,x21302)+E(f659(x21303,x21301,x21304,x21305,x21306,x21307),f659(x21303,x21302,x21304,x21305,x21306,x21307)) % 186.01/186.05 [2131]~E(x21311,x21312)+E(f659(x21313,x21314,x21311,x21315,x21316,x21317),f659(x21313,x21314,x21312,x21315,x21316,x21317)) % 186.01/186.05 [2132]~E(x21321,x21322)+E(f659(x21323,x21324,x21325,x21321,x21326,x21327),f659(x21323,x21324,x21325,x21322,x21326,x21327)) % 186.01/186.05 [2133]~E(x21331,x21332)+E(f659(x21333,x21334,x21335,x21336,x21331,x21337),f659(x21333,x21334,x21335,x21336,x21332,x21337)) % 186.01/186.05 [2134]~E(x21341,x21342)+E(f659(x21343,x21344,x21345,x21346,x21347,x21341),f659(x21343,x21344,x21345,x21346,x21347,x21342)) % 186.01/186.05 [2135]~E(x21351,x21352)+E(f882(x21351,x21353,x21354,x21355),f882(x21352,x21353,x21354,x21355)) % 186.01/186.05 [2136]~E(x21361,x21362)+E(f882(x21363,x21361,x21364,x21365),f882(x21363,x21362,x21364,x21365)) % 186.01/186.05 [2137]~E(x21371,x21372)+E(f882(x21373,x21374,x21371,x21375),f882(x21373,x21374,x21372,x21375)) % 186.01/186.05 [2138]~E(x21381,x21382)+E(f882(x21383,x21384,x21385,x21381),f882(x21383,x21384,x21385,x21382)) % 186.01/186.05 [2139]~E(x21391,x21392)+E(f463(x21391,x21393),f463(x21392,x21393)) % 186.01/186.05 [2140]~E(x21401,x21402)+E(f463(x21403,x21401),f463(x21403,x21402)) % 186.01/186.05 [2141]~E(x21411,x21412)+E(f359(x21411,x21413,x21414,x21415),f359(x21412,x21413,x21414,x21415)) % 186.01/186.05 [2142]~E(x21421,x21422)+E(f359(x21423,x21421,x21424,x21425),f359(x21423,x21422,x21424,x21425)) % 186.01/186.05 [2143]~E(x21431,x21432)+E(f359(x21433,x21434,x21431,x21435),f359(x21433,x21434,x21432,x21435)) % 186.01/186.05 [2144]~E(x21441,x21442)+E(f359(x21443,x21444,x21445,x21441),f359(x21443,x21444,x21445,x21442)) % 186.01/186.05 [2145]~E(x21451,x21452)+E(f497(x21451,x21453),f497(x21452,x21453)) % 186.01/186.05 [2146]~E(x21461,x21462)+E(f497(x21463,x21461),f497(x21463,x21462)) % 186.01/186.05 [2147]~E(x21471,x21472)+E(f721(x21471,x21473),f721(x21472,x21473)) % 186.01/186.05 [2148]~E(x21481,x21482)+E(f721(x21483,x21481),f721(x21483,x21482)) % 186.01/186.05 [2149]~E(x21491,x21492)+E(f285(x21491,x21493,x21494,x21495),f285(x21492,x21493,x21494,x21495)) % 186.01/186.05 [2150]~E(x21501,x21502)+E(f285(x21503,x21501,x21504,x21505),f285(x21503,x21502,x21504,x21505)) % 186.01/186.05 [2151]~E(x21511,x21512)+E(f285(x21513,x21514,x21511,x21515),f285(x21513,x21514,x21512,x21515)) % 186.01/186.05 [2152]~E(x21521,x21522)+E(f285(x21523,x21524,x21525,x21521),f285(x21523,x21524,x21525,x21522)) % 186.01/186.05 [2153]~E(x21531,x21532)+E(f630(x21531,x21533,x21534),f630(x21532,x21533,x21534)) % 186.01/186.05 [2154]~E(x21541,x21542)+E(f630(x21543,x21541,x21544),f630(x21543,x21542,x21544)) % 186.01/186.05 [2155]~E(x21551,x21552)+E(f630(x21553,x21554,x21551),f630(x21553,x21554,x21552)) % 186.01/186.05 [2156]~E(x21561,x21562)+E(f745(x21561,x21563,x21564),f745(x21562,x21563,x21564)) % 186.01/186.05 [2157]~E(x21571,x21572)+E(f745(x21573,x21571,x21574),f745(x21573,x21572,x21574)) % 186.01/186.05 [2158]~E(x21581,x21582)+E(f745(x21583,x21584,x21581),f745(x21583,x21584,x21582)) % 186.01/186.05 [2159]~E(x21591,x21592)+E(f181(x21591,x21593,x21594),f181(x21592,x21593,x21594)) % 186.01/186.05 [2160]~E(x21601,x21602)+E(f181(x21603,x21601,x21604),f181(x21603,x21602,x21604)) % 186.01/186.05 [2161]~E(x21611,x21612)+E(f181(x21613,x21614,x21611),f181(x21613,x21614,x21612)) % 186.01/186.05 [2162]~E(x21621,x21622)+E(f436(x21621),f436(x21622)) % 186.01/186.05 [2163]~E(x21631,x21632)+E(f543(x21631,x21633,x21634,x21635,x21636),f543(x21632,x21633,x21634,x21635,x21636)) % 186.01/186.05 [2164]~E(x21641,x21642)+E(f543(x21643,x21641,x21644,x21645,x21646),f543(x21643,x21642,x21644,x21645,x21646)) % 186.01/186.05 [2165]~E(x21651,x21652)+E(f543(x21653,x21654,x21651,x21655,x21656),f543(x21653,x21654,x21652,x21655,x21656)) % 186.01/186.05 [2166]~E(x21661,x21662)+E(f543(x21663,x21664,x21665,x21661,x21666),f543(x21663,x21664,x21665,x21662,x21666)) % 186.01/186.05 [2167]~E(x21671,x21672)+E(f543(x21673,x21674,x21675,x21676,x21671),f543(x21673,x21674,x21675,x21676,x21672)) % 186.01/186.05 [2168]~E(x21681,x21682)+E(f646(x21681,x21683,x21684,x21685,x21686,x21687,x21688,x21689),f646(x21682,x21683,x21684,x21685,x21686,x21687,x21688,x21689)) % 186.01/186.05 [2169]~E(x21691,x21692)+E(f646(x21693,x21691,x21694,x21695,x21696,x21697,x21698,x21699),f646(x21693,x21692,x21694,x21695,x21696,x21697,x21698,x21699)) % 186.01/186.05 [2170]~E(x21701,x21702)+E(f646(x21703,x21704,x21701,x21705,x21706,x21707,x21708,x21709),f646(x21703,x21704,x21702,x21705,x21706,x21707,x21708,x21709)) % 186.01/186.05 [2171]~E(x21711,x21712)+E(f646(x21713,x21714,x21715,x21711,x21716,x21717,x21718,x21719),f646(x21713,x21714,x21715,x21712,x21716,x21717,x21718,x21719)) % 186.01/186.05 [2172]~E(x21721,x21722)+E(f646(x21723,x21724,x21725,x21726,x21721,x21727,x21728,x21729),f646(x21723,x21724,x21725,x21726,x21722,x21727,x21728,x21729)) % 186.01/186.05 [2173]~E(x21731,x21732)+E(f646(x21733,x21734,x21735,x21736,x21737,x21731,x21738,x21739),f646(x21733,x21734,x21735,x21736,x21737,x21732,x21738,x21739)) % 186.01/186.05 [2174]~E(x21741,x21742)+E(f646(x21743,x21744,x21745,x21746,x21747,x21748,x21741,x21749),f646(x21743,x21744,x21745,x21746,x21747,x21748,x21742,x21749)) % 186.01/186.05 [2175]~E(x21751,x21752)+E(f646(x21753,x21754,x21755,x21756,x21757,x21758,x21759,x21751),f646(x21753,x21754,x21755,x21756,x21757,x21758,x21759,x21752)) % 186.01/186.05 [2176]~E(x21761,x21762)+E(f581(x21761,x21763,x21764),f581(x21762,x21763,x21764)) % 186.01/186.05 [2177]~E(x21771,x21772)+E(f581(x21773,x21771,x21774),f581(x21773,x21772,x21774)) % 186.01/186.05 [2178]~E(x21781,x21782)+E(f581(x21783,x21784,x21781),f581(x21783,x21784,x21782)) % 186.01/186.05 [2179]~E(x21791,x21792)+E(f130(x21791),f130(x21792)) % 186.01/186.05 [2180]~E(x21801,x21802)+E(f673(x21801,x21803),f673(x21802,x21803)) % 186.01/186.05 [2181]~E(x21811,x21812)+E(f673(x21813,x21811),f673(x21813,x21812)) % 186.01/186.05 [2182]~E(x21821,x21822)+E(f515(x21821,x21823,x21824,x21825),f515(x21822,x21823,x21824,x21825)) % 186.01/186.05 [2183]~E(x21831,x21832)+E(f515(x21833,x21831,x21834,x21835),f515(x21833,x21832,x21834,x21835)) % 186.01/186.05 [2184]~E(x21841,x21842)+E(f515(x21843,x21844,x21841,x21845),f515(x21843,x21844,x21842,x21845)) % 186.01/186.05 [2185]~E(x21851,x21852)+E(f515(x21853,x21854,x21855,x21851),f515(x21853,x21854,x21855,x21852)) % 186.01/186.05 [2186]~E(x21861,x21862)+E(f820(x21861,x21863,x21864,x21865),f820(x21862,x21863,x21864,x21865)) % 186.01/186.05 [2187]~E(x21871,x21872)+E(f820(x21873,x21871,x21874,x21875),f820(x21873,x21872,x21874,x21875)) % 186.01/186.05 [2188]~E(x21881,x21882)+E(f820(x21883,x21884,x21881,x21885),f820(x21883,x21884,x21882,x21885)) % 186.01/186.05 [2189]~E(x21891,x21892)+E(f820(x21893,x21894,x21895,x21891),f820(x21893,x21894,x21895,x21892)) % 186.01/186.05 [2190]~E(x21901,x21902)+E(f367(x21901,x21903),f367(x21902,x21903)) % 186.01/186.05 [2191]~E(x21911,x21912)+E(f367(x21913,x21911),f367(x21913,x21912)) % 186.01/186.05 [2192]~E(x21921,x21922)+E(f730(x21921,x21923),f730(x21922,x21923)) % 186.01/186.05 [2193]~E(x21931,x21932)+E(f730(x21933,x21931),f730(x21933,x21932)) % 186.01/186.05 [2194]~E(x21941,x21942)+E(f917(x21941,x21943,x21944),f917(x21942,x21943,x21944)) % 186.01/186.05 [2195]~E(x21951,x21952)+E(f917(x21953,x21951,x21954),f917(x21953,x21952,x21954)) % 186.01/186.05 [2196]~E(x21961,x21962)+E(f917(x21963,x21964,x21961),f917(x21963,x21964,x21962)) % 186.01/186.05 [2197]~E(x21971,x21972)+E(f894(x21971,x21973,x21974,x21975),f894(x21972,x21973,x21974,x21975)) % 186.01/186.05 [2198]~E(x21981,x21982)+E(f894(x21983,x21981,x21984,x21985),f894(x21983,x21982,x21984,x21985)) % 186.01/186.05 [2199]~E(x21991,x21992)+E(f894(x21993,x21994,x21991,x21995),f894(x21993,x21994,x21992,x21995)) % 186.01/186.05 [2200]~E(x22001,x22002)+E(f894(x22003,x22004,x22005,x22001),f894(x22003,x22004,x22005,x22002)) % 186.01/186.05 [2201]~E(x22011,x22012)+E(f417(x22011,x22013),f417(x22012,x22013)) % 186.01/186.05 [2202]~E(x22021,x22022)+E(f417(x22023,x22021),f417(x22023,x22022)) % 186.01/186.05 [2203]~E(x22031,x22032)+E(f774(x22031,x22033,x22034),f774(x22032,x22033,x22034)) % 186.01/186.05 [2204]~E(x22041,x22042)+E(f774(x22043,x22041,x22044),f774(x22043,x22042,x22044)) % 186.01/186.05 [2205]~E(x22051,x22052)+E(f774(x22053,x22054,x22051),f774(x22053,x22054,x22052)) % 186.01/186.05 [2206]~E(x22061,x22062)+E(f838(x22061),f838(x22062)) % 186.01/186.05 [2207]~E(x22071,x22072)+E(f857(x22071,x22073,x22074,x22075,x22076,x22077,x22078,x22079),f857(x22072,x22073,x22074,x22075,x22076,x22077,x22078,x22079)) % 186.01/186.05 [2208]~E(x22081,x22082)+E(f857(x22083,x22081,x22084,x22085,x22086,x22087,x22088,x22089),f857(x22083,x22082,x22084,x22085,x22086,x22087,x22088,x22089)) % 186.01/186.05 [2209]~E(x22091,x22092)+E(f857(x22093,x22094,x22091,x22095,x22096,x22097,x22098,x22099),f857(x22093,x22094,x22092,x22095,x22096,x22097,x22098,x22099)) % 186.01/186.05 [2210]~E(x22101,x22102)+E(f857(x22103,x22104,x22105,x22101,x22106,x22107,x22108,x22109),f857(x22103,x22104,x22105,x22102,x22106,x22107,x22108,x22109)) % 186.01/186.05 [2211]~E(x22111,x22112)+E(f857(x22113,x22114,x22115,x22116,x22111,x22117,x22118,x22119),f857(x22113,x22114,x22115,x22116,x22112,x22117,x22118,x22119)) % 186.01/186.05 [2212]~E(x22121,x22122)+E(f857(x22123,x22124,x22125,x22126,x22127,x22121,x22128,x22129),f857(x22123,x22124,x22125,x22126,x22127,x22122,x22128,x22129)) % 186.01/186.05 [2213]~E(x22131,x22132)+E(f857(x22133,x22134,x22135,x22136,x22137,x22138,x22131,x22139),f857(x22133,x22134,x22135,x22136,x22137,x22138,x22132,x22139)) % 186.01/186.05 [2214]~E(x22141,x22142)+E(f857(x22143,x22144,x22145,x22146,x22147,x22148,x22149,x22141),f857(x22143,x22144,x22145,x22146,x22147,x22148,x22149,x22142)) % 186.01/186.05 [2215]~E(x22151,x22152)+E(f766(x22151,x22153,x22154,x22155,x22156),f766(x22152,x22153,x22154,x22155,x22156)) % 186.01/186.05 [2216]~E(x22161,x22162)+E(f766(x22163,x22161,x22164,x22165,x22166),f766(x22163,x22162,x22164,x22165,x22166)) % 186.01/186.05 [2217]~E(x22171,x22172)+E(f766(x22173,x22174,x22171,x22175,x22176),f766(x22173,x22174,x22172,x22175,x22176)) % 186.01/186.05 [2218]~E(x22181,x22182)+E(f766(x22183,x22184,x22185,x22181,x22186),f766(x22183,x22184,x22185,x22182,x22186)) % 186.01/186.05 [2219]~E(x22191,x22192)+E(f766(x22193,x22194,x22195,x22196,x22191),f766(x22193,x22194,x22195,x22196,x22192)) % 186.01/186.05 [2220]~E(x22201,x22202)+E(f786(x22201,x22203,x22204),f786(x22202,x22203,x22204)) % 186.01/186.05 [2221]~E(x22211,x22212)+E(f786(x22213,x22211,x22214),f786(x22213,x22212,x22214)) % 186.01/186.05 [2222]~E(x22221,x22222)+E(f786(x22223,x22224,x22221),f786(x22223,x22224,x22222)) % 186.01/186.05 [2223]~E(x22231,x22232)+E(f307(x22231,x22233,x22234,x22235),f307(x22232,x22233,x22234,x22235)) % 186.01/186.05 [2224]~E(x22241,x22242)+E(f307(x22243,x22241,x22244,x22245),f307(x22243,x22242,x22244,x22245)) % 186.01/186.05 [2225]~E(x22251,x22252)+E(f307(x22253,x22254,x22251,x22255),f307(x22253,x22254,x22252,x22255)) % 186.01/186.05 [2226]~E(x22261,x22262)+E(f307(x22263,x22264,x22265,x22261),f307(x22263,x22264,x22265,x22262)) % 186.01/186.05 [2227]~E(x22271,x22272)+E(f902(x22271,x22273,x22274,x22275,x22276,x22277),f902(x22272,x22273,x22274,x22275,x22276,x22277)) % 186.01/186.05 [2228]~E(x22281,x22282)+E(f902(x22283,x22281,x22284,x22285,x22286,x22287),f902(x22283,x22282,x22284,x22285,x22286,x22287)) % 186.01/186.05 [2229]~E(x22291,x22292)+E(f902(x22293,x22294,x22291,x22295,x22296,x22297),f902(x22293,x22294,x22292,x22295,x22296,x22297)) % 186.01/186.05 [2230]~E(x22301,x22302)+E(f902(x22303,x22304,x22305,x22301,x22306,x22307),f902(x22303,x22304,x22305,x22302,x22306,x22307)) % 186.01/186.05 [2231]~E(x22311,x22312)+E(f902(x22313,x22314,x22315,x22316,x22311,x22317),f902(x22313,x22314,x22315,x22316,x22312,x22317)) % 186.01/186.05 [2232]~E(x22321,x22322)+E(f902(x22323,x22324,x22325,x22326,x22327,x22321),f902(x22323,x22324,x22325,x22326,x22327,x22322)) % 186.01/186.05 [2233]~E(x22331,x22332)+E(f499(x22331,x22333),f499(x22332,x22333)) % 186.01/186.05 [2234]~E(x22341,x22342)+E(f499(x22343,x22341),f499(x22343,x22342)) % 186.01/186.05 [2235]~E(x22351,x22352)+E(f481(x22351,x22353,x22354,x22355,x22356),f481(x22352,x22353,x22354,x22355,x22356)) % 186.01/186.05 [2236]~E(x22361,x22362)+E(f481(x22363,x22361,x22364,x22365,x22366),f481(x22363,x22362,x22364,x22365,x22366)) % 186.01/186.05 [2237]~E(x22371,x22372)+E(f481(x22373,x22374,x22371,x22375,x22376),f481(x22373,x22374,x22372,x22375,x22376)) % 186.01/186.05 [2238]~E(x22381,x22382)+E(f481(x22383,x22384,x22385,x22381,x22386),f481(x22383,x22384,x22385,x22382,x22386)) % 186.01/186.05 [2239]~E(x22391,x22392)+E(f481(x22393,x22394,x22395,x22396,x22391),f481(x22393,x22394,x22395,x22396,x22392)) % 186.01/186.05 [2240]~E(x22401,x22402)+E(f775(x22401,x22403,x22404,x22405),f775(x22402,x22403,x22404,x22405)) % 186.01/186.05 [2241]~E(x22411,x22412)+E(f775(x22413,x22411,x22414,x22415),f775(x22413,x22412,x22414,x22415)) % 186.01/186.05 [2242]~E(x22421,x22422)+E(f775(x22423,x22424,x22421,x22425),f775(x22423,x22424,x22422,x22425)) % 186.01/186.05 [2243]~E(x22431,x22432)+E(f775(x22433,x22434,x22435,x22431),f775(x22433,x22434,x22435,x22432)) % 186.01/186.05 [2244]~E(x22441,x22442)+E(f399(x22441),f399(x22442)) % 186.01/186.05 [2245]~E(x22451,x22452)+E(f827(x22451,x22453,x22454),f827(x22452,x22453,x22454)) % 186.01/186.05 [2246]~E(x22461,x22462)+E(f827(x22463,x22461,x22464),f827(x22463,x22462,x22464)) % 186.01/186.05 [2247]~E(x22471,x22472)+E(f827(x22473,x22474,x22471),f827(x22473,x22474,x22472)) % 186.01/186.05 [2248]~E(x22481,x22482)+E(f792(x22481,x22483,x22484),f792(x22482,x22483,x22484)) % 186.01/186.05 [2249]~E(x22491,x22492)+E(f792(x22493,x22491,x22494),f792(x22493,x22492,x22494)) % 186.01/186.05 [2250]~E(x22501,x22502)+E(f792(x22503,x22504,x22501),f792(x22503,x22504,x22502)) % 186.01/186.05 [2251]~E(x22511,x22512)+E(f807(x22511,x22513),f807(x22512,x22513)) % 186.01/186.05 [2252]~E(x22521,x22522)+E(f807(x22523,x22521),f807(x22523,x22522)) % 186.01/186.05 [2253]~E(x22531,x22532)+E(f375(x22531,x22533,x22534),f375(x22532,x22533,x22534)) % 186.01/186.05 [2254]~E(x22541,x22542)+E(f375(x22543,x22541,x22544),f375(x22543,x22542,x22544)) % 186.01/186.05 [2255]~E(x22551,x22552)+E(f375(x22553,x22554,x22551),f375(x22553,x22554,x22552)) % 186.01/186.05 [2256]~E(x22561,x22562)+E(f556(x22561),f556(x22562)) % 186.01/186.05 [2257]~E(x22571,x22572)+E(f269(x22571,x22573,x22574,x22575,x22576),f269(x22572,x22573,x22574,x22575,x22576)) % 186.01/186.05 [2258]~E(x22581,x22582)+E(f269(x22583,x22581,x22584,x22585,x22586),f269(x22583,x22582,x22584,x22585,x22586)) % 186.01/186.05 [2259]~E(x22591,x22592)+E(f269(x22593,x22594,x22591,x22595,x22596),f269(x22593,x22594,x22592,x22595,x22596)) % 186.01/186.05 [2260]~E(x22601,x22602)+E(f269(x22603,x22604,x22605,x22601,x22606),f269(x22603,x22604,x22605,x22602,x22606)) % 186.01/186.05 [2261]~E(x22611,x22612)+E(f269(x22613,x22614,x22615,x22616,x22611),f269(x22613,x22614,x22615,x22616,x22612)) % 186.01/186.05 [2262]~E(x22621,x22622)+E(f724(x22621,x22623,x22624,x22625,x22626),f724(x22622,x22623,x22624,x22625,x22626)) % 186.01/186.05 [2263]~E(x22631,x22632)+E(f724(x22633,x22631,x22634,x22635,x22636),f724(x22633,x22632,x22634,x22635,x22636)) % 186.01/186.05 [2264]~E(x22641,x22642)+E(f724(x22643,x22644,x22641,x22645,x22646),f724(x22643,x22644,x22642,x22645,x22646)) % 186.01/186.05 [2265]~E(x22651,x22652)+E(f724(x22653,x22654,x22655,x22651,x22656),f724(x22653,x22654,x22655,x22652,x22656)) % 186.01/186.05 [2266]~E(x22661,x22662)+E(f724(x22663,x22664,x22665,x22666,x22661),f724(x22663,x22664,x22665,x22666,x22662)) % 186.01/186.05 [2267]~E(x22671,x22672)+E(f500(x22671,x22673,x22674,x22675),f500(x22672,x22673,x22674,x22675)) % 186.01/186.05 [2268]~E(x22681,x22682)+E(f500(x22683,x22681,x22684,x22685),f500(x22683,x22682,x22684,x22685)) % 186.01/186.05 [2269]~E(x22691,x22692)+E(f500(x22693,x22694,x22691,x22695),f500(x22693,x22694,x22692,x22695)) % 186.01/186.05 [2270]~E(x22701,x22702)+E(f500(x22703,x22704,x22705,x22701),f500(x22703,x22704,x22705,x22702)) % 186.01/186.05 [2271]~E(x22711,x22712)+E(f420(x22711,x22713),f420(x22712,x22713)) % 186.01/186.05 [2272]~E(x22721,x22722)+E(f420(x22723,x22721),f420(x22723,x22722)) % 186.01/186.05 [2273]~E(x22731,x22732)+E(f825(x22731),f825(x22732)) % 186.01/186.05 [2274]~E(x22741,x22742)+E(f197(x22741,x22743,x22744,x22745),f197(x22742,x22743,x22744,x22745)) % 186.01/186.05 [2275]~E(x22751,x22752)+E(f197(x22753,x22751,x22754,x22755),f197(x22753,x22752,x22754,x22755)) % 186.01/186.05 [2276]~E(x22761,x22762)+E(f197(x22763,x22764,x22761,x22765),f197(x22763,x22764,x22762,x22765)) % 186.01/186.05 [2277]~E(x22771,x22772)+E(f197(x22773,x22774,x22775,x22771),f197(x22773,x22774,x22775,x22772)) % 186.01/186.05 [2278]~E(x22781,x22782)+E(f479(x22781,x22783,x22784),f479(x22782,x22783,x22784)) % 186.01/186.05 [2279]~E(x22791,x22792)+E(f479(x22793,x22791,x22794),f479(x22793,x22792,x22794)) % 186.01/186.05 [2280]~E(x22801,x22802)+E(f479(x22803,x22804,x22801),f479(x22803,x22804,x22802)) % 186.01/186.05 [2281]~E(x22811,x22812)+E(f423(x22811,x22813,x22814,x22815,x22816),f423(x22812,x22813,x22814,x22815,x22816)) % 186.01/186.05 [2282]~E(x22821,x22822)+E(f423(x22823,x22821,x22824,x22825,x22826),f423(x22823,x22822,x22824,x22825,x22826)) % 186.01/186.05 [2283]~E(x22831,x22832)+E(f423(x22833,x22834,x22831,x22835,x22836),f423(x22833,x22834,x22832,x22835,x22836)) % 186.01/186.05 [2284]~E(x22841,x22842)+E(f423(x22843,x22844,x22845,x22841,x22846),f423(x22843,x22844,x22845,x22842,x22846)) % 186.01/186.05 [2285]~E(x22851,x22852)+E(f423(x22853,x22854,x22855,x22856,x22851),f423(x22853,x22854,x22855,x22856,x22852)) % 186.01/186.05 [2286]~E(x22861,x22862)+E(f306(x22861,x22863,x22864),f306(x22862,x22863,x22864)) % 186.01/186.05 [2287]~E(x22871,x22872)+E(f306(x22873,x22871,x22874),f306(x22873,x22872,x22874)) % 186.01/186.05 [2288]~E(x22881,x22882)+E(f306(x22883,x22884,x22881),f306(x22883,x22884,x22882)) % 186.01/186.05 [2289]~E(x22891,x22892)+E(f605(x22891,x22893,x22894,x22895,x22896,x22897),f605(x22892,x22893,x22894,x22895,x22896,x22897)) % 186.01/186.05 [2290]~E(x22901,x22902)+E(f605(x22903,x22901,x22904,x22905,x22906,x22907),f605(x22903,x22902,x22904,x22905,x22906,x22907)) % 186.01/186.05 [2291]~E(x22911,x22912)+E(f605(x22913,x22914,x22911,x22915,x22916,x22917),f605(x22913,x22914,x22912,x22915,x22916,x22917)) % 186.01/186.05 [2292]~E(x22921,x22922)+E(f605(x22923,x22924,x22925,x22921,x22926,x22927),f605(x22923,x22924,x22925,x22922,x22926,x22927)) % 186.01/186.05 [2293]~E(x22931,x22932)+E(f605(x22933,x22934,x22935,x22936,x22931,x22937),f605(x22933,x22934,x22935,x22936,x22932,x22937)) % 186.01/186.05 [2294]~E(x22941,x22942)+E(f605(x22943,x22944,x22945,x22946,x22947,x22941),f605(x22943,x22944,x22945,x22946,x22947,x22942)) % 186.01/186.05 [2295]~E(x22951,x22952)+E(f891(x22951,x22953),f891(x22952,x22953)) % 186.01/186.05 [2296]~E(x22961,x22962)+E(f891(x22963,x22961),f891(x22963,x22962)) % 186.01/186.05 [2297]~E(x22971,x22972)+E(f833(x22971,x22973,x22974),f833(x22972,x22973,x22974)) % 186.01/186.05 [2298]~E(x22981,x22982)+E(f833(x22983,x22981,x22984),f833(x22983,x22982,x22984)) % 186.01/186.05 [2299]~E(x22991,x22992)+E(f833(x22993,x22994,x22991),f833(x22993,x22994,x22992)) % 186.01/186.05 [2300]~E(x23001,x23002)+E(f626(x23001,x23003,x23004,x23005,x23006),f626(x23002,x23003,x23004,x23005,x23006)) % 186.01/186.05 [2301]~E(x23011,x23012)+E(f626(x23013,x23011,x23014,x23015,x23016),f626(x23013,x23012,x23014,x23015,x23016)) % 186.01/186.05 [2302]~E(x23021,x23022)+E(f626(x23023,x23024,x23021,x23025,x23026),f626(x23023,x23024,x23022,x23025,x23026)) % 186.01/186.05 [2303]~E(x23031,x23032)+E(f626(x23033,x23034,x23035,x23031,x23036),f626(x23033,x23034,x23035,x23032,x23036)) % 186.01/186.05 [2304]~E(x23041,x23042)+E(f626(x23043,x23044,x23045,x23046,x23041),f626(x23043,x23044,x23045,x23046,x23042)) % 186.01/186.05 [2305]~E(x23051,x23052)+E(f381(x23051,x23053,x23054),f381(x23052,x23053,x23054)) % 186.01/186.05 [2306]~E(x23061,x23062)+E(f381(x23063,x23061,x23064),f381(x23063,x23062,x23064)) % 186.01/186.05 [2307]~E(x23071,x23072)+E(f381(x23073,x23074,x23071),f381(x23073,x23074,x23072)) % 186.01/186.05 [2308]~E(x23081,x23082)+E(f527(x23081,x23083,x23084,x23085),f527(x23082,x23083,x23084,x23085)) % 186.01/186.05 [2309]~E(x23091,x23092)+E(f527(x23093,x23091,x23094,x23095),f527(x23093,x23092,x23094,x23095)) % 186.01/186.05 [2310]~E(x23101,x23102)+E(f527(x23103,x23104,x23101,x23105),f527(x23103,x23104,x23102,x23105)) % 186.01/186.05 [2311]~E(x23111,x23112)+E(f527(x23113,x23114,x23115,x23111),f527(x23113,x23114,x23115,x23112)) % 186.01/186.05 [2312]~E(x23121,x23122)+E(f202(x23121,x23123,x23124,x23125),f202(x23122,x23123,x23124,x23125)) % 186.01/186.05 [2313]~E(x23131,x23132)+E(f202(x23133,x23131,x23134,x23135),f202(x23133,x23132,x23134,x23135)) % 186.01/186.05 [2314]~E(x23141,x23142)+E(f202(x23143,x23144,x23141,x23145),f202(x23143,x23144,x23142,x23145)) % 186.01/186.05 [2315]~E(x23151,x23152)+E(f202(x23153,x23154,x23155,x23151),f202(x23153,x23154,x23155,x23152)) % 186.01/186.05 [2316]~E(x23161,x23162)+E(f483(x23161,x23163,x23164,x23165,x23166),f483(x23162,x23163,x23164,x23165,x23166)) % 186.01/186.05 [2317]~E(x23171,x23172)+E(f483(x23173,x23171,x23174,x23175,x23176),f483(x23173,x23172,x23174,x23175,x23176)) % 186.01/186.05 [2318]~E(x23181,x23182)+E(f483(x23183,x23184,x23181,x23185,x23186),f483(x23183,x23184,x23182,x23185,x23186)) % 186.01/186.05 [2319]~E(x23191,x23192)+E(f483(x23193,x23194,x23195,x23191,x23196),f483(x23193,x23194,x23195,x23192,x23196)) % 186.01/186.05 [2320]~E(x23201,x23202)+E(f483(x23203,x23204,x23205,x23206,x23201),f483(x23203,x23204,x23205,x23206,x23202)) % 186.01/186.05 [2321]~E(x23211,x23212)+E(f567(x23211,x23213),f567(x23212,x23213)) % 186.01/186.05 [2322]~E(x23221,x23222)+E(f567(x23223,x23221),f567(x23223,x23222)) % 186.01/186.05 [2323]~E(x23231,x23232)+E(f598(x23231,x23233,x23234,x23235,x23236,x23237),f598(x23232,x23233,x23234,x23235,x23236,x23237)) % 186.01/186.05 [2324]~E(x23241,x23242)+E(f598(x23243,x23241,x23244,x23245,x23246,x23247),f598(x23243,x23242,x23244,x23245,x23246,x23247)) % 186.01/186.05 [2325]~E(x23251,x23252)+E(f598(x23253,x23254,x23251,x23255,x23256,x23257),f598(x23253,x23254,x23252,x23255,x23256,x23257)) % 186.01/186.05 [2326]~E(x23261,x23262)+E(f598(x23263,x23264,x23265,x23261,x23266,x23267),f598(x23263,x23264,x23265,x23262,x23266,x23267)) % 186.01/186.05 [2327]~E(x23271,x23272)+E(f598(x23273,x23274,x23275,x23276,x23271,x23277),f598(x23273,x23274,x23275,x23276,x23272,x23277)) % 186.01/186.05 [2328]~E(x23281,x23282)+E(f598(x23283,x23284,x23285,x23286,x23287,x23281),f598(x23283,x23284,x23285,x23286,x23287,x23282)) % 186.01/186.05 [2329]~E(x23291,x23292)+E(f664(x23291,x23293,x23294,x23295),f664(x23292,x23293,x23294,x23295)) % 186.01/186.05 [2330]~E(x23301,x23302)+E(f664(x23303,x23301,x23304,x23305),f664(x23303,x23302,x23304,x23305)) % 186.01/186.05 [2331]~E(x23311,x23312)+E(f664(x23313,x23314,x23311,x23315),f664(x23313,x23314,x23312,x23315)) % 186.01/186.05 [2332]~E(x23321,x23322)+E(f664(x23323,x23324,x23325,x23321),f664(x23323,x23324,x23325,x23322)) % 186.01/186.05 [2333]~E(x23331,x23332)+E(f865(x23331,x23333,x23334,x23335,x23336,x23337,x23338,x23339),f865(x23332,x23333,x23334,x23335,x23336,x23337,x23338,x23339)) % 186.01/186.05 [2334]~E(x23341,x23342)+E(f865(x23343,x23341,x23344,x23345,x23346,x23347,x23348,x23349),f865(x23343,x23342,x23344,x23345,x23346,x23347,x23348,x23349)) % 186.01/186.05 [2335]~E(x23351,x23352)+E(f865(x23353,x23354,x23351,x23355,x23356,x23357,x23358,x23359),f865(x23353,x23354,x23352,x23355,x23356,x23357,x23358,x23359)) % 186.01/186.05 [2336]~E(x23361,x23362)+E(f865(x23363,x23364,x23365,x23361,x23366,x23367,x23368,x23369),f865(x23363,x23364,x23365,x23362,x23366,x23367,x23368,x23369)) % 186.01/186.05 [2337]~E(x23371,x23372)+E(f865(x23373,x23374,x23375,x23376,x23371,x23377,x23378,x23379),f865(x23373,x23374,x23375,x23376,x23372,x23377,x23378,x23379)) % 186.01/186.05 [2338]~E(x23381,x23382)+E(f865(x23383,x23384,x23385,x23386,x23387,x23381,x23388,x23389),f865(x23383,x23384,x23385,x23386,x23387,x23382,x23388,x23389)) % 186.01/186.05 [2339]~E(x23391,x23392)+E(f865(x23393,x23394,x23395,x23396,x23397,x23398,x23391,x23399),f865(x23393,x23394,x23395,x23396,x23397,x23398,x23392,x23399)) % 186.01/186.05 [2340]~E(x23401,x23402)+E(f865(x23403,x23404,x23405,x23406,x23407,x23408,x23409,x23401),f865(x23403,x23404,x23405,x23406,x23407,x23408,x23409,x23402)) % 186.01/186.05 [2341]~E(x23411,x23412)+E(f216(x23411,x23413,x23414,x23415,x23416,x23417,x23418),f216(x23412,x23413,x23414,x23415,x23416,x23417,x23418)) % 186.01/186.05 [2342]~E(x23421,x23422)+E(f216(x23423,x23421,x23424,x23425,x23426,x23427,x23428),f216(x23423,x23422,x23424,x23425,x23426,x23427,x23428)) % 186.01/186.05 [2343]~E(x23431,x23432)+E(f216(x23433,x23434,x23431,x23435,x23436,x23437,x23438),f216(x23433,x23434,x23432,x23435,x23436,x23437,x23438)) % 186.01/186.05 [2344]~E(x23441,x23442)+E(f216(x23443,x23444,x23445,x23441,x23446,x23447,x23448),f216(x23443,x23444,x23445,x23442,x23446,x23447,x23448)) % 186.01/186.05 [2345]~E(x23451,x23452)+E(f216(x23453,x23454,x23455,x23456,x23451,x23457,x23458),f216(x23453,x23454,x23455,x23456,x23452,x23457,x23458)) % 186.01/186.05 [2346]~E(x23461,x23462)+E(f216(x23463,x23464,x23465,x23466,x23467,x23461,x23468),f216(x23463,x23464,x23465,x23466,x23467,x23462,x23468)) % 186.01/186.05 [2347]~E(x23471,x23472)+E(f216(x23473,x23474,x23475,x23476,x23477,x23478,x23471),f216(x23473,x23474,x23475,x23476,x23477,x23478,x23472)) % 186.01/186.05 [2348]~E(x23481,x23482)+E(f553(x23481,x23483,x23484,x23485,x23486),f553(x23482,x23483,x23484,x23485,x23486)) % 186.01/186.05 [2349]~E(x23491,x23492)+E(f553(x23493,x23491,x23494,x23495,x23496),f553(x23493,x23492,x23494,x23495,x23496)) % 186.01/186.05 [2350]~E(x23501,x23502)+E(f553(x23503,x23504,x23501,x23505,x23506),f553(x23503,x23504,x23502,x23505,x23506)) % 186.01/186.05 [2351]~E(x23511,x23512)+E(f553(x23513,x23514,x23515,x23511,x23516),f553(x23513,x23514,x23515,x23512,x23516)) % 186.01/186.05 [2352]~E(x23521,x23522)+E(f553(x23523,x23524,x23525,x23526,x23521),f553(x23523,x23524,x23525,x23526,x23522)) % 186.01/186.05 [2353]~E(x23531,x23532)+E(f688(x23531,x23533,x23534,x23535),f688(x23532,x23533,x23534,x23535)) % 186.01/186.05 [2354]~E(x23541,x23542)+E(f688(x23543,x23541,x23544,x23545),f688(x23543,x23542,x23544,x23545)) % 186.01/186.05 [2355]~E(x23551,x23552)+E(f688(x23553,x23554,x23551,x23555),f688(x23553,x23554,x23552,x23555)) % 186.01/186.05 [2356]~E(x23561,x23562)+E(f688(x23563,x23564,x23565,x23561),f688(x23563,x23564,x23565,x23562)) % 186.01/186.05 [2357]~E(x23571,x23572)+E(f609(x23571,x23573,x23574),f609(x23572,x23573,x23574)) % 186.01/186.05 [2358]~E(x23581,x23582)+E(f609(x23583,x23581,x23584),f609(x23583,x23582,x23584)) % 186.01/186.05 [2359]~E(x23591,x23592)+E(f609(x23593,x23594,x23591),f609(x23593,x23594,x23592)) % 186.01/186.05 [2360]~E(x23601,x23602)+E(f408(x23601,x23603,x23604,x23605),f408(x23602,x23603,x23604,x23605)) % 186.01/186.05 [2361]~E(x23611,x23612)+E(f408(x23613,x23611,x23614,x23615),f408(x23613,x23612,x23614,x23615)) % 186.01/186.05 [2362]~E(x23621,x23622)+E(f408(x23623,x23624,x23621,x23625),f408(x23623,x23624,x23622,x23625)) % 186.01/186.05 [2363]~E(x23631,x23632)+E(f408(x23633,x23634,x23635,x23631),f408(x23633,x23634,x23635,x23632)) % 186.01/186.05 [2364]~E(x23641,x23642)+E(f695(x23641,x23643,x23644,x23645),f695(x23642,x23643,x23644,x23645)) % 186.01/186.05 [2365]~E(x23651,x23652)+E(f695(x23653,x23651,x23654,x23655),f695(x23653,x23652,x23654,x23655)) % 186.01/186.05 [2366]~E(x23661,x23662)+E(f695(x23663,x23664,x23661,x23665),f695(x23663,x23664,x23662,x23665)) % 186.01/186.05 [2367]~E(x23671,x23672)+E(f695(x23673,x23674,x23675,x23671),f695(x23673,x23674,x23675,x23672)) % 186.01/186.05 [2368]~E(x23681,x23682)+E(f610(x23681,x23683,x23684,x23685),f610(x23682,x23683,x23684,x23685)) % 186.01/186.05 [2369]~E(x23691,x23692)+E(f610(x23693,x23691,x23694,x23695),f610(x23693,x23692,x23694,x23695)) % 186.01/186.05 [2370]~E(x23701,x23702)+E(f610(x23703,x23704,x23701,x23705),f610(x23703,x23704,x23702,x23705)) % 186.01/186.05 [2371]~E(x23711,x23712)+E(f610(x23713,x23714,x23715,x23711),f610(x23713,x23714,x23715,x23712)) % 186.01/186.05 [2372]~E(x23721,x23722)+E(f666(x23721,x23723,x23724,x23725),f666(x23722,x23723,x23724,x23725)) % 186.01/186.05 [2373]~E(x23731,x23732)+E(f666(x23733,x23731,x23734,x23735),f666(x23733,x23732,x23734,x23735)) % 186.01/186.05 [2374]~E(x23741,x23742)+E(f666(x23743,x23744,x23741,x23745),f666(x23743,x23744,x23742,x23745)) % 186.01/186.05 [2375]~E(x23751,x23752)+E(f666(x23753,x23754,x23755,x23751),f666(x23753,x23754,x23755,x23752)) % 186.01/186.05 [2376]~E(x23761,x23762)+E(f642(x23761,x23763,x23764,x23765),f642(x23762,x23763,x23764,x23765)) % 186.01/186.05 [2377]~E(x23771,x23772)+E(f642(x23773,x23771,x23774,x23775),f642(x23773,x23772,x23774,x23775)) % 186.01/186.05 [2378]~E(x23781,x23782)+E(f642(x23783,x23784,x23781,x23785),f642(x23783,x23784,x23782,x23785)) % 186.01/186.05 [2379]~E(x23791,x23792)+E(f642(x23793,x23794,x23795,x23791),f642(x23793,x23794,x23795,x23792)) % 186.01/186.05 [2380]~E(x23801,x23802)+E(f647(x23801,x23803,x23804,x23805,x23806,x23807,x23808),f647(x23802,x23803,x23804,x23805,x23806,x23807,x23808)) % 186.01/186.05 [2381]~E(x23811,x23812)+E(f647(x23813,x23811,x23814,x23815,x23816,x23817,x23818),f647(x23813,x23812,x23814,x23815,x23816,x23817,x23818)) % 186.01/186.05 [2382]~E(x23821,x23822)+E(f647(x23823,x23824,x23821,x23825,x23826,x23827,x23828),f647(x23823,x23824,x23822,x23825,x23826,x23827,x23828)) % 186.01/186.05 [2383]~E(x23831,x23832)+E(f647(x23833,x23834,x23835,x23831,x23836,x23837,x23838),f647(x23833,x23834,x23835,x23832,x23836,x23837,x23838)) % 186.01/186.05 [2384]~E(x23841,x23842)+E(f647(x23843,x23844,x23845,x23846,x23841,x23847,x23848),f647(x23843,x23844,x23845,x23846,x23842,x23847,x23848)) % 186.01/186.05 [2385]~E(x23851,x23852)+E(f647(x23853,x23854,x23855,x23856,x23857,x23851,x23858),f647(x23853,x23854,x23855,x23856,x23857,x23852,x23858)) % 186.01/186.05 [2386]~E(x23861,x23862)+E(f647(x23863,x23864,x23865,x23866,x23867,x23868,x23861),f647(x23863,x23864,x23865,x23866,x23867,x23868,x23862)) % 186.01/186.05 [2387]~E(x23871,x23872)+E(f911(x23871,x23873,x23874,x23875,x23876,x23877,x23878),f911(x23872,x23873,x23874,x23875,x23876,x23877,x23878)) % 186.01/186.05 [2388]~E(x23881,x23882)+E(f911(x23883,x23881,x23884,x23885,x23886,x23887,x23888),f911(x23883,x23882,x23884,x23885,x23886,x23887,x23888)) % 186.01/186.05 [2389]~E(x23891,x23892)+E(f911(x23893,x23894,x23891,x23895,x23896,x23897,x23898),f911(x23893,x23894,x23892,x23895,x23896,x23897,x23898)) % 186.01/186.05 [2390]~E(x23901,x23902)+E(f911(x23903,x23904,x23905,x23901,x23906,x23907,x23908),f911(x23903,x23904,x23905,x23902,x23906,x23907,x23908)) % 186.01/186.05 [2391]~E(x23911,x23912)+E(f911(x23913,x23914,x23915,x23916,x23911,x23917,x23918),f911(x23913,x23914,x23915,x23916,x23912,x23917,x23918)) % 186.01/186.05 [2392]~E(x23921,x23922)+E(f911(x23923,x23924,x23925,x23926,x23927,x23921,x23928),f911(x23923,x23924,x23925,x23926,x23927,x23922,x23928)) % 186.01/186.05 [2393]~E(x23931,x23932)+E(f911(x23933,x23934,x23935,x23936,x23937,x23938,x23931),f911(x23933,x23934,x23935,x23936,x23937,x23938,x23932)) % 186.01/186.05 [2394]~E(x23941,x23942)+E(f618(x23941,x23943),f618(x23942,x23943)) % 186.01/186.05 [2395]~E(x23951,x23952)+E(f618(x23953,x23951),f618(x23953,x23952)) % 186.01/186.05 [2396]~E(x23961,x23962)+E(f462(x23961,x23963,x23964,x23965),f462(x23962,x23963,x23964,x23965)) % 186.01/186.05 [2397]~E(x23971,x23972)+E(f462(x23973,x23971,x23974,x23975),f462(x23973,x23972,x23974,x23975)) % 186.01/186.05 [2398]~E(x23981,x23982)+E(f462(x23983,x23984,x23981,x23985),f462(x23983,x23984,x23982,x23985)) % 186.01/186.05 [2399]~E(x23991,x23992)+E(f462(x23993,x23994,x23995,x23991),f462(x23993,x23994,x23995,x23992)) % 186.01/186.05 [2400]~E(x24001,x24002)+E(f658(x24001,x24003,x24004,x24005,x24006,x24007,x24008,x24009),f658(x24002,x24003,x24004,x24005,x24006,x24007,x24008,x24009)) % 186.01/186.05 [2401]~E(x24011,x24012)+E(f658(x24013,x24011,x24014,x24015,x24016,x24017,x24018,x24019),f658(x24013,x24012,x24014,x24015,x24016,x24017,x24018,x24019)) % 186.01/186.05 [2402]~E(x24021,x24022)+E(f658(x24023,x24024,x24021,x24025,x24026,x24027,x24028,x24029),f658(x24023,x24024,x24022,x24025,x24026,x24027,x24028,x24029)) % 186.01/186.05 [2403]~E(x24031,x24032)+E(f658(x24033,x24034,x24035,x24031,x24036,x24037,x24038,x24039),f658(x24033,x24034,x24035,x24032,x24036,x24037,x24038,x24039)) % 186.01/186.05 [2404]~E(x24041,x24042)+E(f658(x24043,x24044,x24045,x24046,x24041,x24047,x24048,x24049),f658(x24043,x24044,x24045,x24046,x24042,x24047,x24048,x24049)) % 186.01/186.05 [2405]~E(x24051,x24052)+E(f658(x24053,x24054,x24055,x24056,x24057,x24051,x24058,x24059),f658(x24053,x24054,x24055,x24056,x24057,x24052,x24058,x24059)) % 186.01/186.05 [2406]~E(x24061,x24062)+E(f658(x24063,x24064,x24065,x24066,x24067,x24068,x24061,x24069),f658(x24063,x24064,x24065,x24066,x24067,x24068,x24062,x24069)) % 186.01/186.05 [2407]~E(x24071,x24072)+E(f658(x24073,x24074,x24075,x24076,x24077,x24078,x24079,x24071),f658(x24073,x24074,x24075,x24076,x24077,x24078,x24079,x24072)) % 186.01/186.05 [2408]~E(x24081,x24082)+E(f599(x24081,x24083,x24084,x24085,x24086,x24087),f599(x24082,x24083,x24084,x24085,x24086,x24087)) % 186.01/186.05 [2409]~E(x24091,x24092)+E(f599(x24093,x24091,x24094,x24095,x24096,x24097),f599(x24093,x24092,x24094,x24095,x24096,x24097)) % 186.01/186.05 [2410]~E(x24101,x24102)+E(f599(x24103,x24104,x24101,x24105,x24106,x24107),f599(x24103,x24104,x24102,x24105,x24106,x24107)) % 186.01/186.05 [2411]~E(x24111,x24112)+E(f599(x24113,x24114,x24115,x24111,x24116,x24117),f599(x24113,x24114,x24115,x24112,x24116,x24117)) % 186.01/186.05 [2412]~E(x24121,x24122)+E(f599(x24123,x24124,x24125,x24126,x24121,x24127),f599(x24123,x24124,x24125,x24126,x24122,x24127)) % 186.01/186.05 [2413]~E(x24131,x24132)+E(f599(x24133,x24134,x24135,x24136,x24137,x24131),f599(x24133,x24134,x24135,x24136,x24137,x24132)) % 186.01/186.05 [2414]~E(x24141,x24142)+E(f662(x24141,x24143),f662(x24142,x24143)) % 186.01/186.05 [2415]~E(x24151,x24152)+E(f662(x24153,x24151),f662(x24153,x24152)) % 186.01/186.05 [2416]~E(x24161,x24162)+E(f587(x24161,x24163,x24164),f587(x24162,x24163,x24164)) % 186.01/186.05 [2417]~E(x24171,x24172)+E(f587(x24173,x24171,x24174),f587(x24173,x24172,x24174)) % 186.01/186.05 [2418]~E(x24181,x24182)+E(f587(x24183,x24184,x24181),f587(x24183,x24184,x24182)) % 186.01/186.05 [2419]~E(x24191,x24192)+E(f357(x24191,x24193,x24194,x24195),f357(x24192,x24193,x24194,x24195)) % 186.01/186.05 [2420]~E(x24201,x24202)+E(f357(x24203,x24201,x24204,x24205),f357(x24203,x24202,x24204,x24205)) % 186.01/186.05 [2421]~E(x24211,x24212)+E(f357(x24213,x24214,x24211,x24215),f357(x24213,x24214,x24212,x24215)) % 186.01/186.05 [2422]~E(x24221,x24222)+E(f357(x24223,x24224,x24225,x24221),f357(x24223,x24224,x24225,x24222)) % 186.01/186.05 [2423]~E(x24231,x24232)+E(f17(x24231,x24233,x24234,x24235),f17(x24232,x24233,x24234,x24235)) % 186.01/186.05 [2424]~E(x24241,x24242)+E(f17(x24243,x24241,x24244,x24245),f17(x24243,x24242,x24244,x24245)) % 186.01/186.05 [2425]~E(x24251,x24252)+E(f17(x24253,x24254,x24251,x24255),f17(x24253,x24254,x24252,x24255)) % 186.01/186.05 [2426]~E(x24261,x24262)+E(f17(x24263,x24264,x24265,x24261),f17(x24263,x24264,x24265,x24262)) % 186.01/186.05 [2427]~E(x24271,x24272)+E(f444(x24271,x24273),f444(x24272,x24273)) % 186.01/186.05 [2428]~E(x24281,x24282)+E(f444(x24283,x24281),f444(x24283,x24282)) % 186.01/186.05 [2429]~E(x24291,x24292)+E(f238(x24291,x24293,x24294,x24295),f238(x24292,x24293,x24294,x24295)) % 186.01/186.05 [2430]~E(x24301,x24302)+E(f238(x24303,x24301,x24304,x24305),f238(x24303,x24302,x24304,x24305)) % 186.01/186.05 [2431]~E(x24311,x24312)+E(f238(x24313,x24314,x24311,x24315),f238(x24313,x24314,x24312,x24315)) % 186.01/186.05 [2432]~E(x24321,x24322)+E(f238(x24323,x24324,x24325,x24321),f238(x24323,x24324,x24325,x24322)) % 186.01/186.05 [2433]~E(x24331,x24332)+E(f530(x24331,x24333,x24334,x24335,x24336,x24337,x24338),f530(x24332,x24333,x24334,x24335,x24336,x24337,x24338)) % 186.01/186.05 [2434]~E(x24341,x24342)+E(f530(x24343,x24341,x24344,x24345,x24346,x24347,x24348),f530(x24343,x24342,x24344,x24345,x24346,x24347,x24348)) % 186.01/186.05 [2435]~E(x24351,x24352)+E(f530(x24353,x24354,x24351,x24355,x24356,x24357,x24358),f530(x24353,x24354,x24352,x24355,x24356,x24357,x24358)) % 186.01/186.05 [2436]~E(x24361,x24362)+E(f530(x24363,x24364,x24365,x24361,x24366,x24367,x24368),f530(x24363,x24364,x24365,x24362,x24366,x24367,x24368)) % 186.01/186.05 [2437]~E(x24371,x24372)+E(f530(x24373,x24374,x24375,x24376,x24371,x24377,x24378),f530(x24373,x24374,x24375,x24376,x24372,x24377,x24378)) % 186.01/186.05 [2438]~E(x24381,x24382)+E(f530(x24383,x24384,x24385,x24386,x24387,x24381,x24388),f530(x24383,x24384,x24385,x24386,x24387,x24382,x24388)) % 186.01/186.05 [2439]~E(x24391,x24392)+E(f530(x24393,x24394,x24395,x24396,x24397,x24398,x24391),f530(x24393,x24394,x24395,x24396,x24397,x24398,x24392)) % 186.01/186.05 [2440]~E(x24401,x24402)+E(f570(x24401,x24403,x24404,x24405),f570(x24402,x24403,x24404,x24405)) % 186.01/186.05 [2441]~E(x24411,x24412)+E(f570(x24413,x24411,x24414,x24415),f570(x24413,x24412,x24414,x24415)) % 186.01/186.05 [2442]~E(x24421,x24422)+E(f570(x24423,x24424,x24421,x24425),f570(x24423,x24424,x24422,x24425)) % 186.01/186.05 [2443]~E(x24431,x24432)+E(f570(x24433,x24434,x24435,x24431),f570(x24433,x24434,x24435,x24432)) % 186.01/186.05 [2444]~E(x24441,x24442)+E(f373(x24441),f373(x24442)) % 186.01/186.05 [2445]~E(x24451,x24452)+E(f516(x24451,x24453,x24454,x24455),f516(x24452,x24453,x24454,x24455)) % 186.01/186.05 [2446]~E(x24461,x24462)+E(f516(x24463,x24461,x24464,x24465),f516(x24463,x24462,x24464,x24465)) % 186.01/186.05 [2447]~E(x24471,x24472)+E(f516(x24473,x24474,x24471,x24475),f516(x24473,x24474,x24472,x24475)) % 186.01/186.05 [2448]~E(x24481,x24482)+E(f516(x24483,x24484,x24485,x24481),f516(x24483,x24484,x24485,x24482)) % 186.01/186.05 [2449]~E(x24491,x24492)+E(f340(x24491),f340(x24492)) % 186.01/186.05 [2450]~E(x24501,x24502)+E(f387(x24501,x24503,x24504),f387(x24502,x24503,x24504)) % 186.01/186.05 [2451]~E(x24511,x24512)+E(f387(x24513,x24511,x24514),f387(x24513,x24512,x24514)) % 186.01/186.05 [2452]~E(x24521,x24522)+E(f387(x24523,x24524,x24521),f387(x24523,x24524,x24522)) % 186.01/186.05 [2453]~E(x24531,x24532)+E(f815(x24531,x24533,x24534,x24535,x24536,x24537,x24538),f815(x24532,x24533,x24534,x24535,x24536,x24537,x24538)) % 186.01/186.05 [2454]~E(x24541,x24542)+E(f815(x24543,x24541,x24544,x24545,x24546,x24547,x24548),f815(x24543,x24542,x24544,x24545,x24546,x24547,x24548)) % 186.01/186.05 [2455]~E(x24551,x24552)+E(f815(x24553,x24554,x24551,x24555,x24556,x24557,x24558),f815(x24553,x24554,x24552,x24555,x24556,x24557,x24558)) % 186.01/186.05 [2456]~E(x24561,x24562)+E(f815(x24563,x24564,x24565,x24561,x24566,x24567,x24568),f815(x24563,x24564,x24565,x24562,x24566,x24567,x24568)) % 186.01/186.05 [2457]~E(x24571,x24572)+E(f815(x24573,x24574,x24575,x24576,x24571,x24577,x24578),f815(x24573,x24574,x24575,x24576,x24572,x24577,x24578)) % 186.01/186.05 [2458]~E(x24581,x24582)+E(f815(x24583,x24584,x24585,x24586,x24587,x24581,x24588),f815(x24583,x24584,x24585,x24586,x24587,x24582,x24588)) % 186.01/186.05 [2459]~E(x24591,x24592)+E(f815(x24593,x24594,x24595,x24596,x24597,x24598,x24591),f815(x24593,x24594,x24595,x24596,x24597,x24598,x24592)) % 186.01/186.05 [2460]~E(x24601,x24602)+E(f691(x24601,x24603,x24604,x24605),f691(x24602,x24603,x24604,x24605)) % 186.01/186.05 [2461]~E(x24611,x24612)+E(f691(x24613,x24611,x24614,x24615),f691(x24613,x24612,x24614,x24615)) % 186.01/186.05 [2462]~E(x24621,x24622)+E(f691(x24623,x24624,x24621,x24625),f691(x24623,x24624,x24622,x24625)) % 186.01/186.05 [2463]~E(x24631,x24632)+E(f691(x24633,x24634,x24635,x24631),f691(x24633,x24634,x24635,x24632)) % 186.01/186.05 [2464]~E(x24641,x24642)+E(f709(x24641,x24643,x24644,x24645),f709(x24642,x24643,x24644,x24645)) % 186.01/186.05 [2465]~E(x24651,x24652)+E(f709(x24653,x24651,x24654,x24655),f709(x24653,x24652,x24654,x24655)) % 186.01/186.05 [2466]~E(x24661,x24662)+E(f709(x24663,x24664,x24661,x24665),f709(x24663,x24664,x24662,x24665)) % 186.01/186.05 [2467]~E(x24671,x24672)+E(f709(x24673,x24674,x24675,x24671),f709(x24673,x24674,x24675,x24672)) % 186.01/186.05 [2468]~E(x24681,x24682)+E(f491(x24681,x24683,x24684),f491(x24682,x24683,x24684)) % 186.01/186.05 [2469]~E(x24691,x24692)+E(f491(x24693,x24691,x24694),f491(x24693,x24692,x24694)) % 186.01/186.05 [2470]~E(x24701,x24702)+E(f491(x24703,x24704,x24701),f491(x24703,x24704,x24702)) % 186.01/186.05 [2471]~E(x24711,x24712)+E(f830(x24711,x24713),f830(x24712,x24713)) % 186.01/186.05 [2472]~E(x24721,x24722)+E(f830(x24723,x24721),f830(x24723,x24722)) % 186.01/186.05 [2473]~E(x24731,x24732)+E(f386(x24731,x24733),f386(x24732,x24733)) % 186.01/186.05 [2474]~E(x24741,x24742)+E(f386(x24743,x24741),f386(x24743,x24742)) % 186.01/186.05 [2475]~E(x24751,x24752)+E(f561(x24751,x24753,x24754),f561(x24752,x24753,x24754)) % 186.01/186.05 [2476]~E(x24761,x24762)+E(f561(x24763,x24761,x24764),f561(x24763,x24762,x24764)) % 186.01/186.05 [2477]~E(x24771,x24772)+E(f561(x24773,x24774,x24771),f561(x24773,x24774,x24772)) % 186.01/186.05 [2478]~E(x24781,x24782)+E(f205(x24781,x24783,x24784,x24785),f205(x24782,x24783,x24784,x24785)) % 186.01/186.05 [2479]~E(x24791,x24792)+E(f205(x24793,x24791,x24794,x24795),f205(x24793,x24792,x24794,x24795)) % 186.01/186.05 [2480]~E(x24801,x24802)+E(f205(x24803,x24804,x24801,x24805),f205(x24803,x24804,x24802,x24805)) % 186.01/186.05 [2481]~E(x24811,x24812)+E(f205(x24813,x24814,x24815,x24811),f205(x24813,x24814,x24815,x24812)) % 186.01/186.05 [2482]~E(x24821,x24822)+E(f821(x24821,x24823,x24824),f821(x24822,x24823,x24824)) % 186.01/186.05 [2483]~E(x24831,x24832)+E(f821(x24833,x24831,x24834),f821(x24833,x24832,x24834)) % 186.01/186.05 [2484]~E(x24841,x24842)+E(f821(x24843,x24844,x24841),f821(x24843,x24844,x24842)) % 186.01/186.05 [2485]~E(x24851,x24852)+E(f477(x24851,x24853,x24854,x24855,x24856),f477(x24852,x24853,x24854,x24855,x24856)) % 186.01/186.05 [2486]~E(x24861,x24862)+E(f477(x24863,x24861,x24864,x24865,x24866),f477(x24863,x24862,x24864,x24865,x24866)) % 186.01/186.05 [2487]~E(x24871,x24872)+E(f477(x24873,x24874,x24871,x24875,x24876),f477(x24873,x24874,x24872,x24875,x24876)) % 186.01/186.05 [2488]~E(x24881,x24882)+E(f477(x24883,x24884,x24885,x24881,x24886),f477(x24883,x24884,x24885,x24882,x24886)) % 186.01/186.05 [2489]~E(x24891,x24892)+E(f477(x24893,x24894,x24895,x24896,x24891),f477(x24893,x24894,x24895,x24896,x24892)) % 186.01/186.05 [2490]~E(x24901,x24902)+E(f426(x24901,x24903),f426(x24902,x24903)) % 186.01/186.05 [2491]~E(x24911,x24912)+E(f426(x24913,x24911),f426(x24913,x24912)) % 186.01/186.05 [2492]~E(x24921,x24922)+E(f246(x24921,x24923),f246(x24922,x24923)) % 186.01/186.05 [2493]~E(x24931,x24932)+E(f246(x24933,x24931),f246(x24933,x24932)) % 186.01/186.05 [2494]~E(x24941,x24942)+E(f320(x24941,x24943),f320(x24942,x24943)) % 186.01/186.05 [2495]~E(x24951,x24952)+E(f320(x24953,x24951),f320(x24953,x24952)) % 186.01/186.05 [2496]~E(x24961,x24962)+E(f474(x24961,x24963,x24964),f474(x24962,x24963,x24964)) % 186.01/186.05 [2497]~E(x24971,x24972)+E(f474(x24973,x24971,x24974),f474(x24973,x24972,x24974)) % 186.01/186.05 [2498]~E(x24981,x24982)+E(f474(x24983,x24984,x24981),f474(x24983,x24984,x24982)) % 186.01/186.05 [2499]~E(x24991,x24992)+E(f213(x24991),f213(x24992)) % 186.01/186.05 [2500]~E(x25001,x25002)+E(f100(x25001,x25003,x25004),f100(x25002,x25003,x25004)) % 186.01/186.05 [2501]~E(x25011,x25012)+E(f100(x25013,x25011,x25014),f100(x25013,x25012,x25014)) % 186.01/186.05 [2502]~E(x25021,x25022)+E(f100(x25023,x25024,x25021),f100(x25023,x25024,x25022)) % 186.01/186.05 [2503]~E(x25031,x25032)+E(f738(x25031,x25033,x25034),f738(x25032,x25033,x25034)) % 186.01/186.05 [2504]~E(x25041,x25042)+E(f738(x25043,x25041,x25044),f738(x25043,x25042,x25044)) % 186.01/186.05 [2505]~E(x25051,x25052)+E(f738(x25053,x25054,x25051),f738(x25053,x25054,x25052)) % 186.01/186.05 [2506]~E(x25061,x25062)+E(f488(x25061,x25063,x25064),f488(x25062,x25063,x25064)) % 186.01/186.05 [2507]~E(x25071,x25072)+E(f488(x25073,x25071,x25074),f488(x25073,x25072,x25074)) % 186.01/186.05 [2508]~E(x25081,x25082)+E(f488(x25083,x25084,x25081),f488(x25083,x25084,x25082)) % 186.01/186.05 [2509]~E(x25091,x25092)+E(f503(x25091,x25093,x25094),f503(x25092,x25093,x25094)) % 186.01/186.05 [2510]~E(x25101,x25102)+E(f503(x25103,x25101,x25104),f503(x25103,x25102,x25104)) % 186.01/186.05 [2511]~E(x25111,x25112)+E(f503(x25113,x25114,x25111),f503(x25113,x25114,x25112)) % 186.01/186.05 [2512]~E(x25121,x25122)+E(f906(x25121,x25123,x25124,x25125,x25126),f906(x25122,x25123,x25124,x25125,x25126)) % 186.01/186.05 [2513]~E(x25131,x25132)+E(f906(x25133,x25131,x25134,x25135,x25136),f906(x25133,x25132,x25134,x25135,x25136)) % 186.01/186.05 [2514]~E(x25141,x25142)+E(f906(x25143,x25144,x25141,x25145,x25146),f906(x25143,x25144,x25142,x25145,x25146)) % 186.01/186.05 [2515]~E(x25151,x25152)+E(f906(x25153,x25154,x25155,x25151,x25156),f906(x25153,x25154,x25155,x25152,x25156)) % 186.01/186.05 [2516]~E(x25161,x25162)+E(f906(x25163,x25164,x25165,x25166,x25161),f906(x25163,x25164,x25165,x25166,x25162)) % 186.01/186.05 [2517]~E(x25171,x25172)+E(f579(x25171,x25173),f579(x25172,x25173)) % 186.01/186.05 [2518]~E(x25181,x25182)+E(f579(x25183,x25181),f579(x25183,x25182)) % 186.01/186.05 [2519]~E(x25191,x25192)+E(f204(x25191,x25193),f204(x25192,x25193)) % 186.01/186.05 [2520]~E(x25201,x25202)+E(f204(x25203,x25201),f204(x25203,x25202)) % 186.01/186.05 [2521]~E(x25211,x25212)+E(f794(x25211,x25213,x25214),f794(x25212,x25213,x25214)) % 186.01/186.05 [2522]~E(x25221,x25222)+E(f794(x25223,x25221,x25224),f794(x25223,x25222,x25224)) % 186.01/186.05 [2523]~E(x25231,x25232)+E(f794(x25233,x25234,x25231),f794(x25233,x25234,x25232)) % 186.01/186.05 [2524]~E(x25241,x25242)+E(f612(x25241,x25243,x25244),f612(x25242,x25243,x25244)) % 186.01/186.05 [2525]~E(x25251,x25252)+E(f612(x25253,x25251,x25254),f612(x25253,x25252,x25254)) % 186.01/186.05 [2526]~E(x25261,x25262)+E(f612(x25263,x25264,x25261),f612(x25263,x25264,x25262)) % 186.01/186.05 [2527]~E(x25271,x25272)+E(f912(x25271,x25273),f912(x25272,x25273)) % 186.01/186.05 [2528]~E(x25281,x25282)+E(f912(x25283,x25281),f912(x25283,x25282)) % 186.01/186.05 [2529]~E(x25291,x25292)+E(f240(x25291,x25293,x25294,x25295),f240(x25292,x25293,x25294,x25295)) % 186.01/186.05 [2530]~E(x25301,x25302)+E(f240(x25303,x25301,x25304,x25305),f240(x25303,x25302,x25304,x25305)) % 186.01/186.05 [2531]~E(x25311,x25312)+E(f240(x25313,x25314,x25311,x25315),f240(x25313,x25314,x25312,x25315)) % 186.01/186.05 [2532]~E(x25321,x25322)+E(f240(x25323,x25324,x25325,x25321),f240(x25323,x25324,x25325,x25322)) % 186.01/186.05 [2533]~E(x25331,x25332)+E(f828(x25331,x25333),f828(x25332,x25333)) % 186.01/186.05 [2534]~E(x25341,x25342)+E(f828(x25343,x25341),f828(x25343,x25342)) % 186.01/186.05 [2535]~E(x25351,x25352)+E(f493(x25351,x25353,x25354),f493(x25352,x25353,x25354)) % 186.01/186.05 [2536]~E(x25361,x25362)+E(f493(x25363,x25361,x25364),f493(x25363,x25362,x25364)) % 186.01/186.05 [2537]~E(x25371,x25372)+E(f493(x25373,x25374,x25371),f493(x25373,x25374,x25372)) % 186.01/186.05 [2538]~E(x25381,x25382)+E(f255(x25381,x25383,x25384),f255(x25382,x25383,x25384)) % 186.01/186.05 [2539]~E(x25391,x25392)+E(f255(x25393,x25391,x25394),f255(x25393,x25392,x25394)) % 186.01/186.05 [2540]~E(x25401,x25402)+E(f255(x25403,x25404,x25401),f255(x25403,x25404,x25402)) % 186.01/186.05 [2541]~E(x25411,x25412)+E(f459(x25411,x25413,x25414,x25415,x25416,x25417),f459(x25412,x25413,x25414,x25415,x25416,x25417)) % 186.01/186.05 [2542]~E(x25421,x25422)+E(f459(x25423,x25421,x25424,x25425,x25426,x25427),f459(x25423,x25422,x25424,x25425,x25426,x25427)) % 186.01/186.05 [2543]~E(x25431,x25432)+E(f459(x25433,x25434,x25431,x25435,x25436,x25437),f459(x25433,x25434,x25432,x25435,x25436,x25437)) % 186.01/186.05 [2544]~E(x25441,x25442)+E(f459(x25443,x25444,x25445,x25441,x25446,x25447),f459(x25443,x25444,x25445,x25442,x25446,x25447)) % 186.01/186.05 [2545]~E(x25451,x25452)+E(f459(x25453,x25454,x25455,x25456,x25451,x25457),f459(x25453,x25454,x25455,x25456,x25452,x25457)) % 186.01/186.05 [2546]~E(x25461,x25462)+E(f459(x25463,x25464,x25465,x25466,x25467,x25461),f459(x25463,x25464,x25465,x25466,x25467,x25462)) % 186.01/186.05 [2547]~E(x25471,x25472)+E(f692(x25471,x25473,x25474,x25475),f692(x25472,x25473,x25474,x25475)) % 186.01/186.05 [2548]~E(x25481,x25482)+E(f692(x25483,x25481,x25484,x25485),f692(x25483,x25482,x25484,x25485)) % 186.01/186.05 [2549]~E(x25491,x25492)+E(f692(x25493,x25494,x25491,x25495),f692(x25493,x25494,x25492,x25495)) % 186.01/186.05 [2550]~E(x25501,x25502)+E(f692(x25503,x25504,x25505,x25501),f692(x25503,x25504,x25505,x25502)) % 186.01/186.05 [2551]~E(x25511,x25512)+E(f475(x25511,x25513,x25514),f475(x25512,x25513,x25514)) % 186.01/186.05 [2552]~E(x25521,x25522)+E(f475(x25523,x25521,x25524),f475(x25523,x25522,x25524)) % 186.01/186.05 [2553]~E(x25531,x25532)+E(f475(x25533,x25534,x25531),f475(x25533,x25534,x25532)) % 186.01/186.05 [2554]~E(x25541,x25542)+E(f377(x25541,x25543),f377(x25542,x25543)) % 186.01/186.05 [2555]~E(x25551,x25552)+E(f377(x25553,x25551),f377(x25553,x25552)) % 186.01/186.05 [2556]~E(x25561,x25562)+E(f427(x25561,x25563,x25564,x25565),f427(x25562,x25563,x25564,x25565)) % 186.01/186.05 [2557]~E(x25571,x25572)+E(f427(x25573,x25571,x25574,x25575),f427(x25573,x25572,x25574,x25575)) % 186.01/186.05 [2558]~E(x25581,x25582)+E(f427(x25583,x25584,x25581,x25585),f427(x25583,x25584,x25582,x25585)) % 186.01/186.05 [2559]~E(x25591,x25592)+E(f427(x25593,x25594,x25595,x25591),f427(x25593,x25594,x25595,x25592)) % 186.01/186.05 [2560]~E(x25601,x25602)+E(f482(x25601,x25603,x25604,x25605,x25606),f482(x25602,x25603,x25604,x25605,x25606)) % 186.01/186.05 [2561]~E(x25611,x25612)+E(f482(x25613,x25611,x25614,x25615,x25616),f482(x25613,x25612,x25614,x25615,x25616)) % 186.01/186.05 [2562]~E(x25621,x25622)+E(f482(x25623,x25624,x25621,x25625,x25626),f482(x25623,x25624,x25622,x25625,x25626)) % 186.01/186.05 [2563]~E(x25631,x25632)+E(f482(x25633,x25634,x25635,x25631,x25636),f482(x25633,x25634,x25635,x25632,x25636)) % 186.01/186.05 [2564]~E(x25641,x25642)+E(f482(x25643,x25644,x25645,x25646,x25641),f482(x25643,x25644,x25645,x25646,x25642)) % 186.01/186.05 [2565]~E(x25651,x25652)+E(f452(x25651,x25653),f452(x25652,x25653)) % 186.01/186.05 [2566]~E(x25661,x25662)+E(f452(x25663,x25661),f452(x25663,x25662)) % 186.01/186.05 [2567]~E(x25671,x25672)+E(f370(x25671,x25673),f370(x25672,x25673)) % 186.01/186.05 [2568]~E(x25681,x25682)+E(f370(x25683,x25681),f370(x25683,x25682)) % 186.01/186.05 [2569]~E(x25691,x25692)+E(f840(x25691,x25693),f840(x25692,x25693)) % 186.01/186.05 [2570]~E(x25701,x25702)+E(f840(x25703,x25701),f840(x25703,x25702)) % 186.01/186.05 [2571]~E(x25711,x25712)+E(f562(x25711,x25713,x25714,x25715,x25716),f562(x25712,x25713,x25714,x25715,x25716)) % 186.01/186.05 [2572]~E(x25721,x25722)+E(f562(x25723,x25721,x25724,x25725,x25726),f562(x25723,x25722,x25724,x25725,x25726)) % 186.01/186.05 [2573]~E(x25731,x25732)+E(f562(x25733,x25734,x25731,x25735,x25736),f562(x25733,x25734,x25732,x25735,x25736)) % 186.01/186.05 [2574]~E(x25741,x25742)+E(f562(x25743,x25744,x25745,x25741,x25746),f562(x25743,x25744,x25745,x25742,x25746)) % 186.01/186.05 [2575]~E(x25751,x25752)+E(f562(x25753,x25754,x25755,x25756,x25751),f562(x25753,x25754,x25755,x25756,x25752)) % 186.01/186.05 [2576]~E(x25761,x25762)+E(f764(x25761,x25763,x25764,x25765,x25766),f764(x25762,x25763,x25764,x25765,x25766)) % 186.01/186.05 [2577]~E(x25771,x25772)+E(f764(x25773,x25771,x25774,x25775,x25776),f764(x25773,x25772,x25774,x25775,x25776)) % 186.01/186.05 [2578]~E(x25781,x25782)+E(f764(x25783,x25784,x25781,x25785,x25786),f764(x25783,x25784,x25782,x25785,x25786)) % 186.01/186.05 [2579]~E(x25791,x25792)+E(f764(x25793,x25794,x25795,x25791,x25796),f764(x25793,x25794,x25795,x25792,x25796)) % 186.01/186.05 [2580]~E(x25801,x25802)+E(f764(x25803,x25804,x25805,x25806,x25801),f764(x25803,x25804,x25805,x25806,x25802)) % 186.01/186.05 [2581]~E(x25811,x25812)+E(f339(x25811,x25813,x25814,x25815),f339(x25812,x25813,x25814,x25815)) % 186.01/186.05 [2582]~E(x25821,x25822)+E(f339(x25823,x25821,x25824,x25825),f339(x25823,x25822,x25824,x25825)) % 186.01/186.05 [2583]~E(x25831,x25832)+E(f339(x25833,x25834,x25831,x25835),f339(x25833,x25834,x25832,x25835)) % 186.01/186.05 [2584]~E(x25841,x25842)+E(f339(x25843,x25844,x25845,x25841),f339(x25843,x25844,x25845,x25842)) % 186.01/186.05 [2585]~E(x25851,x25852)+E(f798(x25851,x25853,x25854),f798(x25852,x25853,x25854)) % 186.01/186.05 [2586]~E(x25861,x25862)+E(f798(x25863,x25861,x25864),f798(x25863,x25862,x25864)) % 186.01/186.05 [2587]~E(x25871,x25872)+E(f798(x25873,x25874,x25871),f798(x25873,x25874,x25872)) % 186.01/186.05 [2588]~E(x25881,x25882)+E(f578(x25881,x25883,x25884,x25885),f578(x25882,x25883,x25884,x25885)) % 186.01/186.05 [2589]~E(x25891,x25892)+E(f578(x25893,x25891,x25894,x25895),f578(x25893,x25892,x25894,x25895)) % 186.01/186.05 [2590]~E(x25901,x25902)+E(f578(x25903,x25904,x25901,x25905),f578(x25903,x25904,x25902,x25905)) % 186.01/186.05 [2591]~E(x25911,x25912)+E(f578(x25913,x25914,x25915,x25911),f578(x25913,x25914,x25915,x25912)) % 186.01/186.05 [2592]~E(x25921,x25922)+E(f284(x25921,x25923,x25924,x25925),f284(x25922,x25923,x25924,x25925)) % 186.01/186.05 [2593]~E(x25931,x25932)+E(f284(x25933,x25931,x25934,x25935),f284(x25933,x25932,x25934,x25935)) % 186.01/186.05 [2594]~E(x25941,x25942)+E(f284(x25943,x25944,x25941,x25945),f284(x25943,x25944,x25942,x25945)) % 186.01/186.05 [2595]~E(x25951,x25952)+E(f284(x25953,x25954,x25955,x25951),f284(x25953,x25954,x25955,x25952)) % 186.01/186.05 [2596]~E(x25961,x25962)+E(f617(x25961,x25963,x25964,x25965,x25966),f617(x25962,x25963,x25964,x25965,x25966)) % 186.01/186.05 [2597]~E(x25971,x25972)+E(f617(x25973,x25971,x25974,x25975,x25976),f617(x25973,x25972,x25974,x25975,x25976)) % 186.01/186.05 [2598]~E(x25981,x25982)+E(f617(x25983,x25984,x25981,x25985,x25986),f617(x25983,x25984,x25982,x25985,x25986)) % 186.01/186.05 [2599]~E(x25991,x25992)+E(f617(x25993,x25994,x25995,x25991,x25996),f617(x25993,x25994,x25995,x25992,x25996)) % 186.01/186.05 [2600]~E(x26001,x26002)+E(f617(x26003,x26004,x26005,x26006,x26001),f617(x26003,x26004,x26005,x26006,x26002)) % 186.01/186.05 [2601]~E(x26011,x26012)+E(f826(x26011,x26013),f826(x26012,x26013)) % 186.01/186.05 [2602]~E(x26021,x26022)+E(f826(x26023,x26021),f826(x26023,x26022)) % 186.01/186.05 [2603]~E(x26031,x26032)+E(f418(x26031,x26033),f418(x26032,x26033)) % 186.01/186.05 [2604]~E(x26041,x26042)+E(f418(x26043,x26041),f418(x26043,x26042)) % 186.01/186.05 [2605]~E(x26051,x26052)+E(f772(x26051,x26053),f772(x26052,x26053)) % 186.01/186.05 [2606]~E(x26061,x26062)+E(f772(x26063,x26061),f772(x26063,x26062)) % 186.01/186.05 [2607]~E(x26071,x26072)+E(f498(x26071,x26073),f498(x26072,x26073)) % 186.01/186.05 [2608]~E(x26081,x26082)+E(f498(x26083,x26081),f498(x26083,x26082)) % 186.01/186.05 [2609]~E(x26091,x26092)+E(f652(x26091,x26093,x26094,x26095,x26096),f652(x26092,x26093,x26094,x26095,x26096)) % 186.01/186.05 [2610]~E(x26101,x26102)+E(f652(x26103,x26101,x26104,x26105,x26106),f652(x26103,x26102,x26104,x26105,x26106)) % 186.01/186.05 [2611]~E(x26111,x26112)+E(f652(x26113,x26114,x26111,x26115,x26116),f652(x26113,x26114,x26112,x26115,x26116)) % 186.01/186.05 [2612]~E(x26121,x26122)+E(f652(x26123,x26124,x26125,x26121,x26126),f652(x26123,x26124,x26125,x26122,x26126)) % 186.01/186.05 [2613]~E(x26131,x26132)+E(f652(x26133,x26134,x26135,x26136,x26131),f652(x26133,x26134,x26135,x26136,x26132)) % 186.01/186.05 [2614]~E(x26141,x26142)+E(f416(x26141,x26143),f416(x26142,x26143)) % 186.01/186.05 [2615]~E(x26151,x26152)+E(f416(x26153,x26151),f416(x26153,x26152)) % 186.01/186.05 [2616]~E(x26161,x26162)+E(f287(x26161,x26163,x26164,x26165),f287(x26162,x26163,x26164,x26165)) % 186.01/186.05 [2617]~E(x26171,x26172)+E(f287(x26173,x26171,x26174,x26175),f287(x26173,x26172,x26174,x26175)) % 186.01/186.05 [2618]~E(x26181,x26182)+E(f287(x26183,x26184,x26181,x26185),f287(x26183,x26184,x26182,x26185)) % 186.01/186.05 [2619]~E(x26191,x26192)+E(f287(x26193,x26194,x26195,x26191),f287(x26193,x26194,x26195,x26192)) % 186.01/186.05 [2620]~E(x26201,x26202)+E(f153(x26201,x26203),f153(x26202,x26203)) % 186.01/186.05 [2621]~E(x26211,x26212)+E(f153(x26213,x26211),f153(x26213,x26212)) % 186.01/186.05 [2622]~E(x26221,x26222)+E(f893(x26221,x26223,x26224),f893(x26222,x26223,x26224)) % 186.01/186.05 [2623]~E(x26231,x26232)+E(f893(x26233,x26231,x26234),f893(x26233,x26232,x26234)) % 186.01/186.05 [2624]~E(x26241,x26242)+E(f893(x26243,x26244,x26241),f893(x26243,x26244,x26242)) % 186.01/186.05 [2625]~E(x26251,x26252)+E(f346(x26251,x26253,x26254,x26255),f346(x26252,x26253,x26254,x26255)) % 186.01/186.05 [2626]~E(x26261,x26262)+E(f346(x26263,x26261,x26264,x26265),f346(x26263,x26262,x26264,x26265)) % 186.01/186.05 [2627]~E(x26271,x26272)+E(f346(x26273,x26274,x26271,x26275),f346(x26273,x26274,x26272,x26275)) % 186.01/186.05 [2628]~E(x26281,x26282)+E(f346(x26283,x26284,x26285,x26281),f346(x26283,x26284,x26285,x26282)) % 186.01/186.05 [2629]~E(x26291,x26292)+E(f395(x26291,x26293,x26294),f395(x26292,x26293,x26294)) % 186.01/186.05 [2630]~E(x26301,x26302)+E(f395(x26303,x26301,x26304),f395(x26303,x26302,x26304)) % 186.01/186.05 [2631]~E(x26311,x26312)+E(f395(x26313,x26314,x26311),f395(x26313,x26314,x26312)) % 186.01/186.05 [2632]~E(x26321,x26322)+E(f415(x26321,x26323,x26324,x26325,x26326,x26327),f415(x26322,x26323,x26324,x26325,x26326,x26327)) % 186.01/186.05 [2633]~E(x26331,x26332)+E(f415(x26333,x26331,x26334,x26335,x26336,x26337),f415(x26333,x26332,x26334,x26335,x26336,x26337)) % 186.01/186.05 [2634]~E(x26341,x26342)+E(f415(x26343,x26344,x26341,x26345,x26346,x26347),f415(x26343,x26344,x26342,x26345,x26346,x26347)) % 186.01/186.05 [2635]~E(x26351,x26352)+E(f415(x26353,x26354,x26355,x26351,x26356,x26357),f415(x26353,x26354,x26355,x26352,x26356,x26357)) % 186.01/186.05 [2636]~E(x26361,x26362)+E(f415(x26363,x26364,x26365,x26366,x26361,x26367),f415(x26363,x26364,x26365,x26366,x26362,x26367)) % 186.01/186.05 [2637]~E(x26371,x26372)+E(f415(x26373,x26374,x26375,x26376,x26377,x26371),f415(x26373,x26374,x26375,x26376,x26377,x26372)) % 186.01/186.05 [2638]~E(x26381,x26382)+E(f712(x26381,x26383,x26384,x26385,x26386),f712(x26382,x26383,x26384,x26385,x26386)) % 186.01/186.05 [2639]~E(x26391,x26392)+E(f712(x26393,x26391,x26394,x26395,x26396),f712(x26393,x26392,x26394,x26395,x26396)) % 186.01/186.05 [2640]~E(x26401,x26402)+E(f712(x26403,x26404,x26401,x26405,x26406),f712(x26403,x26404,x26402,x26405,x26406)) % 186.01/186.05 [2641]~E(x26411,x26412)+E(f712(x26413,x26414,x26415,x26411,x26416),f712(x26413,x26414,x26415,x26412,x26416)) % 186.01/186.05 [2642]~E(x26421,x26422)+E(f712(x26423,x26424,x26425,x26426,x26421),f712(x26423,x26424,x26425,x26426,x26422)) % 186.01/186.05 [2643]~E(x26431,x26432)+E(f776(x26431,x26433),f776(x26432,x26433)) % 186.01/186.05 [2644]~E(x26441,x26442)+E(f776(x26443,x26441),f776(x26443,x26442)) % 186.01/186.05 [2645]~E(x26451,x26452)+E(f235(x26451,x26453,x26454,x26455,x26456),f235(x26452,x26453,x26454,x26455,x26456)) % 186.01/186.05 [2646]~E(x26461,x26462)+E(f235(x26463,x26461,x26464,x26465,x26466),f235(x26463,x26462,x26464,x26465,x26466)) % 186.01/186.05 [2647]~E(x26471,x26472)+E(f235(x26473,x26474,x26471,x26475,x26476),f235(x26473,x26474,x26472,x26475,x26476)) % 186.01/186.05 [2648]~E(x26481,x26482)+E(f235(x26483,x26484,x26485,x26481,x26486),f235(x26483,x26484,x26485,x26482,x26486)) % 186.01/186.05 [2649]~E(x26491,x26492)+E(f235(x26493,x26494,x26495,x26496,x26491),f235(x26493,x26494,x26495,x26496,x26492)) % 186.01/186.05 [2650]~E(x26501,x26502)+E(f778(x26501,x26503,x26504),f778(x26502,x26503,x26504)) % 186.01/186.05 [2651]~E(x26511,x26512)+E(f778(x26513,x26511,x26514),f778(x26513,x26512,x26514)) % 186.01/186.05 [2652]~E(x26521,x26522)+E(f778(x26523,x26524,x26521),f778(x26523,x26524,x26522)) % 186.01/186.05 [2653]~E(x26531,x26532)+E(f645(x26531,x26533,x26534,x26535,x26536,x26537,x26538,x26539),f645(x26532,x26533,x26534,x26535,x26536,x26537,x26538,x26539)) % 186.01/186.05 [2654]~E(x26541,x26542)+E(f645(x26543,x26541,x26544,x26545,x26546,x26547,x26548,x26549),f645(x26543,x26542,x26544,x26545,x26546,x26547,x26548,x26549)) % 186.01/186.05 [2655]~E(x26551,x26552)+E(f645(x26553,x26554,x26551,x26555,x26556,x26557,x26558,x26559),f645(x26553,x26554,x26552,x26555,x26556,x26557,x26558,x26559)) % 186.01/186.05 [2656]~E(x26561,x26562)+E(f645(x26563,x26564,x26565,x26561,x26566,x26567,x26568,x26569),f645(x26563,x26564,x26565,x26562,x26566,x26567,x26568,x26569)) % 186.01/186.05 [2657]~E(x26571,x26572)+E(f645(x26573,x26574,x26575,x26576,x26571,x26577,x26578,x26579),f645(x26573,x26574,x26575,x26576,x26572,x26577,x26578,x26579)) % 186.01/186.05 [2658]~E(x26581,x26582)+E(f645(x26583,x26584,x26585,x26586,x26587,x26581,x26588,x26589),f645(x26583,x26584,x26585,x26586,x26587,x26582,x26588,x26589)) % 186.01/186.05 [2659]~E(x26591,x26592)+E(f645(x26593,x26594,x26595,x26596,x26597,x26598,x26591,x26599),f645(x26593,x26594,x26595,x26596,x26597,x26598,x26592,x26599)) % 186.01/186.05 [2660]~E(x26601,x26602)+E(f645(x26603,x26604,x26605,x26606,x26607,x26608,x26609,x26601),f645(x26603,x26604,x26605,x26606,x26607,x26608,x26609,x26602)) % 186.01/186.05 [2661]~E(x26611,x26612)+E(f467(x26611,x26613,x26614),f467(x26612,x26613,x26614)) % 186.01/186.05 [2662]~E(x26621,x26622)+E(f467(x26623,x26621,x26624),f467(x26623,x26622,x26624)) % 186.01/186.05 [2663]~E(x26631,x26632)+E(f467(x26633,x26634,x26631),f467(x26633,x26634,x26632)) % 186.01/186.05 [2664]~E(x26641,x26642)+E(f472(x26641,x26643,x26644),f472(x26642,x26643,x26644)) % 186.01/186.05 [2665]~E(x26651,x26652)+E(f472(x26653,x26651,x26654),f472(x26653,x26652,x26654)) % 186.01/186.05 [2666]~E(x26661,x26662)+E(f472(x26663,x26664,x26661),f472(x26663,x26664,x26662)) % 186.01/186.05 [2667]~E(x26671,x26672)+E(f625(x26671,x26673,x26674),f625(x26672,x26673,x26674)) % 186.01/186.05 [2668]~E(x26681,x26682)+E(f625(x26683,x26681,x26684),f625(x26683,x26682,x26684)) % 186.01/186.05 [2669]~E(x26691,x26692)+E(f625(x26693,x26694,x26691),f625(x26693,x26694,x26692)) % 186.01/186.05 [2670]~E(x26701,x26702)+E(f512(x26701,x26703,x26704),f512(x26702,x26703,x26704)) % 186.01/186.05 [2671]~E(x26711,x26712)+E(f512(x26713,x26711,x26714),f512(x26713,x26712,x26714)) % 186.01/186.05 [2672]~E(x26721,x26722)+E(f512(x26723,x26724,x26721),f512(x26723,x26724,x26722)) % 186.01/186.05 [2673]~E(x26731,x26732)+E(f890(x26731,x26733),f890(x26732,x26733)) % 186.01/186.05 [2674]~E(x26741,x26742)+E(f890(x26743,x26741),f890(x26743,x26742)) % 186.01/186.05 [2675]~E(x26751,x26752)+E(f425(x26751,x26753),f425(x26752,x26753)) % 186.01/186.05 [2676]~E(x26761,x26762)+E(f425(x26763,x26761),f425(x26763,x26762)) % 186.01/186.05 [2677]~E(x26771,x26772)+E(f714(x26771,x26773,x26774),f714(x26772,x26773,x26774)) % 186.01/186.05 [2678]~E(x26781,x26782)+E(f714(x26783,x26781,x26784),f714(x26783,x26782,x26784)) % 186.01/186.05 [2679]~E(x26791,x26792)+E(f714(x26793,x26794,x26791),f714(x26793,x26794,x26792)) % 186.01/186.05 [2680]~E(x26801,x26802)+E(f862(x26801,x26803,x26804,x26805,x26806,x26807,x26808,x26809),f862(x26802,x26803,x26804,x26805,x26806,x26807,x26808,x26809)) % 186.01/186.05 [2681]~E(x26811,x26812)+E(f862(x26813,x26811,x26814,x26815,x26816,x26817,x26818,x26819),f862(x26813,x26812,x26814,x26815,x26816,x26817,x26818,x26819)) % 186.01/186.05 [2682]~E(x26821,x26822)+E(f862(x26823,x26824,x26821,x26825,x26826,x26827,x26828,x26829),f862(x26823,x26824,x26822,x26825,x26826,x26827,x26828,x26829)) % 186.01/186.05 [2683]~E(x26831,x26832)+E(f862(x26833,x26834,x26835,x26831,x26836,x26837,x26838,x26839),f862(x26833,x26834,x26835,x26832,x26836,x26837,x26838,x26839)) % 186.01/186.05 [2684]~E(x26841,x26842)+E(f862(x26843,x26844,x26845,x26846,x26841,x26847,x26848,x26849),f862(x26843,x26844,x26845,x26846,x26842,x26847,x26848,x26849)) % 186.01/186.05 [2685]~E(x26851,x26852)+E(f862(x26853,x26854,x26855,x26856,x26857,x26851,x26858,x26859),f862(x26853,x26854,x26855,x26856,x26857,x26852,x26858,x26859)) % 186.01/186.05 [2686]~E(x26861,x26862)+E(f862(x26863,x26864,x26865,x26866,x26867,x26868,x26861,x26869),f862(x26863,x26864,x26865,x26866,x26867,x26868,x26862,x26869)) % 186.01/186.05 [2687]~E(x26871,x26872)+E(f862(x26873,x26874,x26875,x26876,x26877,x26878,x26879,x26871),f862(x26873,x26874,x26875,x26876,x26877,x26878,x26879,x26872)) % 186.01/186.05 [2688]~E(x26881,x26882)+E(f443(x26881,x26883),f443(x26882,x26883)) % 186.01/186.05 [2689]~E(x26891,x26892)+E(f443(x26893,x26891),f443(x26893,x26892)) % 186.01/186.05 [2690]~E(x26901,x26902)+E(f496(x26901,x26903,x26904,x26905),f496(x26902,x26903,x26904,x26905)) % 186.01/186.05 [2691]~E(x26911,x26912)+E(f496(x26913,x26911,x26914,x26915),f496(x26913,x26912,x26914,x26915)) % 186.01/186.05 [2692]~E(x26921,x26922)+E(f496(x26923,x26924,x26921,x26925),f496(x26923,x26924,x26922,x26925)) % 186.01/186.05 [2693]~E(x26931,x26932)+E(f496(x26933,x26934,x26935,x26931),f496(x26933,x26934,x26935,x26932)) % 186.01/186.05 [2694]~E(x26941,x26942)+E(f859(x26941,x26943,x26944,x26945,x26946,x26947,x26948),f859(x26942,x26943,x26944,x26945,x26946,x26947,x26948)) % 186.01/186.05 [2695]~E(x26951,x26952)+E(f859(x26953,x26951,x26954,x26955,x26956,x26957,x26958),f859(x26953,x26952,x26954,x26955,x26956,x26957,x26958)) % 186.01/186.05 [2696]~E(x26961,x26962)+E(f859(x26963,x26964,x26961,x26965,x26966,x26967,x26968),f859(x26963,x26964,x26962,x26965,x26966,x26967,x26968)) % 186.01/186.05 [2697]~E(x26971,x26972)+E(f859(x26973,x26974,x26975,x26971,x26976,x26977,x26978),f859(x26973,x26974,x26975,x26972,x26976,x26977,x26978)) % 186.01/186.05 [2698]~E(x26981,x26982)+E(f859(x26983,x26984,x26985,x26986,x26981,x26987,x26988),f859(x26983,x26984,x26985,x26986,x26982,x26987,x26988)) % 186.01/186.05 [2699]~E(x26991,x26992)+E(f859(x26993,x26994,x26995,x26996,x26997,x26991,x26998),f859(x26993,x26994,x26995,x26996,x26997,x26992,x26998)) % 186.01/186.05 [2700]~E(x27001,x27002)+E(f859(x27003,x27004,x27005,x27006,x27007,x27008,x27001),f859(x27003,x27004,x27005,x27006,x27007,x27008,x27002)) % 186.01/186.05 [2701]~E(x27011,x27012)+E(f762(x27011,x27013),f762(x27012,x27013)) % 186.01/186.05 [2702]~E(x27021,x27022)+E(f762(x27023,x27021),f762(x27023,x27022)) % 186.01/186.05 [2703]~E(x27031,x27032)+E(f303(x27031,x27033,x27034),f303(x27032,x27033,x27034)) % 186.01/186.05 [2704]~E(x27041,x27042)+E(f303(x27043,x27041,x27044),f303(x27043,x27042,x27044)) % 186.01/186.05 [2705]~E(x27051,x27052)+E(f303(x27053,x27054,x27051),f303(x27053,x27054,x27052)) % 186.01/186.05 [2706]~E(x27061,x27062)+E(f518(x27061,x27063,x27064,x27065),f518(x27062,x27063,x27064,x27065)) % 186.01/186.05 [2707]~E(x27071,x27072)+E(f518(x27073,x27071,x27074,x27075),f518(x27073,x27072,x27074,x27075)) % 186.01/186.05 [2708]~E(x27081,x27082)+E(f518(x27083,x27084,x27081,x27085),f518(x27083,x27084,x27082,x27085)) % 186.01/186.05 [2709]~E(x27091,x27092)+E(f518(x27093,x27094,x27095,x27091),f518(x27093,x27094,x27095,x27092)) % 186.01/186.05 [2710]~E(x27101,x27102)+E(f768(x27101,x27103,x27104,x27105,x27106),f768(x27102,x27103,x27104,x27105,x27106)) % 186.01/186.05 [2711]~E(x27111,x27112)+E(f768(x27113,x27111,x27114,x27115,x27116),f768(x27113,x27112,x27114,x27115,x27116)) % 186.01/186.05 [2712]~E(x27121,x27122)+E(f768(x27123,x27124,x27121,x27125,x27126),f768(x27123,x27124,x27122,x27125,x27126)) % 186.01/186.05 [2713]~E(x27131,x27132)+E(f768(x27133,x27134,x27135,x27131,x27136),f768(x27133,x27134,x27135,x27132,x27136)) % 186.01/186.05 [2714]~E(x27141,x27142)+E(f768(x27143,x27144,x27145,x27146,x27141),f768(x27143,x27144,x27145,x27146,x27142)) % 186.01/186.05 [2715]~E(x27151,x27152)+E(f524(x27151,x27153,x27154,x27155),f524(x27152,x27153,x27154,x27155)) % 186.01/186.05 [2716]~E(x27161,x27162)+E(f524(x27163,x27161,x27164,x27165),f524(x27163,x27162,x27164,x27165)) % 186.01/186.05 [2717]~E(x27171,x27172)+E(f524(x27173,x27174,x27171,x27175),f524(x27173,x27174,x27172,x27175)) % 186.01/186.05 [2718]~E(x27181,x27182)+E(f524(x27183,x27184,x27185,x27181),f524(x27183,x27184,x27185,x27182)) % 186.01/186.05 [2719]~E(x27191,x27192)+E(f354(x27191,x27193),f354(x27192,x27193)) % 186.01/186.05 [2720]~E(x27201,x27202)+E(f354(x27203,x27201),f354(x27203,x27202)) % 186.01/186.05 [2721]~E(x27211,x27212)+E(f716(x27211,x27213,x27214),f716(x27212,x27213,x27214)) % 186.01/186.05 [2722]~E(x27221,x27222)+E(f716(x27223,x27221,x27224),f716(x27223,x27222,x27224)) % 186.01/186.05 [2723]~E(x27231,x27232)+E(f716(x27233,x27234,x27231),f716(x27233,x27234,x27232)) % 186.01/186.05 [2724]~E(x27241,x27242)+E(f300(x27241,x27243),f300(x27242,x27243)) % 186.01/186.05 [2725]~E(x27251,x27252)+E(f300(x27253,x27251),f300(x27253,x27252)) % 186.01/186.05 [2726]~E(x27261,x27262)+E(f131(x27261),f131(x27262)) % 186.01/186.05 [2727]~E(x27271,x27272)+E(f628(x27271,x27273,x27274,x27275,x27276),f628(x27272,x27273,x27274,x27275,x27276)) % 186.01/186.05 [2728]~E(x27281,x27282)+E(f628(x27283,x27281,x27284,x27285,x27286),f628(x27283,x27282,x27284,x27285,x27286)) % 186.01/186.05 [2729]~E(x27291,x27292)+E(f628(x27293,x27294,x27291,x27295,x27296),f628(x27293,x27294,x27292,x27295,x27296)) % 186.01/186.05 [2730]~E(x27301,x27302)+E(f628(x27303,x27304,x27305,x27301,x27306),f628(x27303,x27304,x27305,x27302,x27306)) % 186.01/186.05 [2731]~E(x27311,x27312)+E(f628(x27313,x27314,x27315,x27316,x27311),f628(x27313,x27314,x27315,x27316,x27312)) % 186.01/186.05 [2732]~E(x27321,x27322)+E(f907(x27321,x27323,x27324,x27325,x27326,x27327),f907(x27322,x27323,x27324,x27325,x27326,x27327)) % 186.01/186.05 [2733]~E(x27331,x27332)+E(f907(x27333,x27331,x27334,x27335,x27336,x27337),f907(x27333,x27332,x27334,x27335,x27336,x27337)) % 186.01/186.05 [2734]~E(x27341,x27342)+E(f907(x27343,x27344,x27341,x27345,x27346,x27347),f907(x27343,x27344,x27342,x27345,x27346,x27347)) % 186.01/186.05 [2735]~E(x27351,x27352)+E(f907(x27353,x27354,x27355,x27351,x27356,x27357),f907(x27353,x27354,x27355,x27352,x27356,x27357)) % 186.01/186.05 [2736]~E(x27361,x27362)+E(f907(x27363,x27364,x27365,x27366,x27361,x27367),f907(x27363,x27364,x27365,x27366,x27362,x27367)) % 186.01/186.05 [2737]~E(x27371,x27372)+E(f907(x27373,x27374,x27375,x27376,x27377,x27371),f907(x27373,x27374,x27375,x27376,x27377,x27372)) % 186.01/186.05 [2738]~E(x27381,x27382)+E(f813(x27381,x27383),f813(x27382,x27383)) % 186.01/186.05 [2739]~E(x27391,x27392)+E(f813(x27393,x27391),f813(x27393,x27392)) % 186.01/186.05 [2740]~E(x27401,x27402)+E(f187(x27401),f187(x27402)) % 186.01/186.05 [2741]~E(x27411,x27412)+E(f207(x27411,x27413,x27414,x27415),f207(x27412,x27413,x27414,x27415)) % 186.01/186.05 [2742]~E(x27421,x27422)+E(f207(x27423,x27421,x27424,x27425),f207(x27423,x27422,x27424,x27425)) % 186.01/186.05 [2743]~E(x27431,x27432)+E(f207(x27433,x27434,x27431,x27435),f207(x27433,x27434,x27432,x27435)) % 186.01/186.05 [2744]~E(x27441,x27442)+E(f207(x27443,x27444,x27445,x27441),f207(x27443,x27444,x27445,x27442)) % 186.01/186.05 [2745]~E(x27451,x27452)+E(f379(x27451,x27453,x27454),f379(x27452,x27453,x27454)) % 186.01/186.05 [2746]~E(x27461,x27462)+E(f379(x27463,x27461,x27464),f379(x27463,x27462,x27464)) % 186.01/186.05 [2747]~E(x27471,x27472)+E(f379(x27473,x27474,x27471),f379(x27473,x27474,x27472)) % 186.01/186.05 [2748]~E(x27481,x27482)+E(f220(x27481,x27483,x27484,x27485,x27486,x27487,x27488),f220(x27482,x27483,x27484,x27485,x27486,x27487,x27488)) % 186.01/186.05 [2749]~E(x27491,x27492)+E(f220(x27493,x27491,x27494,x27495,x27496,x27497,x27498),f220(x27493,x27492,x27494,x27495,x27496,x27497,x27498)) % 186.01/186.05 [2750]~E(x27501,x27502)+E(f220(x27503,x27504,x27501,x27505,x27506,x27507,x27508),f220(x27503,x27504,x27502,x27505,x27506,x27507,x27508)) % 186.01/186.05 [2751]~E(x27511,x27512)+E(f220(x27513,x27514,x27515,x27511,x27516,x27517,x27518),f220(x27513,x27514,x27515,x27512,x27516,x27517,x27518)) % 186.01/186.05 [2752]~E(x27521,x27522)+E(f220(x27523,x27524,x27525,x27526,x27521,x27527,x27528),f220(x27523,x27524,x27525,x27526,x27522,x27527,x27528)) % 186.01/186.05 [2753]~E(x27531,x27532)+E(f220(x27533,x27534,x27535,x27536,x27537,x27531,x27538),f220(x27533,x27534,x27535,x27536,x27537,x27532,x27538)) % 186.01/186.05 [2754]~E(x27541,x27542)+E(f220(x27543,x27544,x27545,x27546,x27547,x27548,x27541),f220(x27543,x27544,x27545,x27546,x27547,x27548,x27542)) % 186.01/186.05 [2755]~E(x27551,x27552)+E(f713(x27551,x27553,x27554),f713(x27552,x27553,x27554)) % 186.01/186.05 [2756]~E(x27561,x27562)+E(f713(x27563,x27561,x27564),f713(x27563,x27562,x27564)) % 186.01/186.05 [2757]~E(x27571,x27572)+E(f713(x27573,x27574,x27571),f713(x27573,x27574,x27572)) % 186.01/186.05 [2758]~E(x27581,x27582)+E(f410(x27581,x27583,x27584,x27585),f410(x27582,x27583,x27584,x27585)) % 186.01/186.05 [2759]~E(x27591,x27592)+E(f410(x27593,x27591,x27594,x27595),f410(x27593,x27592,x27594,x27595)) % 186.01/186.05 [2760]~E(x27601,x27602)+E(f410(x27603,x27604,x27601,x27605),f410(x27603,x27604,x27602,x27605)) % 186.01/186.05 [2761]~E(x27611,x27612)+E(f410(x27613,x27614,x27615,x27611),f410(x27613,x27614,x27615,x27612)) % 186.01/186.05 [2762]~E(x27621,x27622)+E(f385(x27621,x27623),f385(x27622,x27623)) % 186.01/186.05 [2763]~E(x27631,x27632)+E(f385(x27633,x27631),f385(x27633,x27632)) % 186.01/186.05 [2764]~E(x27641,x27642)+E(f855(x27641,x27643,x27644),f855(x27642,x27643,x27644)) % 186.01/186.05 [2765]~E(x27651,x27652)+E(f855(x27653,x27651,x27654),f855(x27653,x27652,x27654)) % 186.01/186.05 [2766]~E(x27661,x27662)+E(f855(x27663,x27664,x27661),f855(x27663,x27664,x27662)) % 186.01/186.05 [2767]~E(x27671,x27672)+E(f591(x27671,x27673),f591(x27672,x27673)) % 186.01/186.05 [2768]~E(x27681,x27682)+E(f591(x27683,x27681),f591(x27683,x27682)) % 186.01/186.05 [2769]~E(x27691,x27692)+E(f343(x27691),f343(x27692)) % 186.01/186.05 [2770]~E(x27701,x27702)+E(f347(x27701,x27703,x27704,x27705),f347(x27702,x27703,x27704,x27705)) % 186.01/186.05 [2771]~E(x27711,x27712)+E(f347(x27713,x27711,x27714,x27715),f347(x27713,x27712,x27714,x27715)) % 186.01/186.05 [2772]~E(x27721,x27722)+E(f347(x27723,x27724,x27721,x27725),f347(x27723,x27724,x27722,x27725)) % 186.01/186.05 [2773]~E(x27731,x27732)+E(f347(x27733,x27734,x27735,x27731),f347(x27733,x27734,x27735,x27732)) % 186.01/186.05 [2774]~E(x27741,x27742)+E(f572(x27741,x27743,x27744),f572(x27742,x27743,x27744)) % 186.01/186.05 [2775]~E(x27751,x27752)+E(f572(x27753,x27751,x27754),f572(x27753,x27752,x27754)) % 186.01/186.05 [2776]~E(x27761,x27762)+E(f572(x27763,x27764,x27761),f572(x27763,x27764,x27762)) % 186.01/186.05 [2777]~E(x27771,x27772)+E(f421(x27771,x27773),f421(x27772,x27773)) % 186.01/186.05 [2778]~E(x27781,x27782)+E(f421(x27783,x27781),f421(x27783,x27782)) % 186.01/186.05 [2779]~E(x27791,x27792)+E(f757(x27791,x27793),f757(x27792,x27793)) % 186.01/186.05 [2780]~E(x27801,x27802)+E(f757(x27803,x27801),f757(x27803,x27802)) % 186.01/186.05 [2781]~E(x27811,x27812)+E(f453(x27811,x27813,x27814),f453(x27812,x27813,x27814)) % 186.01/186.05 [2782]~E(x27821,x27822)+E(f453(x27823,x27821,x27824),f453(x27823,x27822,x27824)) % 186.01/186.05 [2783]~E(x27831,x27832)+E(f453(x27833,x27834,x27831),f453(x27833,x27834,x27832)) % 186.01/186.05 [2784]~E(x27841,x27842)+E(f769(x27841,x27843,x27844,x27845,x27846),f769(x27842,x27843,x27844,x27845,x27846)) % 186.01/186.05 [2785]~E(x27851,x27852)+E(f769(x27853,x27851,x27854,x27855,x27856),f769(x27853,x27852,x27854,x27855,x27856)) % 186.01/186.05 [2786]~E(x27861,x27862)+E(f769(x27863,x27864,x27861,x27865,x27866),f769(x27863,x27864,x27862,x27865,x27866)) % 186.01/186.05 [2787]~E(x27871,x27872)+E(f769(x27873,x27874,x27875,x27871,x27876),f769(x27873,x27874,x27875,x27872,x27876)) % 186.01/186.05 [2788]~E(x27881,x27882)+E(f769(x27883,x27884,x27885,x27886,x27881),f769(x27883,x27884,x27885,x27886,x27882)) % 186.01/186.05 [2789]~E(x27891,x27892)+E(f368(x27891,x27893,x27894),f368(x27892,x27893,x27894)) % 186.01/186.05 [2790]~E(x27901,x27902)+E(f368(x27903,x27901,x27904),f368(x27903,x27902,x27904)) % 186.01/186.05 [2791]~E(x27911,x27912)+E(f368(x27913,x27914,x27911),f368(x27913,x27914,x27912)) % 186.01/186.05 [2792]~E(x27921,x27922)+E(f718(x27921,x27923,x27924,x27925,x27926),f718(x27922,x27923,x27924,x27925,x27926)) % 186.01/186.05 [2793]~E(x27931,x27932)+E(f718(x27933,x27931,x27934,x27935,x27936),f718(x27933,x27932,x27934,x27935,x27936)) % 186.01/186.05 [2794]~E(x27941,x27942)+E(f718(x27943,x27944,x27941,x27945,x27946),f718(x27943,x27944,x27942,x27945,x27946)) % 186.01/186.05 [2795]~E(x27951,x27952)+E(f718(x27953,x27954,x27955,x27951,x27956),f718(x27953,x27954,x27955,x27952,x27956)) % 186.01/186.05 [2796]~E(x27961,x27962)+E(f718(x27963,x27964,x27965,x27966,x27961),f718(x27963,x27964,x27965,x27966,x27962)) % 186.01/186.05 [2797]~E(x27971,x27972)+E(f509(x27971,x27973,x27974),f509(x27972,x27973,x27974)) % 186.01/186.05 [2798]~E(x27981,x27982)+E(f509(x27983,x27981,x27984),f509(x27983,x27982,x27984)) % 186.01/186.05 [2799]~E(x27991,x27992)+E(f509(x27993,x27994,x27991),f509(x27993,x27994,x27992)) % 186.01/186.05 [2800]~E(x28001,x28002)+E(f102(x28001,x28003,x28004,x28005),f102(x28002,x28003,x28004,x28005)) % 186.01/186.05 [2801]~E(x28011,x28012)+E(f102(x28013,x28011,x28014,x28015),f102(x28013,x28012,x28014,x28015)) % 186.01/186.05 [2802]~E(x28021,x28022)+E(f102(x28023,x28024,x28021,x28025),f102(x28023,x28024,x28022,x28025)) % 186.01/186.05 [2803]~E(x28031,x28032)+E(f102(x28033,x28034,x28035,x28031),f102(x28033,x28034,x28035,x28032)) % 186.01/186.05 [2804]~E(x28041,x28042)+E(f914(x28041,x28043,x28044),f914(x28042,x28043,x28044)) % 186.01/186.05 [2805]~E(x28051,x28052)+E(f914(x28053,x28051,x28054),f914(x28053,x28052,x28054)) % 186.01/186.05 [2806]~E(x28061,x28062)+E(f914(x28063,x28064,x28061),f914(x28063,x28064,x28062)) % 186.01/186.05 [2807]~E(x28071,x28072)+E(f223(x28071,x28073),f223(x28072,x28073)) % 186.01/186.05 [2808]~E(x28081,x28082)+E(f223(x28083,x28081),f223(x28083,x28082)) % 186.01/186.05 [2809]~E(x28091,x28092)+E(f523(x28091,x28093,x28094,x28095),f523(x28092,x28093,x28094,x28095)) % 186.01/186.05 [2810]~E(x28101,x28102)+E(f523(x28103,x28101,x28104,x28105),f523(x28103,x28102,x28104,x28105)) % 186.01/186.05 [2811]~E(x28111,x28112)+E(f523(x28113,x28114,x28111,x28115),f523(x28113,x28114,x28112,x28115)) % 186.01/186.05 [2812]~E(x28121,x28122)+E(f523(x28123,x28124,x28125,x28121),f523(x28123,x28124,x28125,x28122)) % 186.01/186.05 [2813]~E(x28131,x28132)+E(f835(x28131,x28133),f835(x28132,x28133)) % 186.01/186.05 [2814]~E(x28141,x28142)+E(f835(x28143,x28141),f835(x28143,x28142)) % 186.01/186.05 [2815]~E(x28151,x28152)+E(f898(x28151,x28153,x28154,x28155),f898(x28152,x28153,x28154,x28155)) % 186.01/186.05 [2816]~E(x28161,x28162)+E(f898(x28163,x28161,x28164,x28165),f898(x28163,x28162,x28164,x28165)) % 186.01/186.05 [2817]~E(x28171,x28172)+E(f898(x28173,x28174,x28171,x28175),f898(x28173,x28174,x28172,x28175)) % 186.01/186.05 [2818]~E(x28181,x28182)+E(f898(x28183,x28184,x28185,x28181),f898(x28183,x28184,x28185,x28182)) % 186.01/186.05 [2819]~E(x28191,x28192)+E(f434(x28191),f434(x28192)) % 186.01/186.05 [2820]~E(x28201,x28202)+E(f304(x28201,x28203,x28204),f304(x28202,x28203,x28204)) % 186.01/186.05 [2821]~E(x28211,x28212)+E(f304(x28213,x28211,x28214),f304(x28213,x28212,x28214)) % 186.01/186.05 [2822]~E(x28221,x28222)+E(f304(x28223,x28224,x28221),f304(x28223,x28224,x28222)) % 186.01/186.05 [2823]~E(x28231,x28232)+E(f212(x28231,x28233,x28234),f212(x28232,x28233,x28234)) % 186.01/186.05 [2824]~E(x28241,x28242)+E(f212(x28243,x28241,x28244),f212(x28243,x28242,x28244)) % 186.01/186.05 [2825]~E(x28251,x28252)+E(f212(x28253,x28254,x28251),f212(x28253,x28254,x28252)) % 186.01/186.05 [2826]~E(x28261,x28262)+E(f451(x28261,x28263),f451(x28262,x28263)) % 186.01/186.05 [2827]~E(x28271,x28272)+E(f451(x28273,x28271),f451(x28273,x28272)) % 186.01/186.05 [2828]~E(x28281,x28282)+E(f433(x28281),f433(x28282)) % 186.01/186.05 [2829]~E(x28291,x28292)+E(f892(x28291,x28293,x28294),f892(x28292,x28293,x28294)) % 186.01/186.05 [2830]~E(x28301,x28302)+E(f892(x28303,x28301,x28304),f892(x28303,x28302,x28304)) % 186.01/186.05 [2831]~E(x28311,x28312)+E(f892(x28313,x28314,x28311),f892(x28313,x28314,x28312)) % 186.01/186.05 [2832]~E(x28321,x28322)+E(f465(x28321),f465(x28322)) % 186.01/186.05 [2833]~E(x28331,x28332)+E(f233(x28331,x28333,x28334,x28335,x28336),f233(x28332,x28333,x28334,x28335,x28336)) % 186.01/186.05 [2834]~E(x28341,x28342)+E(f233(x28343,x28341,x28344,x28345,x28346),f233(x28343,x28342,x28344,x28345,x28346)) % 186.01/186.05 [2835]~E(x28351,x28352)+E(f233(x28353,x28354,x28351,x28355,x28356),f233(x28353,x28354,x28352,x28355,x28356)) % 186.01/186.05 [2836]~E(x28361,x28362)+E(f233(x28363,x28364,x28365,x28361,x28366),f233(x28363,x28364,x28365,x28362,x28366)) % 186.01/186.05 [2837]~E(x28371,x28372)+E(f233(x28373,x28374,x28375,x28376,x28371),f233(x28373,x28374,x28375,x28376,x28372)) % 186.01/186.05 [2838]~E(x28381,x28382)+E(f534(x28381,x28383,x28384,x28385),f534(x28382,x28383,x28384,x28385)) % 186.01/186.05 [2839]~E(x28391,x28392)+E(f534(x28393,x28391,x28394,x28395),f534(x28393,x28392,x28394,x28395)) % 186.01/186.05 [2840]~E(x28401,x28402)+E(f534(x28403,x28404,x28401,x28405),f534(x28403,x28404,x28402,x28405)) % 186.01/186.05 [2841]~E(x28411,x28412)+E(f534(x28413,x28414,x28415,x28411),f534(x28413,x28414,x28415,x28412)) % 186.01/186.05 [2842]~E(x28421,x28422)+E(f268(x28421,x28423,x28424,x28425,x28426),f268(x28422,x28423,x28424,x28425,x28426)) % 186.01/186.05 [2843]~E(x28431,x28432)+E(f268(x28433,x28431,x28434,x28435,x28436),f268(x28433,x28432,x28434,x28435,x28436)) % 186.01/186.05 [2844]~E(x28441,x28442)+E(f268(x28443,x28444,x28441,x28445,x28446),f268(x28443,x28444,x28442,x28445,x28446)) % 186.01/186.05 [2845]~E(x28451,x28452)+E(f268(x28453,x28454,x28455,x28451,x28456),f268(x28453,x28454,x28455,x28452,x28456)) % 186.01/186.05 [2846]~E(x28461,x28462)+E(f268(x28463,x28464,x28465,x28466,x28461),f268(x28463,x28464,x28465,x28466,x28462)) % 186.01/186.05 [2847]~E(x28471,x28472)+E(f640(x28471,x28473,x28474,x28475,x28476),f640(x28472,x28473,x28474,x28475,x28476)) % 186.01/186.05 [2848]~E(x28481,x28482)+E(f640(x28483,x28481,x28484,x28485,x28486),f640(x28483,x28482,x28484,x28485,x28486)) % 186.01/186.05 [2849]~E(x28491,x28492)+E(f640(x28493,x28494,x28491,x28495,x28496),f640(x28493,x28494,x28492,x28495,x28496)) % 186.01/186.05 [2850]~E(x28501,x28502)+E(f640(x28503,x28504,x28505,x28501,x28506),f640(x28503,x28504,x28505,x28502,x28506)) % 186.01/186.05 [2851]~E(x28511,x28512)+E(f640(x28513,x28514,x28515,x28516,x28511),f640(x28513,x28514,x28515,x28516,x28512)) % 186.01/186.05 [2852]~E(x28521,x28522)+E(f889(x28521,x28523,x28524,x28525,x28526,x28527),f889(x28522,x28523,x28524,x28525,x28526,x28527)) % 186.01/186.05 [2853]~E(x28531,x28532)+E(f889(x28533,x28531,x28534,x28535,x28536,x28537),f889(x28533,x28532,x28534,x28535,x28536,x28537)) % 186.01/186.05 [2854]~E(x28541,x28542)+E(f889(x28543,x28544,x28541,x28545,x28546,x28547),f889(x28543,x28544,x28542,x28545,x28546,x28547)) % 186.01/186.05 [2855]~E(x28551,x28552)+E(f889(x28553,x28554,x28555,x28551,x28556,x28557),f889(x28553,x28554,x28555,x28552,x28556,x28557)) % 186.01/186.05 [2856]~E(x28561,x28562)+E(f889(x28563,x28564,x28565,x28566,x28561,x28567),f889(x28563,x28564,x28565,x28566,x28562,x28567)) % 186.01/186.05 [2857]~E(x28571,x28572)+E(f889(x28573,x28574,x28575,x28576,x28577,x28571),f889(x28573,x28574,x28575,x28576,x28577,x28572)) % 186.01/186.05 [2858]~E(x28581,x28582)+E(f839(x28581,x28583),f839(x28582,x28583)) % 186.01/186.05 [2859]~E(x28591,x28592)+E(f839(x28593,x28591),f839(x28593,x28592)) % 186.01/186.05 [2860]~E(x28601,x28602)+E(f355(x28601,x28603),f355(x28602,x28603)) % 186.01/186.05 [2861]~E(x28611,x28612)+E(f355(x28613,x28611),f355(x28613,x28612)) % 186.01/186.05 [2862]~E(x28621,x28622)+E(f781(x28621,x28623,x28624),f781(x28622,x28623,x28624)) % 186.01/186.05 [2863]~E(x28631,x28632)+E(f781(x28633,x28631,x28634),f781(x28633,x28632,x28634)) % 186.01/186.05 [2864]~E(x28641,x28642)+E(f781(x28643,x28644,x28641),f781(x28643,x28644,x28642)) % 186.01/186.05 [2865]~E(x28651,x28652)+E(f234(x28651,x28653,x28654,x28655,x28656),f234(x28652,x28653,x28654,x28655,x28656)) % 186.01/186.05 [2866]~E(x28661,x28662)+E(f234(x28663,x28661,x28664,x28665,x28666),f234(x28663,x28662,x28664,x28665,x28666)) % 186.01/186.05 [2867]~E(x28671,x28672)+E(f234(x28673,x28674,x28671,x28675,x28676),f234(x28673,x28674,x28672,x28675,x28676)) % 186.01/186.05 [2868]~E(x28681,x28682)+E(f234(x28683,x28684,x28685,x28681,x28686),f234(x28683,x28684,x28685,x28682,x28686)) % 186.01/186.05 [2869]~E(x28691,x28692)+E(f234(x28693,x28694,x28695,x28696,x28691),f234(x28693,x28694,x28695,x28696,x28692)) % 186.01/186.05 [2870]~E(x28701,x28702)+E(f227(x28701,x28703),f227(x28702,x28703)) % 186.01/186.05 [2871]~E(x28711,x28712)+E(f227(x28713,x28711),f227(x28713,x28712)) % 186.01/186.05 [2872]~E(x28721,x28722)+E(f391(x28721,x28723),f391(x28722,x28723)) % 186.01/186.05 [2873]~E(x28731,x28732)+E(f391(x28733,x28731),f391(x28733,x28732)) % 186.01/186.05 [2874]~E(x28741,x28742)+E(f575(x28741,x28743),f575(x28742,x28743)) % 186.01/186.05 [2875]~E(x28751,x28752)+E(f575(x28753,x28751),f575(x28753,x28752)) % 186.01/186.05 [2876]~E(x28761,x28762)+E(f341(x28761),f341(x28762)) % 186.01/186.05 [2877]~P1(x28771)+P1(x28772)+~E(x28771,x28772) % 186.01/186.05 [2878]~P2(x28781)+P2(x28782)+~E(x28781,x28782) % 186.01/186.05 [2879]~P109(x28791)+P109(x28792)+~E(x28791,x28792) % 186.01/186.05 [2880]~P3(x28801)+P3(x28802)+~E(x28801,x28802) % 186.01/186.05 [2881]P38(x28812,x28813)+~E(x28811,x28812)+~P38(x28811,x28813) % 186.01/186.05 [2882]P38(x28823,x28822)+~E(x28821,x28822)+~P38(x28823,x28821) % 186.01/186.05 [2883]P30(x28832,x28833,x28834)+~E(x28831,x28832)+~P30(x28831,x28833,x28834) % 186.01/186.05 [2884]P30(x28843,x28842,x28844)+~E(x28841,x28842)+~P30(x28843,x28841,x28844) % 186.01/186.05 [2885]P30(x28853,x28854,x28852)+~E(x28851,x28852)+~P30(x28853,x28854,x28851) % 186.01/186.05 [2886]~P98(x28861)+P98(x28862)+~E(x28861,x28862) % 186.01/186.05 [2887]~P107(x28871)+P107(x28872)+~E(x28871,x28872) % 186.01/186.05 [2888]~P79(x28881)+P79(x28882)+~E(x28881,x28882) % 186.01/186.05 [2889]P26(x28892,x28893,x28894,x28895)+~E(x28891,x28892)+~P26(x28891,x28893,x28894,x28895) % 186.01/186.05 [2890]P26(x28903,x28902,x28904,x28905)+~E(x28901,x28902)+~P26(x28903,x28901,x28904,x28905) % 186.01/186.05 [2891]P26(x28913,x28914,x28912,x28915)+~E(x28911,x28912)+~P26(x28913,x28914,x28911,x28915) % 186.01/186.05 [2892]P26(x28923,x28924,x28925,x28922)+~E(x28921,x28922)+~P26(x28923,x28924,x28925,x28921) % 186.01/186.05 [2893]~P97(x28931)+P97(x28932)+~E(x28931,x28932) % 186.01/186.05 [2894]~P111(x28941)+P111(x28942)+~E(x28941,x28942) % 186.01/186.05 [2895]~P108(x28951)+P108(x28952)+~E(x28951,x28952) % 186.01/186.05 [2896]~P128(x28961)+P128(x28962)+~E(x28961,x28962) % 186.01/186.05 [2897]~P68(x28971)+P68(x28972)+~E(x28971,x28972) % 186.01/186.05 [2898]~P127(x28981)+P127(x28982)+~E(x28981,x28982) % 186.01/186.05 [2899]~P94(x28991)+P94(x28992)+~E(x28991,x28992) % 186.01/186.05 [2900]~P6(x29001)+P6(x29002)+~E(x29001,x29002) % 186.01/186.05 [2901]~P118(x29011)+P118(x29012)+~E(x29011,x29012) % 186.01/186.05 [2902]~P110(x29021)+P110(x29022)+~E(x29021,x29022) % 186.01/186.05 [2903]~P5(x29031)+P5(x29032)+~E(x29031,x29032) % 186.01/186.05 [2904]~P76(x29041)+P76(x29042)+~E(x29041,x29042) % 186.01/186.05 [2905]P27(x29052,x29053,x29054,x29055,x29056)+~E(x29051,x29052)+~P27(x29051,x29053,x29054,x29055,x29056) % 186.01/186.05 [2906]P27(x29063,x29062,x29064,x29065,x29066)+~E(x29061,x29062)+~P27(x29063,x29061,x29064,x29065,x29066) % 186.01/186.05 [2907]P27(x29073,x29074,x29072,x29075,x29076)+~E(x29071,x29072)+~P27(x29073,x29074,x29071,x29075,x29076) % 186.01/186.05 [2908]P27(x29083,x29084,x29085,x29082,x29086)+~E(x29081,x29082)+~P27(x29083,x29084,x29085,x29081,x29086) % 186.01/186.05 [2909]P27(x29093,x29094,x29095,x29096,x29092)+~E(x29091,x29092)+~P27(x29093,x29094,x29095,x29096,x29091) % 186.01/186.05 [2910]~P81(x29101)+P81(x29102)+~E(x29101,x29102) % 186.01/186.05 [2911]~P83(x29111)+P83(x29112)+~E(x29111,x29112) % 186.01/186.05 [2912]~P84(x29121)+P84(x29122)+~E(x29121,x29122) % 186.01/186.05 [2913]~P85(x29131)+P85(x29132)+~E(x29131,x29132) % 186.01/186.05 [2914]~P4(x29141)+P4(x29142)+~E(x29141,x29142) % 186.01/186.05 [2915]~P140(x29151)+P140(x29152)+~E(x29151,x29152) % 186.01/186.05 [2916]~P78(x29161)+P78(x29162)+~E(x29161,x29162) % 186.01/186.05 [2917]~P70(x29171)+P70(x29172)+~E(x29171,x29172) % 186.01/186.05 [2918]P14(x29182,x29183)+~E(x29181,x29182)+~P14(x29181,x29183) % 186.01/186.05 [2919]P14(x29193,x29192)+~E(x29191,x29192)+~P14(x29193,x29191) % 186.01/186.05 [2920]~P131(x29201)+P131(x29202)+~E(x29201,x29202) % 186.01/186.05 [2921]~P112(x29211)+P112(x29212)+~E(x29211,x29212) % 186.01/186.05 [2922]~P113(x29221)+P113(x29222)+~E(x29221,x29222) % 186.01/186.05 [2923]P15(x29232,x29233,x29234)+~E(x29231,x29232)+~P15(x29231,x29233,x29234) % 186.01/186.05 [2924]P15(x29243,x29242,x29244)+~E(x29241,x29242)+~P15(x29243,x29241,x29244) % 186.01/186.05 [2925]P15(x29253,x29254,x29252)+~E(x29251,x29252)+~P15(x29253,x29254,x29251) % 186.01/186.05 [2926]P21(x29262,x29263,x29264,x29265)+~E(x29261,x29262)+~P21(x29261,x29263,x29264,x29265) % 186.01/186.05 [2927]P21(x29273,x29272,x29274,x29275)+~E(x29271,x29272)+~P21(x29273,x29271,x29274,x29275) % 186.01/186.05 [2928]P21(x29283,x29284,x29282,x29285)+~E(x29281,x29282)+~P21(x29283,x29284,x29281,x29285) % 186.01/186.05 [2929]P21(x29293,x29294,x29295,x29292)+~E(x29291,x29292)+~P21(x29293,x29294,x29295,x29291) % 186.01/186.05 [2930]~P87(x29301)+P87(x29302)+~E(x29301,x29302) % 186.01/186.05 [2931]~P89(x29311)+P89(x29312)+~E(x29311,x29312) % 186.01/186.05 [2932]~P69(x29321)+P69(x29322)+~E(x29321,x29322) % 186.01/186.05 [2933]~P99(x29331)+P99(x29332)+~E(x29331,x29332) % 186.01/186.05 [2934]~P101(x29341)+P101(x29342)+~E(x29341,x29342) % 186.01/186.05 [2935]P46(x29352,x29353)+~E(x29351,x29352)+~P46(x29351,x29353) % 186.01/186.05 [2936]P46(x29363,x29362)+~E(x29361,x29362)+~P46(x29363,x29361) % 186.01/186.05 [2937]~P114(x29371)+P114(x29372)+~E(x29371,x29372) % 186.01/186.05 [2938]~P103(x29381)+P103(x29382)+~E(x29381,x29382) % 186.01/186.05 [2939]~P82(x29391)+P82(x29392)+~E(x29391,x29392) % 186.01/186.05 [2940]~P63(x29401)+P63(x29402)+~E(x29401,x29402) % 186.01/186.05 [2941]~P102(x29411)+P102(x29412)+~E(x29411,x29412) % 186.01/186.05 [2942]~P95(x29421)+P95(x29422)+~E(x29421,x29422) % 186.01/186.05 [2943]P29(x29432,x29433)+~E(x29431,x29432)+~P29(x29431,x29433) % 186.01/186.05 [2944]P29(x29443,x29442)+~E(x29441,x29442)+~P29(x29443,x29441) % 186.01/186.05 [2945]~P62(x29451)+P62(x29452)+~E(x29451,x29452) % 186.01/186.05 [2946]P56(x29462,x29463,x29464)+~E(x29461,x29462)+~P56(x29461,x29463,x29464) % 186.01/186.05 [2947]P56(x29473,x29472,x29474)+~E(x29471,x29472)+~P56(x29473,x29471,x29474) % 186.01/186.05 [2948]P56(x29483,x29484,x29482)+~E(x29481,x29482)+~P56(x29483,x29484,x29481) % 186.01/186.05 [2949]~P80(x29491)+P80(x29492)+~E(x29491,x29492) % 186.01/186.05 [2950]P35(x29502,x29503,x29504,x29505,x29506)+~E(x29501,x29502)+~P35(x29501,x29503,x29504,x29505,x29506) % 186.01/186.05 [2951]P35(x29513,x29512,x29514,x29515,x29516)+~E(x29511,x29512)+~P35(x29513,x29511,x29514,x29515,x29516) % 186.01/186.05 [2952]P35(x29523,x29524,x29522,x29525,x29526)+~E(x29521,x29522)+~P35(x29523,x29524,x29521,x29525,x29526) % 186.01/186.05 [2953]P35(x29533,x29534,x29535,x29532,x29536)+~E(x29531,x29532)+~P35(x29533,x29534,x29535,x29531,x29536) % 186.01/186.05 [2954]P35(x29543,x29544,x29545,x29546,x29542)+~E(x29541,x29542)+~P35(x29543,x29544,x29545,x29546,x29541) % 186.01/186.05 [2955]P40(x29552,x29553)+~E(x29551,x29552)+~P40(x29551,x29553) % 186.01/186.05 [2956]P40(x29563,x29562)+~E(x29561,x29562)+~P40(x29563,x29561) % 186.01/186.05 [2957]P147(x29572,x29573,x29574)+~E(x29571,x29572)+~P147(x29571,x29573,x29574) % 186.01/186.05 [2958]P147(x29583,x29582,x29584)+~E(x29581,x29582)+~P147(x29583,x29581,x29584) % 186.01/186.05 [2959]P147(x29593,x29594,x29592)+~E(x29591,x29592)+~P147(x29593,x29594,x29591) % 186.01/186.05 [2960]~P72(x29601)+P72(x29602)+~E(x29601,x29602) % 186.01/186.05 [2961]P8(x29612,x29613)+~E(x29611,x29612)+~P8(x29611,x29613) % 186.01/186.05 [2962]P8(x29623,x29622)+~E(x29621,x29622)+~P8(x29623,x29621) % 186.01/186.05 [2963]~P41(x29631)+P41(x29632)+~E(x29631,x29632) % 186.01/186.05 [2964]P32(x29642,x29643,x29644)+~E(x29641,x29642)+~P32(x29641,x29643,x29644) % 186.01/186.05 [2965]P32(x29653,x29652,x29654)+~E(x29651,x29652)+~P32(x29653,x29651,x29654) % 186.01/186.05 [2966]P32(x29663,x29664,x29662)+~E(x29661,x29662)+~P32(x29663,x29664,x29661) % 186.01/186.05 [2967]P148(x29672,x29673,x29674)+~E(x29671,x29672)+~P148(x29671,x29673,x29674) % 186.01/186.05 [2968]P148(x29683,x29682,x29684)+~E(x29681,x29682)+~P148(x29683,x29681,x29684) % 186.01/186.05 [2969]P148(x29693,x29694,x29692)+~E(x29691,x29692)+~P148(x29693,x29694,x29691) % 186.01/186.05 [2970]~P125(x29701)+P125(x29702)+~E(x29701,x29702) % 186.01/186.05 [2971]~P65(x29711)+P65(x29712)+~E(x29711,x29712) % 186.01/186.05 [2972]~P146(x29721)+P146(x29722)+~E(x29721,x29722) % 186.01/186.05 [2973]~P139(x29731)+P139(x29732)+~E(x29731,x29732) % 186.01/186.05 [2974]~P115(x29741)+P115(x29742)+~E(x29741,x29742) % 186.01/186.05 [2975]~P116(x29751)+P116(x29752)+~E(x29751,x29752) % 186.01/186.05 [2976]P12(x29762,x29763,x29764,x29765)+~E(x29761,x29762)+~P12(x29761,x29763,x29764,x29765) % 186.01/186.05 [2977]P12(x29773,x29772,x29774,x29775)+~E(x29771,x29772)+~P12(x29773,x29771,x29774,x29775) % 186.01/186.05 [2978]P12(x29783,x29784,x29782,x29785)+~E(x29781,x29782)+~P12(x29783,x29784,x29781,x29785) % 186.01/186.05 [2979]P12(x29793,x29794,x29795,x29792)+~E(x29791,x29792)+~P12(x29793,x29794,x29795,x29791) % 186.01/186.05 [2980]P20(x29802,x29803,x29804,x29805)+~E(x29801,x29802)+~P20(x29801,x29803,x29804,x29805) % 186.01/186.05 [2981]P20(x29813,x29812,x29814,x29815)+~E(x29811,x29812)+~P20(x29813,x29811,x29814,x29815) % 186.01/186.05 [2982]P20(x29823,x29824,x29822,x29825)+~E(x29821,x29822)+~P20(x29823,x29824,x29821,x29825) % 186.01/186.05 [2983]P20(x29833,x29834,x29835,x29832)+~E(x29831,x29832)+~P20(x29833,x29834,x29835,x29831) % 186.01/186.05 [2984]P39(x29842,x29843)+~E(x29841,x29842)+~P39(x29841,x29843) % 186.01/186.05 [2985]P39(x29853,x29852)+~E(x29851,x29852)+~P39(x29853,x29851) % 186.01/186.05 [2986]~P71(x29861)+P71(x29862)+~E(x29861,x29862) % 186.01/186.05 [2987]~P121(x29871)+P121(x29872)+~E(x29871,x29872) % 186.01/186.05 [2988]P54(x29882,x29883,x29884)+~E(x29881,x29882)+~P54(x29881,x29883,x29884) % 186.01/186.05 [2989]P54(x29893,x29892,x29894)+~E(x29891,x29892)+~P54(x29893,x29891,x29894) % 186.01/186.05 [2990]P54(x29903,x29904,x29902)+~E(x29901,x29902)+~P54(x29903,x29904,x29901) % 186.01/186.05 [2991]~P73(x29911)+P73(x29912)+~E(x29911,x29912) % 186.01/186.05 [2992]~P7(x29921)+P7(x29922)+~E(x29921,x29922) % 186.01/186.05 [2993]~P142(x29931)+P142(x29932)+~E(x29931,x29932) % 186.01/186.05 [2994]~P74(x29941)+P74(x29942)+~E(x29941,x29942) % 186.01/186.05 [2995]P31(x29952,x29953,x29954)+~E(x29951,x29952)+~P31(x29951,x29953,x29954) % 186.01/186.05 [2996]P31(x29963,x29962,x29964)+~E(x29961,x29962)+~P31(x29963,x29961,x29964) % 186.01/186.05 [2997]P31(x29973,x29974,x29972)+~E(x29971,x29972)+~P31(x29973,x29974,x29971) % 186.01/186.05 [2998]~P135(x29981)+P135(x29982)+~E(x29981,x29982) % 186.01/186.05 [2999]~P86(x29991)+P86(x29992)+~E(x29991,x29992) % 186.01/186.05 [3000]P9(x30002,x30003,x30004)+~E(x30001,x30002)+~P9(x30001,x30003,x30004) % 186.01/186.05 [3001]P9(x30013,x30012,x30014)+~E(x30011,x30012)+~P9(x30013,x30011,x30014) % 186.01/186.05 [3002]P9(x30023,x30024,x30022)+~E(x30021,x30022)+~P9(x30023,x30024,x30021) % 186.01/186.05 [3003]P57(x30032,x30033,x30034)+~E(x30031,x30032)+~P57(x30031,x30033,x30034) % 186.01/186.05 [3004]P57(x30043,x30042,x30044)+~E(x30041,x30042)+~P57(x30043,x30041,x30044) % 186.01/186.05 [3005]P57(x30053,x30054,x30052)+~E(x30051,x30052)+~P57(x30053,x30054,x30051) % 186.01/186.05 [3006]P51(x30062,x30063)+~E(x30061,x30062)+~P51(x30061,x30063) % 186.01/186.05 [3007]P51(x30073,x30072)+~E(x30071,x30072)+~P51(x30073,x30071) % 186.01/186.05 [3008]P25(x30082,x30083,x30084)+~E(x30081,x30082)+~P25(x30081,x30083,x30084) % 186.01/186.05 [3009]P25(x30093,x30092,x30094)+~E(x30091,x30092)+~P25(x30093,x30091,x30094) % 186.01/186.05 [3010]P25(x30103,x30104,x30102)+~E(x30101,x30102)+~P25(x30103,x30104,x30101) % 186.01/186.05 [3011]P36(x30112,x30113,x30114)+~E(x30111,x30112)+~P36(x30111,x30113,x30114) % 186.01/186.05 [3012]P36(x30123,x30122,x30124)+~E(x30121,x30122)+~P36(x30123,x30121,x30124) % 186.01/186.05 [3013]P36(x30133,x30134,x30132)+~E(x30131,x30132)+~P36(x30133,x30134,x30131) % 186.01/186.05 [3014]~P88(x30141)+P88(x30142)+~E(x30141,x30142) % 186.01/186.05 [3015]P59(x30152,x30153)+~E(x30151,x30152)+~P59(x30151,x30153) % 186.01/186.05 [3016]P59(x30163,x30162)+~E(x30161,x30162)+~P59(x30163,x30161) % 186.01/186.05 [3017]P53(x30172,x30173)+~E(x30171,x30172)+~P53(x30171,x30173) % 186.01/186.05 [3018]P53(x30183,x30182)+~E(x30181,x30182)+~P53(x30183,x30181) % 186.01/186.05 [3019]~P141(x30191)+P141(x30192)+~E(x30191,x30192) % 186.01/186.05 [3020]P24(x30202,x30203,x30204,x30205,x30206,x30207)+~E(x30201,x30202)+~P24(x30201,x30203,x30204,x30205,x30206,x30207) % 186.01/186.05 [3021]P24(x30213,x30212,x30214,x30215,x30216,x30217)+~E(x30211,x30212)+~P24(x30213,x30211,x30214,x30215,x30216,x30217) % 186.01/186.05 [3022]P24(x30223,x30224,x30222,x30225,x30226,x30227)+~E(x30221,x30222)+~P24(x30223,x30224,x30221,x30225,x30226,x30227) % 186.01/186.05 [3023]P24(x30233,x30234,x30235,x30232,x30236,x30237)+~E(x30231,x30232)+~P24(x30233,x30234,x30235,x30231,x30236,x30237) % 186.01/186.05 [3024]P24(x30243,x30244,x30245,x30246,x30242,x30247)+~E(x30241,x30242)+~P24(x30243,x30244,x30245,x30246,x30241,x30247) % 186.01/186.05 [3025]P24(x30253,x30254,x30255,x30256,x30257,x30252)+~E(x30251,x30252)+~P24(x30253,x30254,x30255,x30256,x30257,x30251) % 186.01/186.05 [3026]~P93(x30261)+P93(x30262)+~E(x30261,x30262) % 186.01/186.05 [3027]~P119(x30271)+P119(x30272)+~E(x30271,x30272) % 186.01/186.05 [3028]~P66(x30281)+P66(x30282)+~E(x30281,x30282) % 186.01/186.05 [3029]P61(x30292,x30293)+~E(x30291,x30292)+~P61(x30291,x30293) % 186.01/186.05 [3030]P61(x30303,x30302)+~E(x30301,x30302)+~P61(x30303,x30301) % 186.01/186.05 [3031]~P143(x30311)+P143(x30312)+~E(x30311,x30312) % 186.01/186.05 [3032]P52(x30322,x30323)+~E(x30321,x30322)+~P52(x30321,x30323) % 186.01/186.05 [3033]P52(x30333,x30332)+~E(x30331,x30332)+~P52(x30333,x30331) % 186.01/186.05 [3034]P34(x30342,x30343,x30344)+~E(x30341,x30342)+~P34(x30341,x30343,x30344) % 186.01/186.05 [3035]P34(x30353,x30352,x30354)+~E(x30351,x30352)+~P34(x30353,x30351,x30354) % 186.01/186.05 [3036]P34(x30363,x30364,x30362)+~E(x30361,x30362)+~P34(x30363,x30364,x30361) % 186.01/186.05 [3037]~P77(x30371)+P77(x30372)+~E(x30371,x30372) % 186.01/186.05 [3038]~P120(x30381)+P120(x30382)+~E(x30381,x30382) % 186.01/186.05 [3039]~P138(x30391)+P138(x30392)+~E(x30391,x30392) % 186.01/186.05 [3040]P60(x30402,x30403,x30404,x30405)+~E(x30401,x30402)+~P60(x30401,x30403,x30404,x30405) % 186.01/186.05 [3041]P60(x30413,x30412,x30414,x30415)+~E(x30411,x30412)+~P60(x30413,x30411,x30414,x30415) % 186.01/186.05 [3042]P60(x30423,x30424,x30422,x30425)+~E(x30421,x30422)+~P60(x30423,x30424,x30421,x30425) % 186.01/186.05 [3043]P60(x30433,x30434,x30435,x30432)+~E(x30431,x30432)+~P60(x30433,x30434,x30435,x30431) % 186.01/186.05 [3044]~P92(x30441)+P92(x30442)+~E(x30441,x30442) % 186.01/186.05 [3045]P47(x30452,x30453,x30454)+~E(x30451,x30452)+~P47(x30451,x30453,x30454) % 186.01/186.05 [3046]P47(x30463,x30462,x30464)+~E(x30461,x30462)+~P47(x30463,x30461,x30464) % 186.01/186.05 [3047]P47(x30473,x30474,x30472)+~E(x30471,x30472)+~P47(x30473,x30474,x30471) % 186.01/186.05 [3048]P49(x30482,x30483)+~E(x30481,x30482)+~P49(x30481,x30483) % 186.01/186.05 [3049]P49(x30493,x30492)+~E(x30491,x30492)+~P49(x30493,x30491) % 186.01/186.05 [3050]P17(x30502,x30503,x30504)+~E(x30501,x30502)+~P17(x30501,x30503,x30504) % 186.01/186.05 [3051]P17(x30513,x30512,x30514)+~E(x30511,x30512)+~P17(x30513,x30511,x30514) % 186.01/186.05 [3052]P17(x30523,x30524,x30522)+~E(x30521,x30522)+~P17(x30523,x30524,x30521) % 186.01/186.05 [3053]~P129(x30531)+P129(x30532)+~E(x30531,x30532) % 186.01/186.05 [3054]P33(x30542,x30543,x30544,x30545)+~E(x30541,x30542)+~P33(x30541,x30543,x30544,x30545) % 186.01/186.05 [3055]P33(x30553,x30552,x30554,x30555)+~E(x30551,x30552)+~P33(x30553,x30551,x30554,x30555) % 186.01/186.05 [3056]P33(x30563,x30564,x30562,x30565)+~E(x30561,x30562)+~P33(x30563,x30564,x30561,x30565) % 186.01/186.05 [3057]P33(x30573,x30574,x30575,x30572)+~E(x30571,x30572)+~P33(x30573,x30574,x30575,x30571) % 186.01/186.05 [3058]P55(x30582,x30583)+~E(x30581,x30582)+~P55(x30581,x30583) % 186.01/186.05 [3059]P55(x30593,x30592)+~E(x30591,x30592)+~P55(x30593,x30591) % 186.01/186.05 [3060]P18(x30602,x30603,x30604)+~E(x30601,x30602)+~P18(x30601,x30603,x30604) % 186.01/186.05 [3061]P18(x30613,x30612,x30614)+~E(x30611,x30612)+~P18(x30613,x30611,x30614) % 186.01/186.05 [3062]P18(x30623,x30624,x30622)+~E(x30621,x30622)+~P18(x30623,x30624,x30621) % 186.01/186.05 [3063]~P37(x30631)+P37(x30632)+~E(x30631,x30632) % 186.01/186.05 [3064]P23(x30642,x30643,x30644,x30645,x30646,x30647)+~E(x30641,x30642)+~P23(x30641,x30643,x30644,x30645,x30646,x30647) % 186.01/186.05 [3065]P23(x30653,x30652,x30654,x30655,x30656,x30657)+~E(x30651,x30652)+~P23(x30653,x30651,x30654,x30655,x30656,x30657) % 186.01/186.05 [3066]P23(x30663,x30664,x30662,x30665,x30666,x30667)+~E(x30661,x30662)+~P23(x30663,x30664,x30661,x30665,x30666,x30667) % 186.01/186.05 [3067]P23(x30673,x30674,x30675,x30672,x30676,x30677)+~E(x30671,x30672)+~P23(x30673,x30674,x30675,x30671,x30676,x30677) % 186.01/186.05 [3068]P23(x30683,x30684,x30685,x30686,x30682,x30687)+~E(x30681,x30682)+~P23(x30683,x30684,x30685,x30686,x30681,x30687) % 186.01/186.05 [3069]P23(x30693,x30694,x30695,x30696,x30697,x30692)+~E(x30691,x30692)+~P23(x30693,x30694,x30695,x30696,x30697,x30691) % 186.01/186.05 [3070]~P126(x30701)+P126(x30702)+~E(x30701,x30702) % 186.01/186.05 [3071]P16(x30712,x30713)+~E(x30711,x30712)+~P16(x30711,x30713) % 186.01/186.05 [3072]P16(x30723,x30722)+~E(x30721,x30722)+~P16(x30723,x30721) % 186.01/186.05 [3073]~P96(x30731)+P96(x30732)+~E(x30731,x30732) % 186.01/186.05 [3074]~P130(x30741)+P130(x30742)+~E(x30741,x30742) % 186.01/186.05 [3075]P43(x30752,x30753,x30754,x30755,x30756,x30757)+~E(x30751,x30752)+~P43(x30751,x30753,x30754,x30755,x30756,x30757) % 186.01/186.05 [3076]P43(x30763,x30762,x30764,x30765,x30766,x30767)+~E(x30761,x30762)+~P43(x30763,x30761,x30764,x30765,x30766,x30767) % 186.01/186.05 [3077]P43(x30773,x30774,x30772,x30775,x30776,x30777)+~E(x30771,x30772)+~P43(x30773,x30774,x30771,x30775,x30776,x30777) % 186.01/186.05 [3078]P43(x30783,x30784,x30785,x30782,x30786,x30787)+~E(x30781,x30782)+~P43(x30783,x30784,x30785,x30781,x30786,x30787) % 186.01/186.05 [3079]P43(x30793,x30794,x30795,x30796,x30792,x30797)+~E(x30791,x30792)+~P43(x30793,x30794,x30795,x30796,x30791,x30797) % 186.01/186.05 [3080]P43(x30803,x30804,x30805,x30806,x30807,x30802)+~E(x30801,x30802)+~P43(x30803,x30804,x30805,x30806,x30807,x30801) % 186.01/186.05 [3081]P19(x30812,x30813,x30814)+~E(x30811,x30812)+~P19(x30811,x30813,x30814) % 186.01/186.05 [3082]P19(x30823,x30822,x30824)+~E(x30821,x30822)+~P19(x30823,x30821,x30824) % 186.01/186.05 [3083]P19(x30833,x30834,x30832)+~E(x30831,x30832)+~P19(x30833,x30834,x30831) % 186.01/186.05 [3084]~P144(x30841)+P144(x30842)+~E(x30841,x30842) % 186.01/186.05 [3085]P11(x30852,x30853,x30854,x30855,x30856)+~E(x30851,x30852)+~P11(x30851,x30853,x30854,x30855,x30856) % 186.01/186.05 [3086]P11(x30863,x30862,x30864,x30865,x30866)+~E(x30861,x30862)+~P11(x30863,x30861,x30864,x30865,x30866) % 186.01/186.05 [3087]P11(x30873,x30874,x30872,x30875,x30876)+~E(x30871,x30872)+~P11(x30873,x30874,x30871,x30875,x30876) % 186.01/186.05 [3088]P11(x30883,x30884,x30885,x30882,x30886)+~E(x30881,x30882)+~P11(x30883,x30884,x30885,x30881,x30886) % 186.01/186.05 [3089]P11(x30893,x30894,x30895,x30896,x30892)+~E(x30891,x30892)+~P11(x30893,x30894,x30895,x30896,x30891) % 186.01/186.05 [3090]~P134(x30901)+P134(x30902)+~E(x30901,x30902) % 186.01/186.05 [3091]P28(x30912,x30913)+~E(x30911,x30912)+~P28(x30911,x30913) % 186.01/186.05 [3092]P28(x30923,x30922)+~E(x30921,x30922)+~P28(x30923,x30921) % 186.01/186.05 [3093]~P105(x30931)+P105(x30932)+~E(x30931,x30932) % 186.01/186.05 [3094]~P75(x30941)+P75(x30942)+~E(x30941,x30942) % 186.01/186.05 [3095]P58(x30952,x30953,x30954,x30955,x30956)+~E(x30951,x30952)+~P58(x30951,x30953,x30954,x30955,x30956) % 186.01/186.05 [3096]P58(x30963,x30962,x30964,x30965,x30966)+~E(x30961,x30962)+~P58(x30963,x30961,x30964,x30965,x30966) % 186.01/186.05 [3097]P58(x30973,x30974,x30972,x30975,x30976)+~E(x30971,x30972)+~P58(x30973,x30974,x30971,x30975,x30976) % 186.01/186.05 [3098]P58(x30983,x30984,x30985,x30982,x30986)+~E(x30981,x30982)+~P58(x30983,x30984,x30985,x30981,x30986) % 186.01/186.05 [3099]P58(x30993,x30994,x30995,x30996,x30992)+~E(x30991,x30992)+~P58(x30993,x30994,x30995,x30996,x30991) % 186.01/186.05 [3100]~P133(x31001)+P133(x31002)+~E(x31001,x31002) % 186.01/186.05 [3101]~P104(x31011)+P104(x31012)+~E(x31011,x31012) % 186.01/186.05 [3102]~P45(x31021)+P45(x31022)+~E(x31021,x31022) % 186.01/186.05 [3103]~P67(x31031)+P67(x31032)+~E(x31031,x31032) % 186.01/186.05 [3104]~P137(x31041)+P137(x31042)+~E(x31041,x31042) % 186.01/186.05 [3105]~P100(x31051)+P100(x31052)+~E(x31051,x31052) % 186.01/186.05 [3106]P22(x31062,x31063,x31064,x31065,x31066)+~E(x31061,x31062)+~P22(x31061,x31063,x31064,x31065,x31066) % 186.01/186.05 [3107]P22(x31073,x31072,x31074,x31075,x31076)+~E(x31071,x31072)+~P22(x31073,x31071,x31074,x31075,x31076) % 186.01/186.05 [3108]P22(x31083,x31084,x31082,x31085,x31086)+~E(x31081,x31082)+~P22(x31083,x31084,x31081,x31085,x31086) % 186.01/186.05 [3109]P22(x31093,x31094,x31095,x31092,x31096)+~E(x31091,x31092)+~P22(x31093,x31094,x31095,x31091,x31096) % 186.01/186.05 [3110]P22(x31103,x31104,x31105,x31106,x31102)+~E(x31101,x31102)+~P22(x31103,x31104,x31105,x31106,x31101) % 186.01/186.05 [3111]~P136(x31111)+P136(x31112)+~E(x31111,x31112) % 186.01/186.05 [3112]P44(x31122,x31123)+~E(x31121,x31122)+~P44(x31121,x31123) % 186.01/186.05 [3113]P44(x31133,x31132)+~E(x31131,x31132)+~P44(x31133,x31131) % 186.01/186.05 [3114]P13(x31142,x31143,x31144,x31145,x31146,x31147)+~E(x31141,x31142)+~P13(x31141,x31143,x31144,x31145,x31146,x31147) % 186.01/186.05 [3115]P13(x31153,x31152,x31154,x31155,x31156,x31157)+~E(x31151,x31152)+~P13(x31153,x31151,x31154,x31155,x31156,x31157) % 186.01/186.05 [3116]P13(x31163,x31164,x31162,x31165,x31166,x31167)+~E(x31161,x31162)+~P13(x31163,x31164,x31161,x31165,x31166,x31167) % 186.01/186.05 [3117]P13(x31173,x31174,x31175,x31172,x31176,x31177)+~E(x31171,x31172)+~P13(x31173,x31174,x31175,x31171,x31176,x31177) % 186.01/186.05 [3118]P13(x31183,x31184,x31185,x31186,x31182,x31187)+~E(x31181,x31182)+~P13(x31183,x31184,x31185,x31186,x31181,x31187) % 186.01/186.05 [3119]P13(x31193,x31194,x31195,x31196,x31197,x31192)+~E(x31191,x31192)+~P13(x31193,x31194,x31195,x31196,x31197,x31191) % 186.01/186.05 [3120]~P123(x31201)+P123(x31202)+~E(x31201,x31202) % 186.01/186.05 [3121]P50(x31212,x31213,x31214,x31215)+~E(x31211,x31212)+~P50(x31211,x31213,x31214,x31215) % 186.01/186.05 [3122]P50(x31223,x31222,x31224,x31225)+~E(x31221,x31222)+~P50(x31223,x31221,x31224,x31225) % 186.01/186.05 [3123]P50(x31233,x31234,x31232,x31235)+~E(x31231,x31232)+~P50(x31233,x31234,x31231,x31235) % 186.01/186.05 [3124]P50(x31243,x31244,x31245,x31242)+~E(x31241,x31242)+~P50(x31243,x31244,x31245,x31241) % 186.01/186.05 [3125]~P145(x31251)+P145(x31252)+~E(x31251,x31252) % 186.01/186.05 [3126]~P106(x31261)+P106(x31262)+~E(x31261,x31262) % 186.01/186.05 [3127]~P117(x31271)+P117(x31272)+~E(x31271,x31272) % 186.01/186.05 [3128]P48(x31282,x31283,x31284)+~E(x31281,x31282)+~P48(x31281,x31283,x31284) % 186.01/186.05 [3129]P48(x31293,x31292,x31294)+~E(x31291,x31292)+~P48(x31293,x31291,x31294) % 186.01/186.05 [3130]P48(x31303,x31304,x31302)+~E(x31301,x31302)+~P48(x31303,x31304,x31301) % 186.01/186.05 [3131]~P132(x31311)+P132(x31312)+~E(x31311,x31312) % 186.01/186.05 [3132]~P90(x31321)+P90(x31322)+~E(x31321,x31322) % 186.01/186.05 [3133]~P122(x31331)+P122(x31332)+~E(x31331,x31332) % 186.01/186.05 [3134]P10(x31342,x31343,x31344)+~E(x31341,x31342)+~P10(x31341,x31343,x31344) % 186.01/186.05 [3135]P10(x31353,x31352,x31354)+~E(x31351,x31352)+~P10(x31353,x31351,x31354) % 186.01/186.05 [3136]P10(x31363,x31364,x31362)+~E(x31361,x31362)+~P10(x31363,x31364,x31361) % 186.01/186.05 [3137]P42(x31372,x31373,x31374,x31375)+~E(x31371,x31372)+~P42(x31371,x31373,x31374,x31375) % 186.01/186.05 [3138]P42(x31383,x31382,x31384,x31385)+~E(x31381,x31382)+~P42(x31383,x31381,x31384,x31385) % 186.01/186.05 [3139]P42(x31393,x31394,x31392,x31395)+~E(x31391,x31392)+~P42(x31393,x31394,x31391,x31395) % 186.01/186.05 [3140]P42(x31403,x31404,x31405,x31402)+~E(x31401,x31402)+~P42(x31403,x31404,x31405,x31401) % 186.01/186.05 [3141]~P91(x31411)+P91(x31412)+~E(x31411,x31412) % 186.01/186.05 [3142]~P64(x31421)+P64(x31422)+~E(x31421,x31422) % 186.01/186.05 [3143]~P124(x31431)+P124(x31432)+~E(x31431,x31432) % 186.01/186.05 % 186.01/186.05 %------------------------------------------- % 186.12/186.10 cnf(10489,plain, % 186.12/186.10 (~E(f335(a119,x104891),x104891)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10499,plain, % 186.12/186.10 (~E(f335(a119,x104991),x104991)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10512,plain, % 186.12/186.10 (~E(f335(a119,x105121),x105121)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10517,plain, % 186.12/186.10 (~P1(f335(f335(f179(x105171),f120(x105171)),x105172))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10520,plain, % 186.12/186.10 (~P1(f335(f335(f179(x105201),f120(x105201)),x105202))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10523,plain, % 186.12/186.10 (~E(f335(a119,x105231),x105231)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10526,plain, % 186.12/186.10 (~E(f335(a119,x105261),x105261)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10529,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x105291),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(10532,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x105321),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(10549,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x105491)),x105491))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(10552,plain, % 186.12/186.10 (~E(f335(f335(f158(x105521),x105522),x105523),x105523)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(10558,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x105581),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(10561,plain, % 186.12/186.10 (E(f335(f292(x105611,x105611),f271(x105611,x105612)),x105612)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(10564,plain, % 186.12/186.10 (E(f335(f292(x105641,x105641),f271(x105641,x105642)),x105642)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(10569,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x105691),x105691))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(10574,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x105741),x105742)),x105742))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(10577,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x105771),x105772)),x105772))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(10598,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x105981),x105981))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(10601,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f51(a927,x106011,x106012)),x106011))), % 186.12/186.10 inference(rename_variables,[],[4007])). % 186.12/186.10 cnf(10622,plain, % 186.12/186.10 (E(f335(f41(a927),f335(f290(a927),x106221)),x106221)), % 186.12/186.10 inference(rename_variables,[],[3444])). % 186.12/186.10 cnf(10630,plain, % 186.12/186.10 (~E(f335(a119,x106301),x106301)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10633,plain, % 186.12/186.10 (~E(f335(a119,x106331),x106331)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10636,plain, % 186.12/186.10 (~E(f335(a119,x106361),x106361)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10641,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x106411),f335(a119,x106411)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10650,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x106501),x106501))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(10657,plain, % 186.12/186.10 (E(f335(f292(x106571,x106571),f271(x106571,x106572)),x106572)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(10660,plain, % 186.12/186.10 (E(f335(f292(x106601,x106601),f271(x106601,x106602)),x106602)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(10677,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x106771),x106771))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(10682,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x106821),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(10685,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x106851,a922)),x106852),f250(f934(x106851,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(10690,plain, % 186.12/186.10 (~P1(f335(f335(f179(x106901),f120(x106901)),x106902))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10719,plain, % 186.12/186.10 (~E(f335(f335(f158(x107191),x107192),x107193),x107193)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(10722,plain, % 186.12/186.10 (~E(f335(a119,x107221),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[4724])). % 186.12/186.10 cnf(10733,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x107331),x107331))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(10738,plain, % 186.12/186.10 (~E(f335(a119,x107381),x107381)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10741,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x107411,f934(x107412,a922))),x107413),x107414))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(10748,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x107481),x107481))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(10761,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x107611),f335(a119,x107611)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10782,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x107821,a922)),x107822),f250(f934(x107821,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(10785,plain, % 186.12/186.10 (~P1(f335(f335(f179(x107851),f120(x107851)),x107852))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10804,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108041),f120(x108041)),x108042))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10811,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108111),f120(x108111)),x108112))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10822,plain, % 186.12/186.10 (~E(f335(a119,x108221),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[4724])). % 186.12/186.10 cnf(10827,plain, % 186.12/186.10 (P1(f335(f335(f337(x108271),x108272),f250(f934(x108271,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(10834,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108341),f120(x108341)),x108342))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10839,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x108391),f335(a119,x108391)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10842,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108421),f120(x108421)),x108422))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10845,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108451),f120(x108451)),x108452))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10848,plain, % 186.12/186.10 (~P1(f335(f68(x108481,x108482,f195(f934(x108481,a922))),x108483))), % 186.12/186.10 inference(rename_variables,[],[4796])). % 186.12/186.10 cnf(10851,plain, % 186.12/186.10 (~P1(f335(f68(x108511,x108512,f195(f934(x108511,a922))),x108513))), % 186.12/186.10 inference(rename_variables,[],[4796])). % 186.12/186.10 cnf(10854,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x108541,f934(x108542,a922))),x108543),x108544))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(10857,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x108571),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(10862,plain, % 186.12/186.10 (~P1(f335(f335(f179(x108621),f120(x108621)),x108622))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(10873,plain, % 186.12/186.10 (~E(f335(a119,x108731),x108731)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(10898,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x108981),x108981))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(10901,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x109011),f335(f335(f87(a927),x109011),x109011)))), % 186.12/186.10 inference(rename_variables,[],[3813])). % 186.12/186.10 cnf(10904,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x109041),f335(f335(f87(a927),x109041),x109041)))), % 186.12/186.10 inference(rename_variables,[],[3813])). % 186.12/186.10 cnf(10907,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x109071),f335(a119,f335(f335(f86(a927),x109072),x109071))))), % 186.12/186.10 inference(rename_variables,[],[4000])). % 186.12/186.10 cnf(10912,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x109121),f335(a119,x109121)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10915,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x109151),f335(a119,x109151)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10918,plain, % 186.12/186.10 (P1(f335(f335(f337(x109181),x109182),f250(f934(x109181,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(10937,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x109371)),x109371))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(10940,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x109401)),x109401))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(10943,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x109431),x109432)),x109432))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(10946,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x109461),x109462)),x109462))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(10949,plain, % 186.12/186.10 (P1(f335(f250(f934(x109491,a922)),x109492))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(10952,plain, % 186.12/186.10 (E(f335(f41(a927),f335(f290(a927),x109521)),x109521)), % 186.12/186.10 inference(rename_variables,[],[3444])). % 186.12/186.10 cnf(10955,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x109551),f335(a119,x109551)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(10962,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x109621),x109621))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(10967,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x109671),x109671))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(10976,plain, % 186.12/186.10 (E(f335(f292(x109761,x109761),f271(x109761,x109762)),x109762)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(10979,plain, % 186.12/186.10 (P1(f335(f250(f934(x109791,a922)),x109792))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(10982,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x109821))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(10985,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x109851,a922)),f195(f934(x109851,a922))),x109852))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(10988,plain, % 186.12/186.10 (P1(f335(f250(f934(x109881,a922)),x109882))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(10991,plain, % 186.12/186.10 (P1(f335(f250(f934(x109911,a922)),x109912))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(10994,plain, % 186.12/186.10 (P1(f335(f250(f934(x109941,a922)),x109942))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(10997,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x109971),f335(f335(f87(a927),x109971),x109971)))), % 186.12/186.10 inference(rename_variables,[],[3813])). % 186.12/186.10 cnf(11039,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x110391),x110391))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11050,plain, % 186.12/186.10 (~P1(f335(f335(f179(x110501),f120(x110501)),x110502))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(11059,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x110591),f335(a119,x110591)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(11062,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x110621),x110621))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(11067,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x110671),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11082,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x110821),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11085,plain, % 186.12/186.10 (~P1(f335(f335(f244(f934(x110851,a922)),x110852),f195(f934(x110851,a922))))), % 186.12/186.10 inference(rename_variables,[],[4794])). % 186.12/186.10 cnf(11088,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x110881),x110881))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11091,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x110911),x110911))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11106,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x111061),x111061))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(11115,plain, % 186.12/186.10 (~P1(f335(f335(f337(x111151),x111152),f195(f934(x111151,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11122,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x111221),x111221))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11125,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x111251,a922)),f335(f318(x111252,x111251,x111253),f335(f319(x111252,x111251,x111253),x111254))),x111254))), % 186.12/186.10 inference(rename_variables,[],[4429])). % 186.12/186.10 cnf(11134,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x111341,a922)),f335(f179(x111341),f335(f143(x111341,x111342),x111343))),f335(f179(x111341),x111343)))), % 186.12/186.10 inference(rename_variables,[],[4199])). % 186.12/186.10 cnf(11137,plain, % 186.12/186.10 (E(f335(f318(x111371,x111371,f5(x111371)),x111372),x111372)), % 186.12/186.10 inference(rename_variables,[],[3605])). % 186.12/186.10 cnf(11142,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x111421))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(11145,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x111451),x111451))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11148,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x111481),x111481))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(11157,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x111571),x111571))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(11168,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x111681),f335(f335(f87(a927),x111681),x111681)))), % 186.12/186.10 inference(rename_variables,[],[3813])). % 186.12/186.10 cnf(11174,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x111741),f335(a119,f335(f335(f86(a927),x111742),x111741))))), % 186.12/186.10 inference(rename_variables,[],[4000])). % 186.12/186.10 cnf(11181,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x111811),x111811))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11184,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x111841),x111841))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(11187,plain, % 186.12/186.10 (~E(f335(a119,x111871),x111871)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11192,plain, % 186.12/186.10 (P1(f335(f335(f337(x111921),x111922),f250(f934(x111921,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11197,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x111971),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11212,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x112121))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(11219,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x112191),x112191))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11228,plain, % 186.12/186.10 (~P1(f335(f335(f337(x112281),x112282),f195(f934(x112281,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11236,plain, % 186.12/186.10 (P1(f335(f335(f337(x112361),x112362),f250(f934(x112361,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11239,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x112391),f928(x112391))),f335(f335(f260(f928(x112391),f928(x112391)),x112392),f120(x112391))),f152(x112391,x112393)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11249,plain, % 186.12/186.10 (~P1(f335(f335(f337(x112491),x112492),f195(f934(x112491,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11252,plain, % 186.12/186.10 (~P1(f335(f335(f337(x112521),x112522),f195(f934(x112521,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11255,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x112551,a922)),x112552),f335(f335(f317(x112551),x112553),x112552)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(11258,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x112581),x112581))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(11261,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x112611,a922)),x112612),f335(f335(f317(x112611),x112613),x112612)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(11264,plain, % 186.12/186.10 (E(f335(f318(x112641,x112641,f5(x112641)),x112642),x112642)), % 186.12/186.10 inference(rename_variables,[],[3605])). % 186.12/186.10 cnf(11281,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x112811,a922)),x112812),f335(f335(f317(x112811),x112813),x112812)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(11294,plain, % 186.12/186.10 (~E(f335(a119,x112941),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[4724])). % 186.12/186.10 cnf(11297,plain, % 186.12/186.10 (~P1(f335(f335(f179(x112971),f120(x112971)),x112972))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(11310,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x113101),f335(a119,x113101)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(11320,plain, % 186.12/186.10 (~E(f335(f318(x113201,f934(x113201,a922),x113202),x113203),f335(f316(x113201),x113203))), % 186.12/186.10 inference(rename_variables,[],[4784])). % 186.12/186.10 cnf(11323,plain, % 186.12/186.10 (~P1(f335(f335(f337(x113231),x113232),f195(f934(x113231,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11326,plain, % 186.12/186.10 (~P1(f335(f335(f337(x113261),x113262),f195(f934(x113261,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11329,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x113291,x113291)),f335(f335(f260(x113291,x113291),x113292),x113293)),f160(x113291,f120(f934(x113291,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11332,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x113321,x113321)),f335(f335(f260(x113321,x113321),x113322),x113323)),f160(x113321,f120(f934(x113321,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11337,plain, % 186.12/186.10 (~P1(f335(f335(f337(x113371),x113372),f195(f934(x113371,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11340,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x113401,x113401)),f335(f335(f260(x113401,x113401),x113402),x113402)),f315(x113401,x113403)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(11343,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x113431,a922)),f335(f179(x113431),f183(x113431,x113432,x113433))),f335(f179(x113431),x113432)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(11346,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x113461,a922)),x113462),f250(f934(x113461,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(11362,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x113621,a922)),f195(f934(x113621,a922))),x113622))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(11373,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x113731),f928(x113731))),f335(f335(f260(f928(x113731),f928(x113731)),x113732),f120(x113731))),f154(x113731,x113733)))), % 186.12/186.10 inference(rename_variables,[],[4803])). % 186.12/186.10 cnf(11384,plain, % 186.12/186.10 (~E(f335(a119,x113841),x113841)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11387,plain, % 186.12/186.10 (~E(f335(a119,x113871),x113871)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11394,plain, % 186.12/186.10 (~E(f335(a119,x113941),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[4724])). % 186.12/186.10 cnf(11399,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x113991,a922)),x113992),x113992))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(11406,plain, % 186.12/186.10 (~E(f335(a119,x114061),x114061)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11409,plain, % 186.12/186.10 (~E(f335(a119,x114091),x114091)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11414,plain, % 186.12/186.10 (P26(x114141,x114141,f5(x114141),x114142)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(11419,plain, % 186.12/186.10 (~E(f335(f318(x114191,f934(x114191,a922),x114192),x114193),f335(f316(x114191),x114193))), % 186.12/186.10 inference(rename_variables,[],[4784])). % 186.12/186.10 cnf(11424,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x114241,a922)),x114242),f250(f934(x114241,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(11440,plain, % 186.12/186.10 (~P1(f335(f335(f337(x114401),x114402),f195(f934(x114401,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11443,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x114431)),x114431))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(11448,plain, % 186.12/186.10 (~P1(f335(f335(f337(x114481),x114482),f195(f934(x114481,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11459,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x114591)),x114591))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(11462,plain, % 186.12/186.10 (~P1(f335(f335(f337(x114621),x114622),f195(f934(x114621,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11475,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x114751,x114751)),f335(f335(f260(x114751,x114751),x114752),x114752)),f315(x114751,x114753)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(11478,plain, % 186.12/186.10 (P1(f335(f335(f337(x114781),x114782),f250(f934(x114781,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11481,plain, % 186.12/186.10 (P1(f335(f335(f337(x114811),x114812),f250(f934(x114811,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11488,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x114881),f928(x114881))),f335(f335(f260(f928(x114881),f928(x114881)),x114882),f120(x114881))),f152(x114881,x114883)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11491,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x114911),f928(x114911))),f335(f335(f260(f928(x114911),f928(x114911)),x114912),f120(x114911))),f154(x114911,x114913)))), % 186.12/186.10 inference(rename_variables,[],[4803])). % 186.12/186.10 cnf(11494,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x114941),f928(x114941))),f335(f335(f260(f928(x114941),f928(x114941)),x114942),f120(x114941))),f164(x114941,x114943)))), % 186.12/186.10 inference(rename_variables,[],[4804])). % 186.12/186.10 cnf(11499,plain, % 186.12/186.10 (~P1(f335(f335(f244(f934(x114991,a922)),x114992),f195(f934(x114991,a922))))), % 186.12/186.10 inference(rename_variables,[],[4794])). % 186.12/186.10 cnf(11502,plain, % 186.12/186.10 (~P1(f335(f335(f337(x115021),x115022),f195(f934(x115021,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11509,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115091,a922)),x115092),f250(f934(x115091,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(11516,plain, % 186.12/186.10 (~P1(f335(f335(f179(x115161),f120(x115161)),x115162))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(11521,plain, % 186.12/186.10 (~P1(f335(f335(f337(x115211),x115212),f195(f934(x115211,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11524,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x115241,x115241)),f335(f335(f260(x115241,x115241),x115242),x115243)),f160(x115241,f120(f934(x115241,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11527,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115271,a922)),x115272),x115272))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(11530,plain, % 186.12/186.10 (~P1(f335(f335(f337(x115301),x115302),f195(f934(x115301,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11533,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115331,a922)),f195(f934(x115331,a922))),x115332))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(11536,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x115361,x115361)),f335(f335(f260(x115361,x115361),x115362),x115362)),f315(x115361,x115363)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(11547,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x115471),f928(x115471))),f335(f335(f260(f928(x115471),f928(x115471)),x115472),f120(x115471))),f164(x115471,x115473)))), % 186.12/186.10 inference(rename_variables,[],[4804])). % 186.12/186.10 cnf(11554,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x115541),f928(x115541))),f335(f335(f260(f928(x115541),f928(x115541)),f120(x115541)),x115542)),f152(x115541,x115543)))), % 186.12/186.10 inference(rename_variables,[],[4805])). % 186.12/186.10 cnf(11562,plain, % 186.12/186.10 (P1(f335(f335(f337(x115621),x115622),f250(f934(x115621,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11567,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115671,a922)),f195(f934(x115671,a922))),x115672))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(11570,plain, % 186.12/186.10 (~P1(f335(f335(f337(x115701),x115702),f195(f934(x115701,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11573,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115731,a922)),x115732),f250(f934(x115731,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(11578,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x115781,a922)),f195(f934(x115781,a922))),x115782))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(11591,plain, % 186.12/186.10 (P1(f335(f250(f934(x115911,a922)),x115912))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(11599,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x115991),f928(x115991))),f335(f335(f260(f928(x115991),f928(x115991)),x115992),f120(x115991))),f152(x115991,x115993)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11602,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x116021),f928(x116021))),f335(f335(f260(f928(x116021),f928(x116021)),x116022),f120(x116021))),f154(x116021,x116023)))), % 186.12/186.10 inference(rename_variables,[],[4803])). % 186.12/186.10 cnf(11605,plain, % 186.12/186.10 (~E(f335(f335(f158(x116051),x116052),x116053),x116053)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(11608,plain, % 186.12/186.10 (~E(f335(a119,x116081),x116081)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11611,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116111),x116112),f195(f934(x116111,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11616,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116161),x116162),f195(f934(x116161,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11619,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116191),x116192),f195(f934(x116191,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11622,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(f928(x116221),f928(x116221))),f335(f335(f260(f928(x116221),f928(x116221)),x116222),x116222)),f165(x116221,f315(x116221,x116223))))), % 186.12/186.10 inference(rename_variables,[],[4324])). % 186.12/186.10 cnf(11625,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x116251),f928(x116251))),f335(f335(f260(f928(x116251),f928(x116251)),x116252),f120(x116251))),f152(x116251,x116253)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11635,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x116351,x116351)),f335(f335(f260(x116351,x116351),x116352),x116353)),f160(x116351,f120(f934(x116351,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11638,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116381),x116382),f195(f934(x116381,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11641,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116411),x116412),f195(f934(x116411,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11644,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x116441,f934(x116442,a922))),x116443),x116444))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(11647,plain, % 186.12/186.10 (P1(f335(f335(f337(x116471),x116472),f250(f934(x116471,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11650,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x116501),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11655,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x116551,x116551)),f335(f335(f260(x116551,x116551),x116552),x116553)),f160(x116551,f120(f934(x116551,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11664,plain, % 186.12/186.10 (~E(f335(f318(x116641,f934(x116641,a922),x116642),x116643),f335(f316(x116641),x116643))), % 186.12/186.10 inference(rename_variables,[],[4784])). % 186.12/186.10 cnf(11667,plain, % 186.12/186.10 (~E(f335(f318(x116671,f934(x116671,a922),x116672),x116673),f335(f316(x116671),x116673))), % 186.12/186.10 inference(rename_variables,[],[4784])). % 186.12/186.10 cnf(11669,plain, % 186.12/186.10 (E(f335(f335(f260(a927,a927),f667(f315(a927,a325),a325,a927,f335(f335(f260(a927,a927),x116691),f335(a119,x116691)),a927,a927)),f668(f315(a927,a325),a325,a927,f335(f335(f260(a927,a927),x116691),f335(a119,x116691)),a927,a927)),f335(f335(f260(a927,a927),x116691),f335(a119,x116691)))), % 186.12/186.10 inference(scs_inference,[],[3785,4712,10489,10499,10512,10523,10526,10630,10633,10636,10738,10873,11187,11384,11387,11406,11409,4724,10722,10822,11294,3337,3391,3509,10561,10564,10657,10660,3486,4009,3380,3446,3377,3407,3389,4022,3605,11137,3479,4188,4737,10552,10719,4784,11320,11419,11664,3652,3444,10622,4331,4190,11340,11475,4802,11239,11488,11599,4803,11373,11491,4804,11494,4805,11554,4806,3464,3745,3914,3849,4066,3616,10641,10761,10839,10912,10915,10955,11059,11310,4002,3532,4777,10529,10532,10558,10682,10857,11067,11082,11197,4790,3989,3754,4138,3575,3577,3551,4774,4732,4324,11622,4782,10517,10520,10690,10785,10804,10811,10834,10842,10845,10862,11050,11297,4293,4199,11134,4247,3915,4281,3932,10685,10782,11346,11424,11509,4794,11085,11499,3548,10650,10748,10898,10962,11039,11088,11091,11122,11145,11181,11219,3549,10677,10733,10967,11062,3550,4773,10569,10598,11106,11148,3701,10827,10918,11192,11236,11478,11481,11562,4786,11115,11228,11249,11252,11323,11326,11337,11440,11448,11462,11502,11521,11530,11570,11611,11616,11619,11638,3609,10949,10979,10988,10991,10994,3641,4070,4007,10601,4783,10549,10937,10940,11443,3569,10982,11142,4372,4780,4078,4765,4768,3525,3529,4767,4766,4796,10848,4801,11329,11332,11524,11635,4156,3997,11255,11261,3846,11399,3999,10985,11362,11533,11567,3702,3813,10901,10904,10997,11168,4799,4800,10741,10854,4429,4335,4031,4797,10574,10577,10943,4000,10907,4267,4816,4842,4897,4901,4931,4946,4953,4955,4991,4996,5025,5031,5117,5143,5144,5159,5181,5209,5210,5233,5234,5248,5251,5276,5282,5298,5302,5303,5304,5309,5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169])). % 186.12/186.10 cnf(11672,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x116721),f928(x116721))),f335(f335(f260(f928(x116721),f928(x116721)),x116722),f120(x116721))),f152(x116721,x116723)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11678,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x116781),f928(x116781))),f335(f335(f260(f928(x116781),f928(x116781)),x116782),f120(x116781))),f152(x116781,x116783)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(11681,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116811),x116812),f195(f934(x116811,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11686,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116861),x116862),f195(f934(x116861,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11689,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116891),x116892),f195(f934(x116891,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11692,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116921),x116922),f195(f934(x116921,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11695,plain, % 186.12/186.10 (~P1(f335(f335(f337(x116951),x116952),f195(f934(x116951,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11698,plain, % 186.12/186.10 (P1(f335(f335(f337(x116981),f335(x116982,x116983)),f335(f318(x116984,x116981,x116982),f250(f934(x116984,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(11701,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(x117011,x117011)),f335(f335(f260(x117011,x117011),x117012),x117013)),f160(x117011,f120(f934(x117011,a927)))))), % 186.12/186.10 inference(rename_variables,[],[4801])). % 186.12/186.10 cnf(11709,plain, % 186.12/186.10 (E(f121(x117091,f120(x117091)),f120(x117091))), % 186.12/186.10 inference(rename_variables,[],[3391])). % 186.12/186.10 cnf(11712,plain, % 186.12/186.10 (~E(f335(a119,x117121),x117121)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11719,plain, % 186.12/186.10 (~E(f335(a119,x117191),x117191)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11724,plain, % 186.12/186.10 (E(f335(f292(x117241,x117241),f271(x117241,x117242)),x117242)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11727,plain, % 186.12/186.10 (E(f335(f292(x117271,x117271),f271(x117271,x117272)),x117272)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11733,plain, % 186.12/186.10 (~E(f335(a119,x117331),x117331)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11738,plain, % 186.12/186.10 (~E(f335(f335(f86(a1),x117381),x117381),a104)), % 186.12/186.10 inference(rename_variables,[],[4735])). % 186.12/186.10 cnf(11745,plain, % 186.12/186.10 (E(f335(f335(f23(a927),f2(a927)),x117451),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[3465])). % 186.12/186.10 cnf(11748,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x117481),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11755,plain, % 186.12/186.10 (E(f335(f335(f86(a1),f335(f335(f87(a1),x117551),f335(f335(f42(a1),x117552),x117551))),f51(a1,x117552,x117551)),x117552)), % 186.12/186.10 inference(rename_variables,[],[4103])). % 186.12/186.10 cnf(11779,plain, % 186.12/186.10 (~E(f335(a119,x117791),x117791)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11782,plain, % 186.12/186.10 (~E(f335(a119,x117821),x117821)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11808,plain, % 186.12/186.10 (~P1(f335(f335(f179(x118081),f120(x118081)),x118082))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(11814,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),f2(a927)),f335(a119,x118141)))), % 186.12/186.10 inference(rename_variables,[],[3628])). % 186.12/186.10 cnf(11815,plain, % 186.12/186.10 (~E(f335(a119,x118151),x118151)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11818,plain, % 186.12/186.10 (P1(f335(f335(f337(x118181),x118182),f250(f934(x118181,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(11830,plain, % 186.12/186.10 (~E(f335(a119,x118301),x118301)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11833,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x118331),x118331))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(11840,plain, % 186.12/186.10 (P1(f335(f72(x118401,x118402,x118403,x118404,f195(f934(x118401,a922))),x118404))), % 186.12/186.10 inference(rename_variables,[],[4468])). % 186.12/186.10 cnf(11841,plain, % 186.12/186.10 (E(f335(f292(x118411,x118411),f271(x118411,x118412)),x118412)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11854,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x118541),x118542)),x118542))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(11857,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x118571)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(11871,plain, % 186.12/186.10 (~E(f335(f335(f108(a927),f335(a119,x118711)),x118711),f335(a119,x118711))), % 186.12/186.10 inference(scs_inference,[],[3785,4712,10489,10499,10512,10523,10526,10630,10633,10636,10738,10873,11187,11384,11387,11406,11409,11608,11712,11719,11733,11779,11782,11815,3469,4724,10722,10822,11294,3156,3163,3167,3168,3174,3182,3185,3189,3205,3220,3241,3242,3247,3254,3298,3299,3301,3317,3321,3337,4708,3391,11709,3509,10561,10564,10657,10660,10976,11724,11727,3486,4009,3380,4103,11755,3446,3377,3407,3389,4022,3605,11137,3479,4188,4737,10552,10719,4784,11320,11419,11664,11667,3652,3443,3444,10622,10952,3358,3465,11745,4331,4190,11340,11475,11536,4802,11239,11488,11599,11625,11672,11678,4803,11373,11491,11602,4804,11494,4805,11554,4806,3464,3745,3914,4735,3849,4066,3616,10641,10761,10839,10912,10915,10955,11059,11310,4002,3532,3628,4777,10529,10532,10558,10682,10857,11067,11082,11197,11650,11748,4790,3989,3754,4138,3575,3577,3551,4774,4732,3738,4791,4324,11622,3872,4782,10517,10520,10690,10785,10804,10811,10834,10842,10845,10862,11050,11297,11516,4293,4199,11134,4247,3915,4281,3932,10685,10782,11346,11424,11509,4794,11085,11499,3548,10650,10748,10898,10962,11039,11088,11091,11122,11145,11181,11219,3549,10677,10733,10967,11062,11184,3550,4773,10569,10598,11106,11148,3701,10827,10918,11192,11236,11478,11481,11562,11647,4786,11115,11228,11249,11252,11323,11326,11337,11440,11448,11462,11502,11521,11530,11570,11611,11616,11619,11638,11641,11681,11686,11689,11692,3609,10949,10979,10988,10991,10994,3641,4070,4007,10601,4783,10549,10937,10940,11443,11459,3569,10982,11142,4372,4780,4078,4765,4768,3525,3529,4767,4766,4468,4796,10848,10851,4801,11329,11332,11524,11635,11655,4156,3997,11255,11261,3846,11399,3999,10985,11362,11533,11567,3702,3813,10901,10904,10997,11168,4799,4800,10741,10854,4429,4335,4031,4797,10574,10577,10943,10946,4000,10907,4267,4816,4842,4897,4901,4931,4946,4953,4955,4991,4996,5025,5031,5117,5143,5144,5159,5181,5209,5210,5233,5234,5248,5251,5276,5282,5298,5302,5303,5304,5309,5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169,10179,10180,10200,10205,10300,10389,10390,10391,10392,10455,10473,2,8,9,4829,4830,4848,4890,4891,4893,4916,4924,4925,4935,4980,4982,5030,5160,5161,5175,5198,5254,5255,5261,5262,5264,5266,5275,5278,5279,5287,5300,5301,5307,5328,5329,5347,5352,5353,5354,5355,5359,5367,5370,5377,5432,5437,5438,5443,5449,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607])). % 186.12/186.10 cnf(11880,plain, % 186.12/186.10 (E(f335(f292(x118801,x118801),f271(x118801,x118802)),x118802)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11885,plain, % 186.12/186.10 (E(f335(f292(x118851,x118851),f271(x118851,x118852)),x118852)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11888,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x118881)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(11893,plain, % 186.12/186.10 (~E(f335(a119,x118931),x118931)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11902,plain, % 186.12/186.10 (~P1(f335(f335(f179(x119021),f120(x119021)),x119022))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(11923,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x119231)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(11926,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x119261),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(11927,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x119271),f335(a119,x119271)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(11930,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x119301)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(11933,plain, % 186.12/186.10 (~P1(f335(f335(f337(x119331),x119332),f195(f934(x119331,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(11934,plain, % 186.12/186.10 (P1(f335(f335(f337(f934(x119341,a922)),x119342),f335(f316(x119341),x119342)))), % 186.12/186.10 inference(rename_variables,[],[3915])). % 186.12/186.10 cnf(11949,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x119491)),x119491))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(11950,plain, % 186.12/186.10 (~E(f335(a119,x119501),x119501)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11960,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x119601),x119602)),x119601))), % 186.12/186.10 inference(rename_variables,[],[4798])). % 186.12/186.10 cnf(11963,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x119631)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(11966,plain, % 186.12/186.10 (~E(f335(a119,x119661),x119661)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(11979,plain, % 186.12/186.10 (P1(f335(f335(f337(x119791),x119792),f335(f335(f317(x119791),x119792),x119793)))), % 186.12/186.10 inference(rename_variables,[],[3862])). % 186.12/186.10 cnf(11980,plain, % 186.12/186.10 (~P1(f335(f335(f243(a1),f2(a1)),f335(f85(a1),f335(f107(a1),f335(a119,x119801)))))), % 186.12/186.10 inference(rename_variables,[],[4799])). % 186.12/186.10 cnf(11983,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),f335(f335(f23(a927),x119831),x119832)),f335(a119,x119831)))), % 186.12/186.10 inference(rename_variables,[],[4002])). % 186.12/186.10 cnf(11986,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f51(a927,x119861,x119862)),x119861))), % 186.12/186.10 inference(rename_variables,[],[4007])). % 186.12/186.10 cnf(11992,plain, % 186.12/186.10 (E(f335(f292(x119921,x119921),f271(x119921,x119922)),x119922)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(11997,plain, % 186.12/186.10 (E(f335(f335(f141(x119971),f176(x119971,x119972,x119973)),f176(x119971,x119974,x119973)),f335(f335(f141(x119971),f176(x119971,x119974,x119973)),f176(x119971,x119972,x119973)))), % 186.12/186.10 inference(rename_variables,[],[4117])). % 186.12/186.10 cnf(12002,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x120021)),x120021))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12011,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x120111),x120111))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12014,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f51(a927,x120141,x120142)),x120141))), % 186.12/186.10 inference(rename_variables,[],[4007])). % 186.12/186.10 cnf(12015,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x120151))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(12017,plain, % 186.12/186.10 (~P1(f335(f335(f243(a1),f84(a1)),f2(a1)))), % 186.12/186.10 inference(scs_inference,[],[3785,4712,10489,10499,10512,10523,10526,10630,10633,10636,10738,10873,11187,11384,11387,11406,11409,11608,11712,11719,11733,11779,11782,11815,11830,11893,11950,3469,4724,10722,10822,11294,3155,3156,3163,3164,3167,3168,3174,3182,3183,3185,3189,3192,3193,3205,3220,3241,3242,3247,3254,3298,3299,3301,3315,3317,3321,3337,4708,4117,11997,3391,11709,3509,10561,10564,10657,10660,10976,11724,11727,11841,11880,11885,3486,4009,3380,3747,4103,11755,3446,3377,3407,3402,3389,3390,4022,3605,11137,3479,4188,4737,10552,10719,4784,11320,11419,11664,11667,3652,3443,3444,10622,10952,3706,3358,3465,11745,4331,4190,11340,11475,11536,4802,11239,11488,11599,11625,11672,11678,4803,11373,11491,11602,4804,11494,4805,11554,4806,3464,3745,3914,4604,4605,4735,3849,4066,3616,10641,10761,10839,10912,10915,10955,11059,11310,11927,4002,3532,3628,4777,10529,10532,10558,10682,10857,11067,11082,11197,11650,11748,4790,11857,11888,11923,11930,3989,3754,4138,3575,3577,3551,4774,4732,3738,4791,4324,11622,3872,4782,10517,10520,10690,10785,10804,10811,10834,10842,10845,10862,11050,11297,11516,11808,4293,4199,11134,4247,3915,4281,3932,10685,10782,11346,11424,11509,4794,11085,11499,3548,10650,10748,10898,10962,11039,11088,11091,11122,11145,11181,11219,3549,10677,10733,10967,11062,11184,3550,4773,10569,10598,11106,11148,11157,3701,10827,10918,11192,11236,11478,11481,11562,11647,4786,11115,11228,11249,11252,11323,11326,11337,11440,11448,11462,11502,11521,11530,11570,11611,11616,11619,11638,11641,11681,11686,11689,11692,11695,3609,10949,10979,10988,10991,10994,3648,3641,4070,4007,10601,11986,4783,10549,10937,10940,11443,11459,11949,3569,10982,11142,11212,4372,4780,4078,4765,4768,3525,3529,4767,4766,3862,4468,4796,10848,10851,4801,11329,11332,11524,11635,11655,4156,3997,11255,11261,3846,11399,3999,10985,11362,11533,11567,3702,3813,10901,10904,10997,11168,4799,4800,10741,10854,4429,4335,4031,4797,10574,10577,10943,10946,4798,4000,10907,4267,4816,4842,4897,4901,4931,4946,4953,4955,4991,4996,5025,5031,5117,5143,5144,5159,5181,5209,5210,5233,5234,5248,5251,5276,5282,5298,5302,5303,5304,5309,5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169,10179,10180,10200,10205,10300,10389,10390,10391,10392,10455,10473,2,8,9,4829,4830,4848,4890,4891,4893,4916,4924,4925,4935,4980,4982,5030,5160,5161,5175,5198,5254,5255,5261,5262,5264,5266,5275,5278,5279,5287,5300,5301,5307,5328,5329,5347,5352,5353,5354,5355,5359,5367,5370,5377,5432,5437,5438,5443,5449,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5697,5702,5704,5740,5742,5743,5745,5746,5748,5749,5751,5760,5765,5766,5767,5769,5771,5772,5773,5774,5775,5776,5785,5795,5798,5809,5825,5826,5829,5839,5841,5842,5843,5870,5880,5895,5896,5905,5906,5908,5910,5915,5950,5955,5957,6016,6051,6052])). % 186.12/186.10 cnf(12032,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x120321),x120321))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12035,plain, % 186.12/186.10 (P1(f335(f335(f337(x120351),f335(x120352,x120353)),f335(f318(x120354,x120351,x120352),f250(f934(x120354,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(12036,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x120361)),x120361))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12039,plain, % 186.12/186.10 (P1(f335(f335(f337(x120391),f335(x120392,x120393)),f335(f318(x120394,x120391,x120392),f250(f934(x120394,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(12040,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x120401),x120402)),x120402))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(12045,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x120451),x120452)),x120451))), % 186.12/186.10 inference(rename_variables,[],[4798])). % 186.12/186.10 cnf(12048,plain, % 186.12/186.10 (~P1(f335(f335(f179(x120481),f120(x120481)),x120482))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(12051,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x120511),x120511))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12057,plain, % 186.12/186.10 (~P36(x120571,x120572,f120(x120571))), % 186.12/186.10 inference(rename_variables,[],[4748])). % 186.12/186.10 cnf(12060,plain, % 186.12/186.10 (P1(f335(f335(f337(x120601),x120602),f250(f934(x120601,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(12061,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x120611)),x120611))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12074,plain, % 186.12/186.10 (~P1(f335(f335(f337(x120741),x120742),f195(f934(x120741,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12077,plain, % 186.12/186.10 (E(f335(f335(f16(x120771,x120772),x120773),x120774),x120773)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(12080,plain, % 186.12/186.10 (E(f335(f335(f16(x120801,x120802),x120803),x120804),x120803)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(12095,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x120951),x120951))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12098,plain, % 186.12/186.10 (P1(f335(f67(x120981),f335(f179(x120981),x120982)))), % 186.12/186.10 inference(rename_variables,[],[3588])). % 186.12/186.10 cnf(12101,plain, % 186.12/186.10 (P1(f335(f67(x121011),f335(f179(x121011),x121012)))), % 186.12/186.10 inference(rename_variables,[],[3588])). % 186.12/186.10 cnf(12104,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),f335(f85(a1),f335(f107(a1),x121041))),f335(f107(a1),x121042)))), % 186.12/186.10 inference(rename_variables,[],[4032])). % 186.12/186.10 cnf(12107,plain, % 186.12/186.10 (~P1(f335(f335(f337(x121071),x121072),f195(f934(x121071,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12128,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x121281),x121281))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12131,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x121311),x121311))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12140,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x121401),x121401))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12143,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x121431),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12148,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x121481),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12157,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x121571))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(12158,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x121581)),x121581))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12161,plain, % 186.12/186.10 (~P1(f335(f335(f179(x121611),f120(x121611)),x121612))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(12164,plain, % 186.12/186.10 (~P1(f335(f335(f179(x121641),f120(x121641)),x121642))), % 186.12/186.10 inference(rename_variables,[],[4782])). % 186.12/186.10 cnf(12167,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x121671),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12168,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x121681),f335(a119,x121681)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12187,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x121871)),x121871))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12190,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x121901)),x121901))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12193,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x121931)),x121931))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12196,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x121961)),x121961))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12199,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x121991),x121991))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12202,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x122021),x122021))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12205,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x122051),x122051))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12208,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x122081),x122081))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12225,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x122251),x122251))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12228,plain, % 186.12/186.10 (P26(a927,a927,a119,x122281)), % 186.12/186.10 inference(rename_variables,[],[3753])). % 186.12/186.10 cnf(12231,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x122311),x122311))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12242,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x122421),x122421))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12245,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(f933(f928(x122451),f928(x122451)),a922)),f165(x122451,x122452)),f315(f928(x122451),f164(x122451,x122452))))), % 186.12/186.10 inference(rename_variables,[],[4252])). % 186.12/186.10 cnf(12252,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x122521),f335(a119,x122521)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12255,plain, % 186.12/186.10 (P1(f335(f335(f337(f934(x122551,a922)),x122552),f335(f316(x122551),x122552)))), % 186.12/186.10 inference(rename_variables,[],[3915])). % 186.12/186.10 cnf(12256,plain, % 186.12/186.10 (~E(f335(a119,x122561),x122561)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12261,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x122611),x122611))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12266,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x122661),x122661))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12273,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x122731,x122732)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(12280,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x122801,a922)),x122802),f335(f335(f317(x122801),x122803),x122802)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(12283,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x122831),x122831))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12284,plain, % 186.12/186.10 (~E(f335(a119,x122841),x122841)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12295,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x122951),x122951))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12296,plain, % 186.12/186.10 (~E(f335(a119,x122961),x122961)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12299,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x122991),x122991))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12302,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x123021),x123021))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12305,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x123051),x123051))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12308,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x123081),x123081))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12311,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x123111),x123111))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12314,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123141),x123141))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12317,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123171),x123171))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12318,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x123181),f335(a119,x123181)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12325,plain, % 186.12/186.10 (~E(f335(a119,x123251),x123251)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12330,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123301),x123301))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12331,plain, % 186.12/186.10 (~E(f335(a119,x123311),x123311)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12334,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x123341),x123341))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12351,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x123511),x123511))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(12356,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x123561))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(12370,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123701),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12373,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123731),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12376,plain, % 186.12/186.10 (~P1(f335(f335(f337(x123761),x123762),f195(f934(x123761,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12379,plain, % 186.12/186.10 (~P1(f335(f335(f337(x123791),x123792),f195(f934(x123791,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12382,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123821),x123821))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12385,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123851),x123851))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12388,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123881),x123881))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12391,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x123911),x123911))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12394,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x123941),f335(a119,x123941)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12401,plain, % 186.12/186.10 (P1(f335(f335(f337(f934(x124011,a922)),x124012),f335(f316(x124011),x124012)))), % 186.12/186.10 inference(rename_variables,[],[3915])). % 186.12/186.10 cnf(12406,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124061,a922)),x124062),f335(f335(f317(x124061),x124063),x124062)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(12413,plain, % 186.12/186.10 (~P1(f335(f335(f337(x124131),x124132),f195(f934(x124131,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12422,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124221,a922)),x124222),f250(f934(x124221,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12423,plain, % 186.12/186.10 (~E(f335(a119,x124231),x124231)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12426,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124261,a922)),f335(f179(x124261),f335(f143(x124261,x124262),x124263))),f335(f179(x124261),x124263)))), % 186.12/186.10 inference(rename_variables,[],[4199])). % 186.12/186.10 cnf(12432,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x124321),f335(a119,x124321)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12441,plain, % 186.12/186.10 (E(f335(f292(x124411,x124411),f271(x124411,x124412)),x124412)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12452,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x124521)),x124521))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(12453,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x124531),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12458,plain, % 186.12/186.10 (P1(f335(f67(x124581),f195(f934(x124581,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(12459,plain, % 186.12/186.10 (~P1(f335(f335(f337(x124591),x124592),f195(f934(x124591,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12466,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124661,a922)),f335(f179(x124661),f183(x124661,x124662,x124663))),f335(f179(x124661),x124662)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(12469,plain, % 186.12/186.10 (P26(x124691,x124691,f5(x124691),x124692)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12474,plain, % 186.12/186.10 (P1(f335(f335(f337(f934(x124741,a922)),x124742),f335(f316(x124741),x124742)))), % 186.12/186.10 inference(rename_variables,[],[3915])). % 186.12/186.10 cnf(12481,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x124811),x124811))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12484,plain, % 186.12/186.10 (~P1(f335(f335(f337(x124841),x124842),f195(f934(x124841,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12487,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124871,a922)),x124872),f335(f335(f317(x124871),x124873),x124872)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(12488,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x124881,a922)),x124882),f250(f934(x124881,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12495,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x124951),x124951))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12498,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x124981),x124981))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12501,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x125011),x125011))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12504,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x125041),x125041))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12507,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x125071),f335(a119,x125071)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12510,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x125101),f335(a119,x125101)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12513,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x125131,a922)),x125132),x125132))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12520,plain, % 186.12/186.10 (P1(f335(f335(f337(f934(x125201,a922)),x125202),f335(f316(x125201),x125202)))), % 186.12/186.10 inference(rename_variables,[],[3915])). % 186.12/186.10 cnf(12529,plain, % 186.12/186.10 (~E(f335(a119,x125291),x125291)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12530,plain, % 186.12/186.10 (E(f335(f318(x125301,x125301,f5(x125301)),x125302),x125302)), % 186.12/186.10 inference(rename_variables,[],[3605])). % 186.12/186.10 cnf(12533,plain, % 186.12/186.10 (P33(x125331,x125332,f120(x125331),f120(x125331))), % 186.12/186.10 inference(rename_variables,[],[3794])). % 186.12/186.10 cnf(12536,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x125361,a922)),f335(f179(x125361),f183(x125361,x125362,x125363))),f335(f179(x125361),x125362)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(12537,plain, % 186.12/186.10 (P1(f335(f67(x125371),f335(f179(x125371),x125372)))), % 186.12/186.10 inference(rename_variables,[],[3588])). % 186.12/186.10 cnf(12548,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x125481),x125481))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12551,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x125511),x125511))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12556,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x125561))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(12563,plain, % 186.12/186.10 (P14(a927,f335(f175(a927),f335(f335(f161(f928(x125631),a927),f196(f928(x125631))),f186(x125631,x125632))))), % 186.12/186.10 inference(rename_variables,[],[4113])). % 186.12/186.10 cnf(12566,plain, % 186.12/186.10 (P26(x125661,x125661,f5(x125661),x125662)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12569,plain, % 186.12/186.10 (P26(x125691,x125691,f5(x125691),x125692)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12572,plain, % 186.12/186.10 (P1(f335(f335(f337(f928(x125721)),f120(x125721)),f168(x125721,x125722)))), % 186.12/186.10 inference(rename_variables,[],[3745])). % 186.12/186.10 cnf(12575,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x125751,f934(x125752,a922))),x125753),x125754))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(12580,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x125801),x125801))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12581,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x125811))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(12584,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x125841,f934(x125842,a922))),x125843),x125844))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(12587,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(f933(f928(x125871),f928(x125871)),a922)),f165(x125871,x125872)),f315(f928(x125871),f164(x125871,x125872))))), % 186.12/186.10 inference(rename_variables,[],[4252])). % 186.12/186.10 cnf(12593,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x125931,a922)),f335(f318(x125932,x125931,x125933),f335(f319(x125932,x125931,x125933),x125934))),x125934))), % 186.12/186.10 inference(rename_variables,[],[4429])). % 186.12/186.10 cnf(12596,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x125961,a922)),f335(f179(x125961),f183(x125961,x125962,x125963))),f335(f179(x125961),x125962)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(12597,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x125971,a922)),f335(f179(x125971),f335(f143(x125971,x125972),x125973))),f335(f179(x125971),x125973)))), % 186.12/186.10 inference(rename_variables,[],[4199])). % 186.12/186.10 cnf(12600,plain, % 186.12/186.10 (~P1(f335(f335(f244(f934(x126001,a922)),x126002),f195(f934(x126001,a922))))), % 186.12/186.10 inference(rename_variables,[],[4794])). % 186.12/186.10 cnf(12608,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x126081,a922)),f335(f318(x126082,x126081,x126083),f335(f319(x126082,x126081,x126083),x126084))),x126084))), % 186.12/186.10 inference(rename_variables,[],[4429])). % 186.12/186.10 cnf(12613,plain, % 186.12/186.10 (P1(f335(f335(f337(f928(x126131)),f120(x126131)),f168(x126131,x126132)))), % 186.12/186.10 inference(rename_variables,[],[3745])). % 186.12/186.10 cnf(12616,plain, % 186.12/186.10 (~P1(f335(f335(f337(f933(f928(x126161),f928(x126161))),f335(f335(f260(f928(x126161),f928(x126161)),x126162),f120(x126161))),f152(x126161,x126163)))), % 186.12/186.10 inference(rename_variables,[],[4802])). % 186.12/186.10 cnf(12619,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x126191),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12621,plain, % 186.12/186.10 (~P1(f335(f67(x126211),f250(f934(x126211,a922))))), % 186.12/186.10 inference(scs_inference,[],[3785,11414,12469,12566,3794,3802,3519,4747,4748,3417,3420,4746,4712,10489,10499,10512,10523,10526,10630,10633,10636,10738,10873,11187,11384,11387,11406,11409,11608,11712,11719,11733,11779,11782,11815,11830,11893,11950,11966,12256,12284,12296,12325,12331,12423,3753,3469,4724,10722,10822,11294,3155,3156,3159,3160,3163,3164,3166,3167,3168,3170,3174,3176,3182,3183,3185,3189,3192,3193,3205,3208,3220,3226,3241,3242,3247,3254,3298,3299,3301,3306,3310,3315,3317,3321,3337,4708,4117,11997,3391,11709,3509,10561,10564,10657,10660,10976,11724,11727,11841,11880,11885,11992,3486,3495,4009,4317,3380,3747,4103,11755,3446,3377,3407,3402,3389,3390,4022,3427,3605,11137,11264,3479,4188,4737,10552,10719,3539,12077,4784,11320,11419,11664,11667,3652,3443,3444,10622,10952,3706,3358,3465,11745,4331,4190,11340,11475,11536,4802,11239,11488,11599,11625,11672,11678,4803,11373,11491,11602,4804,11494,4805,11554,4806,3464,3745,12572,12613,3914,4604,4605,4735,3849,4066,4113,3731,3992,3616,10641,10761,10839,10912,10915,10955,11059,11310,11927,12168,12252,12318,12394,12432,12507,4002,11983,3532,3628,11814,3812,4777,10529,10532,10558,10682,10857,11067,11082,11197,11650,11748,11926,12143,12148,12167,12370,12373,12453,4790,11857,11888,11923,11930,11963,3989,3754,3755,4138,3575,3577,3551,4774,4732,3738,4791,4324,11622,3872,3588,12098,12101,4782,10517,10520,10690,10785,10804,10811,10834,10842,10845,10862,11050,11297,11516,11808,11902,12048,12161,4293,4252,12245,12587,4199,11134,12426,4247,11343,12466,12536,3915,11934,12255,12401,12474,12520,4281,3932,10685,10782,11346,11424,11509,11573,12422,4794,11085,11499,3548,10650,10748,10898,10962,11039,11088,11091,11122,11145,11181,11219,11258,12051,12095,12225,12283,12299,12302,12305,12308,12481,12495,12498,12501,12504,3549,10677,10733,10967,11062,11184,11833,12128,12131,12140,12231,12242,12261,12266,12311,12334,3550,3624,12458,4773,10569,10598,11106,11148,11157,12011,12032,12199,12202,12205,12208,12295,12314,12317,12330,12382,12385,12388,12391,12548,3701,10827,10918,11192,11236,11478,11481,11562,11647,11818,12060,4786,11115,11228,11249,11252,11323,11326,11337,11440,11448,11462,11502,11521,11530,11570,11611,11616,11619,11638,11641,11681,11686,11689,11692,11695,11933,12074,12107,12376,12379,12413,12459,3609,10949,10979,10988,10991,10994,3648,3641,4070,4007,10601,11986,12014,4783,10549,10937,10940,11443,11459,11949,12002,12036,12061,12158,12187,12190,12193,12196,12452,3569,10982,11142,11212,12015,12157,12356,12556,4032,4372,4780,4044,4078,4765,4768,3525,3529,4767,4766,3862,4468,4796,10848,10851,4801,11329,11332,11524,11635,11655,4156,11698,12035,3997,11255,11261,11281,12280,12406,3846,11399,11527,12513,3999,10985,11362,11533,11567,3702,3813,10901,10904,10997,11168,4799,11980,4800,10741,10854,11644,12575,4429,11125,12593,4335,4031,3975,4797,10574,10577,10943,10946,11854,4798,11960,4000,10907,4267,4816,4842,4897,4901,4931,4946,4953,4955,4991,4996,5025,5031,5117,5143,5144,5159,5181,5209,5210,5233,5234,5248,5251,5276,5282,5298,5302,5303,5304,5309,5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169,10179,10180,10200,10205,10300,10389,10390,10391,10392,10455,10473,2,8,9,4829,4830,4848,4890,4891,4893,4916,4924,4925,4935,4980,4982,5030,5160,5161,5175,5198,5254,5255,5261,5262,5264,5266,5275,5278,5279,5287,5300,5301,5307,5328,5329,5347,5352,5353,5354,5355,5359,5367,5370,5377,5432,5437,5438,5443,5449,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5697,5702,5704,5740,5742,5743,5745,5746,5748,5749,5751,5760,5765,5766,5767,5769,5771,5772,5773,5774,5775,5776,5785,5795,5798,5809,5825,5826,5829,5839,5841,5842,5843,5870,5880,5895,5896,5905,5906,5908,5910,5915,5950,5955,5957,6016,6051,6052,6057,6063,6066,6067,6068,6069,6088,6092,6093,6102,6124,6153,6172,6176,6177,6179,6202,6206,6209,6210,6211,6227,6238,6239,6270,6271,6275,6296,6299,6302,6323,6324,6352,6355,6363,6372,6374,6382,6386,6394,6395,6396,6397,6427,6444,6495,6532,6534,6555,6556,6563,6567,6568,6571,6585,6600,6621,6622,6625,6628,6637,6652,6673,6679,6681,6696,6697,6700,6701,6703,6705,6706,6707,6709,6711,6713,6719,6720,6722,6723,6729,6731,6773,6779,6795,6797,6798,6799,6832,6837,6839,6844,6845,6855,6859,6871,6894,6895,6897,6898,6909,6913,6916,6934,6937,6957,6986,6987,6988,6994,7008,7027,7029,7031,7033,7038,7044,7046,7060,7065,7066,7101,7102,7103,7117,7118,7120,7121,7139,7141,7156,7182,7206,7217,7219,7221,7223,7224,7255,7256,7260,7261,7268,7269,7271,7273,7295,7304,7305,7316,7326,7366,7376,7380,7387,7398,7403,7405,7412,7420,7433,7450,7471,7473,7492,7549,7550,7551,7553,7555,7559,7560,7565,7626,7655,7670,7686,7717,7720,7742,7764,7782,7785,7786,7796,7816,7818,7820,7822,7823,7824,7849,7875,7876,7907,7909,7910,7911,7916,7937,7954,7959,7965,7967,7975,7987,7988,7990,8011,8017,8038,8104,8105,8106,8153,8159,8160,8184,8185,8202,8203,8204,8261,8262,8291,8321,8330,8341,8354,8383,8387,8393])). % 186.12/186.10 cnf(12622,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x126221,a922)),x126222),x126222))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12625,plain, % 186.12/186.10 (~P1(f335(f335(f337(x126251),x126252),f195(f934(x126251,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12628,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x126281,f934(x126282,a922))),x126283),x126284))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(12631,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x126311,a922)),f335(f318(x126312,x126311,x126313),f335(f319(x126312,x126311,x126313),x126314))),x126314))), % 186.12/186.10 inference(rename_variables,[],[4429])). % 186.12/186.10 cnf(12632,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x126321,a922)),x126322),x126322))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12637,plain, % 186.12/186.10 (E(f335(f292(x126371,x126371),f271(x126371,x126372)),x126372)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12640,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x126401,a922)),f335(f179(x126401),f183(x126401,x126402,x126403))),f335(f179(x126401),x126402)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(12641,plain, % 186.12/186.10 (P1(f335(f67(x126411),f335(f179(x126411),x126412)))), % 186.12/186.10 inference(rename_variables,[],[3588])). % 186.12/186.10 cnf(12644,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x126441),x126441))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12647,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x126471),x126471))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12650,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x126501),x126501))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12661,plain, % 186.12/186.10 (P26(x126611,x126611,f5(x126611),x126612)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12669,plain, % 186.12/186.10 (~P1(f335(f335(f337(x126691),x126692),f195(f934(x126691,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12672,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x126721,x126721)),f335(f335(f260(x126721,x126721),x126722),x126722)),f315(x126721,x126723)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(12675,plain, % 186.12/186.10 (~P1(f335(f335(f337(x126751),x126752),f195(f934(x126751,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12678,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x126781,x126781)),f335(f335(f260(x126781,x126781),x126782),x126782)),f315(x126781,x126783)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(12688,plain, % 186.12/186.10 (~E(f335(f335(f158(x126881),x126882),x126883),x126883)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(12695,plain, % 186.12/186.10 (P1(f335(f335(f337(x126951),x126952),f250(f934(x126951,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(12696,plain, % 186.12/186.10 (~E(f335(a119,x126961),x126961)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12699,plain, % 186.12/186.10 (P1(f335(f335(f337(f928(x126991)),f120(x126991)),f168(x126991,x126992)))), % 186.12/186.10 inference(rename_variables,[],[3745])). % 186.12/186.10 cnf(12700,plain, % 186.12/186.10 (~E(f335(f335(f158(x127001),x127002),x127003),f120(x127001))), % 186.12/186.10 inference(rename_variables,[],[4744])). % 186.12/186.10 cnf(12703,plain, % 186.12/186.10 (P26(x127031,x127031,f5(x127031),x127032)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12706,plain, % 186.12/186.10 (P1(f335(f335(f337(x127061),f335(x127062,x127063)),f335(f318(x127064,x127061,x127062),f250(f934(x127064,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(12707,plain, % 186.12/186.10 (P26(x127071,x127071,f5(x127071),x127072)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12710,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127101,a922)),f195(f934(x127101,a922))),x127102))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(12711,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127111,a922)),x127112),x127112))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12714,plain, % 186.12/186.10 (P1(f335(f335(f337(x127141),f335(x127142,x127143)),f335(f318(x127144,x127141,x127142),f250(f934(x127144,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(12715,plain, % 186.12/186.10 (P26(x127151,x127151,f5(x127151),x127152)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12718,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(f928(x127181),f928(x127181))),f335(f335(f260(f928(x127181),f928(x127181)),f120(x127181)),f120(x127181))),f165(x127181,x127182)))), % 186.12/186.10 inference(rename_variables,[],[4331])). % 186.12/186.10 cnf(12722,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x127221),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(12728,plain, % 186.12/186.10 (E(f335(f335(f141(x127281),x127282),f120(x127281)),x127282)), % 186.12/186.10 inference(rename_variables,[],[3480])). % 186.12/186.10 cnf(12729,plain, % 186.12/186.10 (~E(f335(f335(f158(x127291),x127292),x127293),x127293)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(12732,plain, % 186.12/186.10 (E(f335(f335(f141(x127321),x127322),f120(x127321)),x127322)), % 186.12/186.10 inference(rename_variables,[],[3480])). % 186.12/186.10 cnf(12733,plain, % 186.12/186.10 (~E(f335(f335(f158(x127331),x127332),x127333),x127333)), % 186.12/186.10 inference(rename_variables,[],[4737])). % 186.12/186.10 cnf(12736,plain, % 186.12/186.10 (E(f335(f335(f141(x127361),x127362),f120(x127361)),x127362)), % 186.12/186.10 inference(rename_variables,[],[3480])). % 186.12/186.10 cnf(12743,plain, % 186.12/186.10 (P53(x127431,f271(x127431,x127432))), % 186.12/186.10 inference(rename_variables,[],[3421])). % 186.12/186.10 cnf(12746,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127461,a922)),f335(f179(x127461),f335(f143(x127461,x127462),x127463))),f335(f179(x127461),x127463)))), % 186.12/186.10 inference(rename_variables,[],[4199])). % 186.12/186.10 cnf(12747,plain, % 186.12/186.10 (E(f335(f318(x127471,x127471,f5(x127471)),x127472),x127472)), % 186.12/186.10 inference(rename_variables,[],[3605])). % 186.12/186.10 cnf(12752,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127521,a922)),x127522),f250(f934(x127521,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12756,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x127561),x127561))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12757,plain, % 186.12/186.10 (~E(f335(a119,x127571),x127571)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12760,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127601,a922)),f195(f934(x127601,a922))),x127602))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(12763,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x127631),x127631))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12766,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127661,a922)),x127662),x127662))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12771,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127711,a922)),x127712),f335(f335(f317(x127711),x127713),x127712)))), % 186.12/186.10 inference(rename_variables,[],[3997])). % 186.12/186.10 cnf(12774,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x127741,a922)),x127742),x127742))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12775,plain, % 186.12/186.10 (~P1(f335(f335(f337(x127751),x127752),f195(f934(x127751,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12778,plain, % 186.12/186.10 (~P1(f335(f335(f337(x127781),x127782),f195(f934(x127781,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12787,plain, % 186.12/186.10 (P26(x127871,x127871,f5(x127871),x127872)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12790,plain, % 186.12/186.10 (E(f335(f196(f928(x127901)),f176(x127901,x127902,x127903)),x127902)), % 186.12/186.10 inference(rename_variables,[],[3615])). % 186.12/186.10 cnf(12793,plain, % 186.12/186.10 (P27(x127931,x127931,f25(x127931),x127932,x127932)), % 186.12/186.10 inference(rename_variables,[],[4214])). % 186.12/186.10 cnf(12796,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x127961),x127961))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12797,plain, % 186.12/186.10 (P1(f335(f250(f934(x127971,a922)),x127972))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(12800,plain, % 186.12/186.10 (~P1(f335(f335(f337(x128001),x128002),f195(f934(x128001,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12803,plain, % 186.12/186.10 (P1(f335(f335(f337(x128031),f335(x128032,x128033)),f335(f318(x128034,x128031,x128032),f250(f934(x128034,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(12804,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x128041,x128041)),f335(f335(f260(x128041,x128041),x128042),x128042)),f315(x128041,x128043)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(12807,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x128071,x128071)),f335(f335(f260(x128071,x128071),x128072),x128072)),f315(x128071,x128073)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(12810,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x128101),x128101))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(12811,plain, % 186.12/186.10 (P1(f335(f250(f934(x128111,a922)),x128112))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(12814,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x128141,a922)),x128142),f250(f934(x128141,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12815,plain, % 186.12/186.10 (P27(x128151,x128151,f25(x128151),x128152,x128152)), % 186.12/186.10 inference(rename_variables,[],[4214])). % 186.12/186.10 cnf(12818,plain, % 186.12/186.10 (P1(f335(f67(x128181),f335(f179(x128181),x128182)))), % 186.12/186.10 inference(rename_variables,[],[3588])). % 186.12/186.10 cnf(12828,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x128281,f934(x128282,a922))),x128283),x128284))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(12831,plain, % 186.12/186.10 (~P1(f335(f335(f195(f934(x128311,f934(x128312,a922))),x128313),x128314))), % 186.12/186.10 inference(rename_variables,[],[4800])). % 186.12/186.10 cnf(12834,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x128341,a922)),x128342),f250(f934(x128341,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12837,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(x128371,x128371)),f335(f335(f260(x128371,x128371),x128372),x128372)),f315(x128371,x128373)))), % 186.12/186.10 inference(rename_variables,[],[4190])). % 186.12/186.10 cnf(12840,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),f335(f335(f86(a927),x128401),x128402)),x128402))), % 186.12/186.10 inference(rename_variables,[],[4797])). % 186.12/186.10 cnf(12841,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x128411),f335(a119,x128411)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(12844,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x128441,a922)),x128442),f250(f934(x128441,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(12847,plain, % 186.12/186.10 (E(f335(f292(x128471,x128471),f271(x128471,x128472)),x128472)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12858,plain, % 186.12/186.10 (~P1(f335(f335(f337(x128581),x128582),f195(f934(x128581,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12859,plain, % 186.12/186.10 (P1(f335(f335(f337(f933(f928(x128591),f928(x128591))),f335(f335(f260(f928(x128591),f928(x128591)),f120(x128591)),f120(x128591))),f165(x128591,x128592)))), % 186.12/186.10 inference(rename_variables,[],[4331])). % 186.12/186.10 cnf(12864,plain, % 186.12/186.10 (~P1(f335(f335(f337(x128641),x128642),f195(f934(x128641,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12869,plain, % 186.12/186.10 (P32(x128691,x128692,f120(x128691))), % 186.12/186.10 inference(rename_variables,[],[3485])). % 186.12/186.10 cnf(12872,plain, % 186.12/186.10 (E(f335(f196(f928(x128721)),f176(x128721,x128722,x128723)),x128722)), % 186.12/186.10 inference(rename_variables,[],[3615])). % 186.12/186.10 cnf(12875,plain, % 186.12/186.10 (~P1(f335(f335(f337(x128751),x128752),f195(f934(x128751,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12881,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x128811),x128811))), % 186.12/186.10 inference(rename_variables,[],[4773])). % 186.12/186.10 cnf(12884,plain, % 186.12/186.10 (P1(f335(f335(f337(x128841),x128842),f250(f934(x128841,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(12890,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x128901,a922)),x128902),x128902))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(12893,plain, % 186.12/186.10 (~P1(f335(f335(f337(x128931),x128932),f195(f934(x128931,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(12896,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),f2(a1)),f335(f335(f252(a1),f335(f81(a1),x128961)),x128962)))), % 186.12/186.10 inference(rename_variables,[],[4031])). % 186.12/186.10 cnf(12899,plain, % 186.12/186.10 (~E(f335(a119,x128991),x128991)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(12901,plain, % 186.12/186.10 (E(f335(f292(x129011,x129011),f271(x129011,x129012)),x129012)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12903,plain, % 186.12/186.10 (P38(x129031,f160(x129031,x129032))), % 186.12/186.10 inference(rename_variables,[],[3417])). % 186.12/186.10 cnf(12907,plain, % 186.12/186.10 (E(f335(f292(x129071,x129071),f271(x129071,x129072)),x129072)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12909,plain, % 186.12/186.10 (P26(x129091,x129091,f5(x129091),x129092)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12911,plain, % 186.12/186.10 (P26(x129111,x129111,f5(x129111),x129112)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(12918,plain, % 186.12/186.10 (E(f335(f292(x129181,x129181),f271(x129181,x129182)),x129182)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12920,plain, % 186.12/186.10 (E(f335(f292(x129201,x129201),f271(x129201,x129202)),x129202)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12922,plain, % 186.12/186.10 (E(f335(f292(x129221,x129221),f271(x129221,x129222)),x129222)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12924,plain, % 186.12/186.10 (P27(x129241,x129241,f25(x129241),x129242,x129242)), % 186.12/186.10 inference(rename_variables,[],[4214])). % 186.12/186.10 cnf(12926,plain, % 186.12/186.10 (P27(x129261,x129261,f25(x129261),x129262,x129262)), % 186.12/186.10 inference(rename_variables,[],[4214])). % 186.12/186.10 cnf(12928,plain, % 186.12/186.10 (P27(x129281,x129281,f25(x129281),x129282,x129282)), % 186.12/186.10 inference(rename_variables,[],[4214])). % 186.12/186.10 cnf(12933,plain, % 186.12/186.10 (E(f335(f292(x129331,x129331),f271(x129331,x129332)),x129332)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12937,plain, % 186.12/186.10 (E(f335(f292(x129371,x129371),f271(x129371,x129372)),x129372)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12939,plain, % 186.12/186.10 (P15(x129391,f934(x129391,a922),f317(x129391))), % 186.12/186.10 inference(rename_variables,[],[3522])). % 186.12/186.10 cnf(12945,plain, % 186.12/186.10 (E(f335(f292(x129451,x129451),f271(x129451,x129452)),x129452)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12947,plain, % 186.12/186.10 (P56(x129471,x129471,f271(x129471,x129472))), % 186.12/186.10 inference(rename_variables,[],[3519])). % 186.12/186.10 cnf(12966,plain, % 186.12/186.10 (E(f335(f292(x129661,x129661),f271(x129661,x129662)),x129662)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12977,plain, % 186.12/186.10 (P39(x129771,f271(x129771,x129772))), % 186.12/186.10 inference(rename_variables,[],[3418])). % 186.12/186.10 cnf(12981,plain, % 186.12/186.10 (P54(x129811,x129812,f271(x129811,x129812))), % 186.12/186.10 inference(rename_variables,[],[3518])). % 186.12/186.10 cnf(12983,plain, % 186.12/186.10 (P54(x129831,x129832,f271(x129831,x129832))), % 186.12/186.10 inference(rename_variables,[],[3518])). % 186.12/186.10 cnf(12985,plain, % 186.12/186.10 (P54(x129851,x129852,f271(x129851,x129852))), % 186.12/186.10 inference(rename_variables,[],[3518])). % 186.12/186.10 cnf(12987,plain, % 186.12/186.10 (E(f335(f292(x129871,x129871),f271(x129871,x129872)),x129872)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(12991,plain, % 186.12/186.10 (E(f195(f934(f933(x129911,x129911),a922)),f271(x129911,f195(f934(x129911,a922))))), % 186.12/186.10 inference(rename_variables,[],[3619])). % 186.12/186.10 cnf(12993,plain, % 186.12/186.10 (P57(x129931,f195(f934(x129931,a922)),x129932)), % 186.12/186.10 inference(rename_variables,[],[3567])). % 186.12/186.10 cnf(12997,plain, % 186.12/186.10 (P25(x129971,x129972,f195(f934(f926(x129971),a922)))), % 186.12/186.10 inference(rename_variables,[],[3603])). % 186.12/186.10 cnf(13007,plain, % 186.12/186.10 (P53(x130071,f271(x130071,x130072))), % 186.12/186.10 inference(rename_variables,[],[3421])). % 186.12/186.10 cnf(13014,plain, % 186.12/186.10 (P33(x130141,x130142,f120(x130141),f120(x130141))), % 186.12/186.10 inference(rename_variables,[],[3794])). % 186.12/186.10 cnf(13016,plain, % 186.12/186.10 (P33(x130161,x130162,f120(x130161),f120(x130161))), % 186.12/186.10 inference(rename_variables,[],[3794])). % 186.12/186.10 cnf(13023,plain, % 186.12/186.10 (P43(x130231,x130232,x130233,x130234,f195(f934(x130231,a922)),x130234)), % 186.12/186.10 inference(rename_variables,[],[4490])). % 186.12/186.10 cnf(13034,plain, % 186.12/186.10 (E(f195(f934(f933(x130341,x130341),a922)),f271(x130341,f195(f934(x130341,a922))))), % 186.12/186.10 inference(rename_variables,[],[3619])). % 186.12/186.10 cnf(13049,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x130491),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13058,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x130581)),f335(f85(a1),f335(f107(a1),x130582))))), % 186.12/186.10 inference(rename_variables,[],[4795])). % 186.12/186.10 cnf(13068,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x130681),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13071,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x130711),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13074,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x130741,x130742)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13077,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x130771,x130772)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13080,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x130801,x130802)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13083,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x130831,x130832)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13090,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),f335(f85(a1),f335(f107(a1),x130901))),f335(f107(a1),x130902)))), % 186.12/186.10 inference(rename_variables,[],[4032])). % 186.12/186.10 cnf(13095,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x130951),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13096,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x130961),x130961))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13103,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x131031),f335(a119,x131031)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(13110,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x131101),x131101))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13113,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x131131,x131132)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13116,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x131161,x131162)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13119,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x131191),x131191))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13120,plain, % 186.12/186.10 (~E(f335(a119,x131201),f2(a927))), % 186.12/186.10 inference(rename_variables,[],[4724])). % 186.12/186.10 cnf(13137,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f51(a927,x131371,x131372)),x131371))), % 186.12/186.10 inference(rename_variables,[],[4007])). % 186.12/186.10 cnf(13142,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x131421),f335(a119,x131421)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(13145,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x131451),f335(a119,x131451)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(13146,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x131461),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13155,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x131551)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(13156,plain, % 186.12/186.10 (P1(f335(f250(f934(x131561,a922)),x131562))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(13159,plain, % 186.12/186.10 (~P1(f335(f335(f244(a1),f335(f107(a1),x131591)),f2(a1)))), % 186.12/186.10 inference(rename_variables,[],[4790])). % 186.12/186.10 cnf(13160,plain, % 186.12/186.10 (P1(f335(f250(f934(x131601,a922)),x131602))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(13163,plain, % 186.12/186.10 (P1(f335(f250(f934(x131631,a922)),x131632))), % 186.12/186.10 inference(rename_variables,[],[3609])). % 186.12/186.10 cnf(13174,plain, % 186.12/186.10 (~P1(f335(f335(f337(x131741),x131742),f195(f934(x131741,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13175,plain, % 186.12/186.10 (P1(f335(f67(x131751),f195(f934(x131751,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13184,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),f2(a927)),x131841))), % 186.12/186.10 inference(rename_variables,[],[3569])). % 186.12/186.10 cnf(13187,plain, % 186.12/186.10 (~P1(f335(f335(f337(x131871),x131872),f195(f934(x131871,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13190,plain, % 186.12/186.10 (~P1(f335(f335(f337(x131901),x131902),f195(f934(x131901,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13195,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x131951),x131951))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13203,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x132031),f335(a119,x132031)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(13206,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132061),x132061))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13211,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132111),x132111))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13214,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132141),x132141))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13217,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132171),x132171))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13220,plain, % 186.12/186.10 (E(f335(f335(f23(f934(x132201,a922)),f195(f934(x132201,a922))),x132202),f195(f934(x132201,a922)))), % 186.12/186.10 inference(rename_variables,[],[3817])). % 186.12/186.10 cnf(13221,plain, % 186.12/186.10 (P1(f335(f67(x132211),f195(f934(x132211,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13224,plain, % 186.12/186.10 (E(f335(f335(f23(f934(x132241,a922)),f195(f934(x132241,a922))),x132242),f195(f934(x132241,a922)))), % 186.12/186.10 inference(rename_variables,[],[3817])). % 186.12/186.10 cnf(13225,plain, % 186.12/186.10 (P1(f335(f67(x132251),f195(f934(x132251,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13228,plain, % 186.12/186.10 (E(f335(f335(f23(f934(x132281,a922)),f195(f934(x132281,a922))),x132282),f195(f934(x132281,a922)))), % 186.12/186.10 inference(rename_variables,[],[3817])). % 186.12/186.10 cnf(13229,plain, % 186.12/186.10 (P1(f335(f67(x132291),f195(f934(x132291,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13232,plain, % 186.12/186.10 (E(f335(f335(f23(f934(x132321,a922)),f195(f934(x132321,a922))),x132322),f195(f934(x132321,a922)))), % 186.12/186.10 inference(rename_variables,[],[3817])). % 186.12/186.10 cnf(13233,plain, % 186.12/186.10 (P1(f335(f67(x132331),f195(f934(x132331,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13237,plain, % 186.12/186.10 (E(f335(f292(x132371,x132371),f271(x132371,x132372)),x132372)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(13242,plain, % 186.12/186.10 (E(f335(f335(f23(f934(x132421,a922)),f195(f934(x132421,a922))),x132422),f195(f934(x132421,a922)))), % 186.12/186.10 inference(rename_variables,[],[3817])). % 186.12/186.10 cnf(13243,plain, % 186.12/186.10 (P1(f335(f67(x132431),f195(f934(x132431,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13247,plain, % 186.12/186.10 (P1(f335(f67(x132471),f195(f934(x132471,a922))))), % 186.12/186.10 inference(rename_variables,[],[3624])). % 186.12/186.10 cnf(13250,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132501),x132501))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13254,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x132541),x132541))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13261,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132611),x132611))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13274,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x132741),x132741))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13277,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x132771),x132771))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13284,plain, % 186.12/186.10 (~P1(f335(f335(f337(x132841),x132842),f195(f934(x132841,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13295,plain, % 186.12/186.10 (P1(f335(f335(f337(x132951),x132952),f250(f934(x132951,a922))))), % 186.12/186.10 inference(rename_variables,[],[3701])). % 186.12/186.10 cnf(13296,plain, % 186.12/186.10 (E(f335(f199(x132961,x132962),x132963),f128(x132961,x132962))), % 186.12/186.10 inference(rename_variables,[],[3463])). % 186.12/186.10 cnf(13299,plain, % 186.12/186.10 (P1(f335(f335(f337(x132991),f335(x132992,x132993)),f335(f318(x132994,x132991,x132992),f250(f934(x132994,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(13303,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133031,a922)),x133032),f250(f934(x133031,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(13306,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133061,a922)),x133062),x133062))), % 186.12/186.10 inference(rename_variables,[],[3846])). % 186.12/186.10 cnf(13312,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x133121),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13313,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x133131),x133131))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13317,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x133171),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13318,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x133181),x133181))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13323,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x133231),x133231))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13330,plain, % 186.12/186.10 (E(f335(f335(f16(x133301,x133302),x133303),x133304),x133303)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13333,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133331,a922)),f335(f179(x133331),f183(x133331,x133332,x133333))),f335(f179(x133331),x133332)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(13337,plain, % 186.12/186.10 (~P1(f335(f335(f244(a927),x133371),f2(a927)))), % 186.12/186.10 inference(rename_variables,[],[4777])). % 186.12/186.10 cnf(13338,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x133381),x133381))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13343,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),x133431),x133431))), % 186.12/186.10 inference(rename_variables,[],[3549])). % 186.12/186.10 cnf(13348,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x133481),x133481))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13351,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x133511),x133511))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13354,plain, % 186.12/186.10 (~P1(f335(f335(f243(a927),f335(a119,x133541)),x133541))), % 186.12/186.10 inference(rename_variables,[],[4783])). % 186.12/186.10 cnf(13360,plain, % 186.12/186.10 (P1(f335(f335(f337(x133601),f335(x133602,x133603)),f335(f318(x133604,x133601,x133602),f250(f934(x133604,a922)))))), % 186.12/186.10 inference(rename_variables,[],[4156])). % 186.12/186.10 cnf(13361,plain, % 186.12/186.10 (P26(x133611,x133611,f5(x133611),x133612)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13366,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133661,a922)),x133662),f250(f934(x133661,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(13367,plain, % 186.12/186.10 (P26(x133671,x133671,f5(x133671),x133672)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13371,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133711,a922)),x133712),f250(f934(x133711,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(13372,plain, % 186.12/186.10 (P26(x133721,x133721,f5(x133721),x133722)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13376,plain, % 186.12/186.10 (P26(x133761,x133761,f5(x133761),x133762)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13379,plain, % 186.12/186.10 (~P1(f335(f335(f244(f934(x133791,a922)),x133792),f195(f934(x133791,a922))))), % 186.12/186.10 inference(rename_variables,[],[4794])). % 186.12/186.10 cnf(13382,plain, % 186.12/186.10 (P26(x133821,x133821,f5(x133821),x133822)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13385,plain, % 186.12/186.10 (P26(x133851,x133851,f5(x133851),x133852)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13391,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133911,a922)),x133912),f250(f934(x133911,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(13396,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x133961,a922)),f195(f934(x133961,a922))),x133962))), % 186.12/186.10 inference(rename_variables,[],[3999])). % 186.12/186.10 cnf(13400,plain, % 186.12/186.10 (E(f335(f292(x134001,x134001),f271(x134001,x134002)),x134002)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(13404,plain, % 186.12/186.10 (~P1(f335(f335(f337(x134041),x134042),f195(f934(x134041,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13409,plain, % 186.12/186.10 (P26(x134091,x134091,f5(x134091),x134092)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13412,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x134121,a922)),x134122),f250(f934(x134121,a922))))), % 186.12/186.10 inference(rename_variables,[],[3932])). % 186.12/186.10 cnf(13420,plain, % 186.12/186.10 (E(f335(f335(f16(x134201,x134202),x134203),x134204),x134203)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13423,plain, % 186.12/186.10 (~P1(f335(f335(f337(x134231),x134232),f195(f934(x134231,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13426,plain, % 186.12/186.10 (~P1(f335(f335(f337(x134261),x134262),f195(f934(x134261,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13430,plain, % 186.12/186.10 (P1(f335(f335(f243(a927),x134301),x134301))), % 186.12/186.10 inference(rename_variables,[],[3548])). % 186.12/186.10 cnf(13433,plain, % 186.12/186.10 (P1(f335(f335(f244(a927),x134331),f335(a119,x134331)))), % 186.12/186.10 inference(rename_variables,[],[3616])). % 186.12/186.10 cnf(13434,plain, % 186.12/186.10 (~E(f335(a119,x134341),x134341)), % 186.12/186.10 inference(rename_variables,[],[4712])). % 186.12/186.10 cnf(13447,plain, % 186.12/186.10 (P1(f335(f335(f243(a1),f2(a1)),f335(f107(a1),x134471)))), % 186.12/186.10 inference(rename_variables,[],[3648])). % 186.12/186.10 cnf(13457,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x134571,a922)),f335(f179(x134571),f183(x134571,x134572,x134573))),f335(f179(x134571),x134572)))), % 186.12/186.10 inference(rename_variables,[],[4247])). % 186.12/186.10 cnf(13462,plain, % 186.12/186.10 (~P1(f335(f335(f337(x134621),x134622),f195(f934(x134621,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13465,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x134651,x134652)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13466,plain, % 186.12/186.10 (E(f335(f335(f242(a927),f335(a119,x134661)),f335(a119,x134662)),f335(a119,f335(f335(f242(a927),x134661),x134662)))), % 186.12/186.10 inference(rename_variables,[],[3720])). % 186.12/186.10 cnf(13469,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x134691,x134692)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13470,plain, % 186.12/186.10 (E(f335(f335(f241(a927),f335(a119,x134701)),f335(a119,x134702)),f335(a119,f335(f335(f241(a927),x134701),x134702)))), % 186.12/186.10 inference(rename_variables,[],[3719])). % 186.12/186.10 cnf(13473,plain, % 186.12/186.10 (P1(f335(f67(a927),f313(a927,x134731,x134732)))), % 186.12/186.10 inference(rename_variables,[],[3755])). % 186.12/186.10 cnf(13482,plain, % 186.12/186.10 (~P1(f335(f335(f337(x134821),x134822),f195(f934(x134821,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13483,plain, % 186.12/186.10 (E(f335(f335(f16(x134831,x134832),x134833),x134834),x134833)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13486,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x134861,a922)),f335(f179(x134861),f335(f143(x134861,x134862),x134863))),f335(f179(x134861),x134863)))), % 186.12/186.10 inference(rename_variables,[],[4199])). % 186.12/186.10 cnf(13487,plain, % 186.12/186.10 (E(f335(f335(f16(x134871,x134872),x134873),x134874),x134873)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13490,plain, % 186.12/186.10 (P1(f335(f335(f243(f934(x134901,a922)),f335(f179(x134901),f335(f335(f182(x134901),x134902),x134903))),f335(f179(x134901),x134903)))), % 186.12/186.10 inference(rename_variables,[],[4242])). % 186.12/186.10 cnf(13491,plain, % 186.12/186.10 (E(f335(f335(f16(x134911,x134912),x134913),x134914),x134913)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13495,plain, % 186.12/186.10 (E(f335(f335(f16(x134951,x134952),x134953),x134954),x134953)), % 186.12/186.10 inference(rename_variables,[],[3539])). % 186.12/186.10 cnf(13513,plain, % 186.12/186.10 (P26(x135131,x135131,f5(x135131),x135132)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13516,plain, % 186.12/186.10 (~P1(f335(f335(f337(x135161),x135162),f195(f934(x135161,a922))))), % 186.12/186.10 inference(rename_variables,[],[4786])). % 186.12/186.10 cnf(13517,plain, % 186.12/186.10 (E(f335(f292(x135171,x135171),f271(x135171,x135172)),x135172)), % 186.12/186.10 inference(rename_variables,[],[3509])). % 186.12/186.10 cnf(13518,plain, % 186.12/186.10 (P26(x135181,x135181,f5(x135181),x135182)), % 186.12/186.10 inference(rename_variables,[],[3785])). % 186.12/186.10 cnf(13527,plain, % 186.12/186.10 (P1(f335(f335(f244(f934(a1,a922)),f311(a1,f84(a1),f2(a1))),f311(a1,f2(a1),f84(a1))))), % 186.12/186.10 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5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169,10179,10180,10200,10205,10300,10389,10390,10391,10392,10455,10473,2,8,9,4829,4830,4848,4890,4891,4893,4916,4924,4925,4935,4980,4982,5030,5160,5161,5175,5198,5254,5255,5261,5262,5264,5266,5275,5278,5279,5287,5300,5301,5307,5328,5329,5347,5352,5353,5354,5355,5359,5367,5370,5377,5432,5437,5438,5443,5449,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5697,5702,5704,5740,5742,5743,5745,5746,5748,5749,5751,5760,5765,5766,5767,5769,5771,5772,5773,5774,5775,5776,5785,5795,5798,5809,5825,5826,5829,5839,5841,5842,5843,5870,5880,5895,5896,5905,5906,5908,5910,5915,5950,5955,5957,6016,6051,6052,6057,6063,6066,6067,6068,6069,6088,6092,6093,6102,6124,6153,6172,6176,6177,6179,6202,6206,6209,6210,6211,6227,6238,6239,6270,6271,6275,6296,6299,6302,6323,6324,6352,6355,6363,6372,6374,6382,6386,6394,6395,6396,6397,6427,6444,6495,6532,6534,6555,6556,6563,6567,6568,6571,6585,6600,6621,6622,6625,6628,6637,6652,6673,6679,6681,6696,6697,6700,6701,6703,6705,6706,6707,6709,6711,6713,6719,6720,6722,6723,6729,6731,6773,6779,6795,6797,6798,6799,6832,6837,6839,6844,6845,6855,6859,6871,6894,6895,6897,6898,6909,6913,6916,6934,6937,6957,6986,6987,6988,6994,7008,7027,7029,7031,7033,7038,7044,7046,7060,7065,7066,7101,7102,7103,7117,7118,7120,7121,7139,7141,7156,7182,7206,7217,7219,7221,7223,7224,7255,7256,7260,7261,7268,7269,7271,7273,7295,7304,7305,7316,7326,7366,7376,7380,7387,7398,7403,7405,7412,7420,7433,7450,7471,7473,7492,7549,7550,7551,7553,7555,7559,7560,7565,7626,7655,7670,7686,7717,7720,7742,7764,7782,7785,7786,7796,7816,7818,7820,7822,7823,7824,7849,7875,7876,7907,7909,7910,7911,7916,7937,7954,7959,7965,7967,7975,7987,7988,7990,8011,8017,8038,8104,8105,8106,8153,8159,8160,8184,8185,8202,8203,8204,8261,8262,8291,8321,8330,8341,8354,8383,8387,8393,8405,8423,8428,8450,8496,8526,8540,8559,8562,8588,8614,8672,8673,8676,8677,8746,8780,8781,8782,8783,8810,8842,8871,8879,8880,8921,8942,8987,9003,9049,9052,9067,9074,9116,9159,9160,9178,9179,9193,9310,9316,9320,9340,9351,9374,9376,9379,9385,9387,9388,9398,9399,9418,9424,9434,9441,9483,9501,9556,9557,9563,9602,9625,9630,9669,9679,9682,9683,9685,9686,9698,9721,9736,9745,9746,9748,9750,9779,9900,9901,9951,9952,9992,10027,10139,10209,10279,10362,10380,10385,3,2877,2881,2882,2888,2889,2890,2891,2892,2894,2900,2903,2905,2906,2907,2908,2909,2914,2919,2922,2923,2925,2935,2944,2945,2946,2947,2948,2950,2951,2953,2954,2955,2956,2957,2958,2959,2962,2963,2964,2965,2966,2967,2968,2969,2976,2978,2984,2985,2988,2989,2990,2992,3000,3001,3002,3003,3004,3008,3009,3010,3011,3012,3013,3017,3018,3029,3054,3056,3057,3058,3059,3075,3078,3079,3080,3097,3098,3114,3115,3117,3118,3123,3124,5527,5566,5713,5714,5715,5796,5894,5924,5958,5974,5976,5982,6044,6045,6046,6047,6055,6090,6222,6259,6269,6293,6327,6364,6511,6516,6553,6554,6576,6578,6580,6587,6588,6589,6590,6591,6592,6593,6594,6674,6743,6744,6831,6866,6867,6906,6907,7045,7059,7129,7130,7136,7157,7188,7190,7194,7238,7258,7259,7277,7278,7315,7360,7361,7457,7528,7529,7530,7531,7548,7581,7631,7632,7641,7646,7647,7658,7689,7690,7691,7692,7830,7831,7833,7835,7841,7842,8046,8052,8053,8063,8101,8102,8179,8220,8274,8296,8297,8369,8464,8536,8537,8541,8574,8636,8637,8704,8722,8723,8724,8725,8875,9135,9136,9207,9221,9274,9275,9395,9427,9453,9485,9526,9719,9842,9987,10178,10234,10236,10398,6657,6658,6746,6766,6767,7179,7396,8717,8796,9043,9232,9233,9301,9302,9480,9574,9575,9576,9577,9782,10051,10065,10441,10442,6728,8628])). % 186.12/186.10 cnf(13529,plain, % 186.12/186.10 (P1(f335(f335(f244(f934(a1,a922)),f311(a1,f2(a1),f2(a1))),f311(a1,f335(f85(a1),f335(f107(a1),f335(a119,x135291))),f2(a1))))), % 186.12/186.11 inference(scs_inference,[],[4807,4214,12793,12815,12924,12926,12928,3785,11414,12469,12566,12569,12661,12703,12707,12715,12787,12909,12911,13361,13367,13372,13376,13382,13385,13409,13513,13518,3794,12533,13014,13016,3802,3518,12981,12983,12985,3519,12947,3485,12869,4747,4748,12057,4490,13023,3522,12939,3355,3417,12903,3418,12977,3419,3420,3421,12743,13007,4746,3848,4712,10489,10499,10512,10523,10526,10630,10633,10636,10738,10873,11187,11384,11387,11406,11409,11608,11712,11719,11733,11779,11782,11815,11830,11893,11950,11966,12256,12284,12296,12325,12331,12423,12529,12696,12757,12899,13434,3604,3567,12993,3753,12228,3469,4724,10722,10822,11294,11394,13120,3155,3156,3159,3160,3163,3164,3166,3167,3168,3170,3174,3175,3176,3177,3180,3182,3183,3184,3185,3189,3192,3193,3205,3208,3214,3220,3226,3232,3241,3242,3247,3254,3257,3267,3268,3271,3272,3273,3285,3298,3299,3301,3306,3310,3311,3314,3315,3316,3317,3321,3333,4707,3337,3416,4708,3887,4117,11997,3391,11709,3530,3506,3509,10561,10564,10657,10660,10976,11724,11727,11841,11880,11885,11992,12441,12637,12847,12901,12907,12918,12920,12922,12933,12937,12945,12966,12987,13237,13400,13517,3480,12728,12732,12736,3486,3495,4009,4317,3463,13296,3615,12790,12872,3380,3381,3747,4103,11755,3603,12997,3446,3377,3407,3867,3402,3601,4223,4111,3930,4670,3389,3390,3361,3367,4022,3427,3605,11137,11264,12530,12747,3479,4188,4737,10552,10719,11605,12688,12729,12733,4744,12700,3539,12077,12080,13330,13420,13483,13487,13491,13495,4146,4784,11320,11419,11664,11667,3949,3536,3652,3873,3644,4762,3619,12991,13034,3443,3444,10622,10952,4771,3706,3435,3358,3465,11745,4331,12718,12859,4190,11340,11475,11536,12672,12678,12804,12807,12837,4802,11239,11488,11599,11625,11672,11678,12616,4803,11373,11491,11602,4804,11494,11547,4805,11554,4806,3464,3745,12572,12613,12699,3914,3694,4604,4605,3766,4735,11738,3891,3849,3893,4066,3817,13220,13224,13228,13232,13242,4113,12563,3731,3992,3616,10641,10761,10839,10912,10915,10955,11059,11310,11927,12168,12252,12318,12394,12432,12507,12510,12841,13103,13142,13145,13203,13433,4002,11983,3532,3628,11814,3812,4777,10529,10532,10558,10682,10857,11067,11082,11197,11650,11748,11926,12143,12148,12167,12370,12373,12453,12619,12722,13049,13068,13071,13095,13146,13312,13317,13337,4790,11857,11888,11923,11930,11963,13155,13159,3989,3754,3755,12273,13074,13077,13080,13083,13113,13116,13465,13469,13473,4138,3719,13470,3720,13466,3575,3577,3551,4774,3442,4732,3940,4253,3738,4791,4324,11622,3872,3588,12098,12101,12537,12641,12818,4782,10517,10520,10690,10785,10804,10811,10834,10842,10845,10862,11050,11297,11516,11808,11902,12048,12161,12164,4293,4252,12245,12587,4199,11134,12426,12597,12746,13486,4242,13490,4247,11343,12466,12536,12596,12640,13333,13457,3915,11934,12255,12401,12474,12520,4281,3932,10685,10782,11346,11424,11509,11573,12422,12488,12752,12814,12834,12844,13303,13366,13371,13391,13412,4794,11085,11499,12600,13379,3548,10650,10748,10898,10962,11039,11088,11091,11122,11145,11181,11219,11258,12051,12095,12225,12283,12299,12302,12305,12308,12481,12495,12498,12501,12504,12580,12644,12763,12810,13096,13119,13195,13206,13211,13214,13217,13250,13261,13274,13323,13348,13351,13430,3549,10677,10733,10967,11062,11184,11833,12128,12131,12140,12231,12242,12261,12266,12311,12334,12351,13110,13254,13277,13313,13318,13338,13343,3550,3624,12458,13175,13221,13225,13229,13233,13243,13247,4773,10569,10598,11106,11148,11157,12011,12032,12199,12202,12205,12208,12295,12314,12317,12330,12382,12385,12388,12391,12548,12551,12647,12650,12756,12796,12881,3701,10827,10918,11192,11236,11478,11481,11562,11647,11818,12060,12695,12884,13295,4786,11115,11228,11249,11252,11323,11326,11337,11440,11448,11462,11502,11521,11530,11570,11611,11616,11619,11638,11641,11681,11686,11689,11692,11695,11933,12074,12107,12376,12379,12413,12459,12484,12625,12669,12675,12775,12778,12800,12858,12864,12875,12893,13174,13187,13190,13284,13404,13423,13426,13462,13482,13516,3609,10949,10979,10988,10991,10994,11591,12797,12811,13156,13160,13163,3648,13447,3641,4070,4007,10601,11986,12014,13137,4783,10549,10937,10940,11443,11459,11949,12002,12036,12061,12158,12187,12190,12193,12196,12452,13354,3569,10982,11142,11212,12015,12157,12356,12556,12581,13184,4032,12104,13090,4372,3760,4780,4044,4078,4765,4768,4769,3525,3529,4767,4766,4541,3862,11979,4468,11840,4796,10848,10851,4801,11329,11332,11524,11635,11655,11701,4156,11698,12035,12039,12706,12714,12803,13299,13360,3997,11255,11261,11281,12280,12406,12487,12771,3846,11399,11527,12513,12622,12632,12711,12766,12774,12890,13306,4329,3999,10985,11362,11533,11567,11578,12710,12760,13396,3702,3813,10901,10904,10997,11168,3815,4799,11980,4795,13058,4800,10741,10854,11644,12575,12584,12628,12828,12831,4429,11125,12593,12608,12631,4335,4031,12896,3975,3976,4797,10574,10577,10943,10946,11854,12040,12840,4798,11960,12045,4000,10907,11174,4267,4816,4842,4897,4901,4931,4946,4953,4955,4991,4996,5025,5031,5117,5143,5144,5159,5181,5209,5210,5233,5234,5248,5251,5276,5282,5298,5302,5303,5304,5309,5310,5333,5358,5360,5361,5371,5376,5382,5418,5419,5427,5435,5439,5441,5455,5458,5464,5469,5470,5483,5489,5492,5493,5497,5530,5544,5553,5555,5556,5559,5560,5561,5571,5573,5579,5580,5581,5587,5591,5592,5593,5601,5605,5606,5611,5624,5632,5644,5646,5654,5656,5657,5660,5664,5691,5705,5706,5721,5733,5755,5761,5783,5784,5787,5806,5814,5815,5820,5821,5831,5833,5845,5849,5858,5859,5861,5862,5878,5883,5892,5893,5904,5911,5925,5929,5932,5938,5939,5940,5943,5948,5984,5985,5988,5990,5992,5994,5995,5996,5998,6000,6002,6007,6014,6029,6043,6049,6050,6053,6064,6065,6072,6076,6078,6083,6091,6127,6140,6149,6152,6161,6165,6166,6167,6168,6169,6173,6178,6188,6194,6212,6216,6225,6254,6268,6294,6311,6312,6315,6329,6331,6333,6335,6350,6351,6354,6356,6359,6360,6375,6383,6384,6385,6387,6389,6424,6425,6430,6433,6439,6443,6477,6479,6481,6483,6492,6494,6496,6502,6504,6509,6512,6520,6528,6530,6531,6537,6558,6559,6560,6561,6562,6564,6570,6575,6608,6609,6612,6613,6614,6616,6617,6618,6619,6627,6659,6660,6661,6670,6691,6692,6712,6714,6726,6727,6733,6763,6765,6780,6784,6819,6821,6822,6876,6899,6942,6956,6963,6972,6973,6974,6975,6992,6993,7000,7012,7015,7017,7018,7019,7021,7023,7037,7048,7049,7050,7063,7115,7126,7128,7149,7150,7184,7191,7198,7228,7257,7313,7342,7397,7418,7426,7429,7489,7502,7564,7566,7580,7589,7590,7591,7607,7611,7613,7659,7669,7672,7687,7734,7736,7739,7780,7781,7799,7867,7885,7908,7931,7943,7957,7968,7979,7980,8006,8008,8010,8019,8055,8066,8091,8118,8150,8182,8215,8254,8270,8272,8288,8289,8351,8362,8427,8451,8456,8471,8498,8499,8538,8539,8556,8595,8597,8599,8606,8621,8625,8640,8661,8669,8671,8681,8686,8690,8691,8692,8693,8694,8695,8714,8729,8730,8748,8749,8754,8755,8756,8757,8758,8776,8777,8778,8788,8801,8804,8815,8820,8822,8824,8825,8826,8833,8839,8847,8850,8867,8868,8877,8878,8886,8905,8918,8922,8943,8965,8966,8969,8970,8976,8985,8986,9009,9020,9030,9031,9032,9035,9058,9059,9070,9119,9125,9131,9133,9149,9152,9163,9164,9165,9176,9240,9271,9272,9273,9288,9305,9313,9314,9342,9343,9411,9442,9448,9458,9459,9460,9469,9497,9513,9517,9521,9543,9544,9571,9633,9638,9641,9673,9674,9675,9699,9700,9716,9737,9743,9755,9780,9801,9810,9811,9812,9813,9828,9830,9835,9865,9866,9872,9873,9918,9919,9930,9931,9956,9975,9977,9978,9986,9991,9998,10022,10046,10057,10059,10063,10114,10150,10160,10162,10166,10167,10169,10179,10180,10200,10205,10300,10389,10390,10391,10392,10455,10473,2,8,9,4829,4830,4848,4890,4891,4893,4916,4924,4925,4935,4980,4982,5030,5160,5161,5175,5198,5254,5255,5261,5262,5264,5266,5275,5278,5279,5287,5300,5301,5307,5328,5329,5347,5352,5353,5354,5355,5359,5367,5370,5377,5432,5437,5438,5443,5449,5480,5490,5495,5511,5528,5529,5536,5537,5538,5549,5567,5569,5570,5577,5584,5585,5597,5598,5599,5600,5602,5603,5607,5608,5609,5610,5640,5641,5642,5650,5651,5652,5653,5697,5702,5704,5740,5742,5743,5745,5746,5748,5749,5751,5760,5765,5766,5767,5769,5771,5772,5773,5774,5775,5776,5785,5795,5798,5809,5825,5826,5829,5839,5841,5842,5843,5870,5880,5895,5896,5905,5906,5908,5910,5915,5950,5955,5957,6016,6051,6052,6057,6063,6066,6067,6068,6069,6088,6092,6093,6102,6124,6153,6172,6176,6177,6179,6202,6206,6209,6210,6211,6227,6238,6239,6270,6271,6275,6296,6299,6302,6323,6324,6352,6355,6363,6372,6374,6382,6386,6394,6395,6396,6397,6427,6444,6495,6532,6534,6555,6556,6563,6567,6568,6571,6585,6600,6621,6622,6625,6628,6637,6652,6673,6679,6681,6696,6697,6700,6701,6703,6705,6706,6707,6709,6711,6713,6719,6720,6722,6723,6729,6731,6773,6779,6795,6797,6798,6799,6832,6837,6839,6844,6845,6855,6859,6871,6894,6895,6897,6898,6909,6913,6916,6934,6937,6957,6986,6987,6988,6994,7008,7027,7029,7031,7033,7038,7044,7046,7060,7065,7066,7101,7102,7103,7117,7118,7120,7121,7139,7141,7156,7182,7206,7217,7219,7221,7223,7224,7255,7256,7260,7261,7268,7269,7271,7273,7295,7304,7305,7316,7326,7366,7376,7380,7387,7398,7403,7405,7412,7420,7433,7450,7471,7473,7492,7549,7550,7551,7553,7555,7559,7560,7565,7626,7655,7670,7686,7717,7720,7742,7764,7782,7785,7786,7796,7816,7818,7820,7822,7823,7824,7849,7875,7876,7907,7909,7910,7911,7916,7937,7954,7959,7965,7967,7975,7987,7988,7990,8011,8017,8038,8104,8105,8106,8153,8159,8160,8184,8185,8202,8203,8204,8261,8262,8291,8321,8330,8341,8354,8383,8387,8393,8405,8423,8428,8450,8496,8526,8540,8559,8562,8588,8614,8672,8673,8676,8677,8746,8780,8781,8782,8783,8810,8842,8871,8879,8880,8921,8942,8987,9003,9049,9052,9067,9074,9116,9159,9160,9178,9179,9193,9310,9316,9320,9340,9351,9374,9376,9379,9385,9387,9388,9398,9399,9418,9424,9434,9441,9483,9501,9556,9557,9563,9602,9625,9630,9669,9679,9682,9683,9685,9686,9698,9721,9736,9745,9746,9748,9750,9779,9900,9901,9951,9952,9992,10027,10139,10209,10279,10362,10380,10385,3,2877,2881,2882,2888,2889,2890,2891,2892,2894,2900,2903,2905,2906,2907,2908,2909,2914,2919,2922,2923,2925,2935,2944,2945,2946,2947,2948,2950,2951,2953,2954,2955,2956,2957,2958,2959,2962,2963,2964,2965,2966,2967,2968,2969,2976,2978,2984,2985,2988,2989,2990,2992,3000,3001,3002,3003,3004,3008,3009,3010,3011,3012,3013,3017,3018,3029,3054,3056,3057,3058,3059,3075,3078,3079,3080,3097,3098,3114,3115,3117,3118,3123,3124,5527,5566,5713,5714,5715,5796,5894,5924,5958,5974,5976,5982,6044,6045,6046,6047,6055,6090,6222,6259,6269,6293,6327,6364,6511,6516,6553,6554,6576,6578,6580,6587,6588,6589,6590,6591,6592,6593,6594,6674,6743,6744,6831,6866,6867,6906,6907,7045,7059,7129,7130,7136,7157,7188,7190,7194,7238,7258,7259,7277,7278,7315,7360,7361,7457,7528,7529,7530,7531,7548,7581,7631,7632,7641,7646,7647,7658,7689,7690,7691,7692,7830,7831,7833,7835,7841,7842,8046,8052,8053,8063,8101,8102,8179,8220,8274,8296,8297,8369,8464,8536,8537,8541,8574,8636,8637,8704,8722,8723,8724,8725,8875,9135,9136,9207,9221,9274,9275,9395,9427,9453,9485,9526,9719,9842,9987,10178,10234,10236,10398,6657,6658,6746,6766,6767,7179,7396,8717,8796,9043,9232,9233,9301,9302,9480,9574,9575,9576,9577,9782,10051,10065,10441,10442,6728,8628,8629])). % 186.12/186.11 cnf(13779,plain, % 186.12/186.11 (P1(f335(f335(f243(f934(x137791,a922)),f335(f179(x137791),f183(x137791,x137792,x137793))),f335(f179(x137791),x137792)))), % 186.12/186.11 inference(rename_variables,[],[4247])). % 186.12/186.11 cnf(13810,plain, % 186.12/186.11 ($false), % 186.12/186.11 inference(scs_inference,[],[4331,3550,4190,3624,4802,4786,4247,13779,3549,4007,3813,4773,4797,11871,13527,13529,11669,12017,12621,3197,8,7191,7401,8820,6012,5849,7397,8055,8969,9059,6354,10300,7023,8867,8539,9448,6000,5234,5984,7426,7943,6620,7429,4931]), % 186.12/186.11 ['proof']). % 186.12/186.11 % SZS output end Proof % 186.12/186.11 % Total time :163.590000s %------------------------------------------------------------------------------